Schmidt, B., Ingerslev, C., Brenner, B., etal. “Tunnel Structures” Structural Engineering Handbook. Ed. Lian Duan Boca Raton: CRC Press LLC, 2001

15B Tunnel Structures Birger Schmidt Parsons Brinckerhoff

Christian Ingerslev Parsons Brinckerhoff

Brian Brenner Parsons Brinckerhoff

Jaw-Nan Wang Parsons Brinckerhoff

15B.1 Introduction What Is a Tunnel? • Fundamental Approach to Underground Design • Immersed and Floating Tunnels • Cut-and-Cover Tunnels • Bored and Mined Tunnels in Soil or Rock

15B.2 Immersed and Floating Tunnels Introduction • Sizing of Tunnel Sections • Principles of Design • Analysis • Methods of Constructing Elements: Concrete and Steel • Tunnel Joints • Construction Aspects • Protection Against Ship Traffic and Currents

15B.3 Cut-and-Cover Tunnels Introduction • Structural Analysis • Methods of Framing • Analysis in Section: Typical Frame and BOEF Methods of Analysis • Loading • Finite Element Analysis • Buoyancy • Evaluation of Construction Impact and Mitigation

15B.4 Tunnel Linings for Bored and Mined Tunnels Introduction • Mechanized Tunneling Through Soil • Linings for Tunnels in Soil • Bored Tunnels in Rock • Sequential Excavation and Support for Rock Tunnels • Selection of Lining System in a Rock Tunnel • Structural Design of Permanent Concrete Linings in Rock • Design of Segmental Concrete Linings

15B.5 Seismic Analysis and Design Introduction • Performance Record During Earthquakes • Design and Analysis Approach for Ground Shaking Effects • Tunnel Subject to Large Displacements • Shaft Structures and Interface Joints

15B.1

Introduction

What Is a Tunnel? Tunnels are located either below the ground or below a body of water. Almost all tunnels serve as part of the infrastructure of cities and countries, conveying water or sewage or serving as transportation arteries. In cities, tunnels are often selected because they can be built without taking up precious surface space. In the open country, tunnels are more often employed to traverse obstacles such as mountains, rivers, lakes, and fjords. The depth, cross-section, and alignment of tunnels are controlled by the functional requirements of the facility, by geographical and environmental constraints, and by issues of constructibility under the prevailing geotechnical conditions.

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The three principal types and methods of tunnel construction are • Immersed or floating tunnels, made from very large precast concrete or concrete-filled steel elements, floated out and placed in a prepared trench below the water or anchored or supported below the water surface. • Cut-and-cover tunnels, built by excavating a trench, constructing the concrete structure in the trench, and covering it over. • Bored or mined tunnels, excavated through rock either by blasting or by tunnel-boring machines, or excavated through soil using more-or-less mechanized shields. At shallow depth and for short water crossings, the cut-and-cover tunnels are more economical. Per unit length, immersed or floating tunnels are more costly than bored or mined tunnels, but because they can often be made shallower and therefore shorter, and because they may serve their function better than other choices, the overall cost can be less. This chapter deals with the structural design and selection of structural systems for these types of tunnel structures. Methods of construction are important in the selection of structural systems and details, but space does not permit this chapter to do justice to all the complex methods of tunnel construction through a great variety of geologic environments. The chapter includes methods for seismic analysis of underground structures.

Fundamental Approach to Underground Design Underground design must achieve functionality, stability, and safety of the underground openings during construction and for the lifetime of the structure thereafter. There is no recognized U.S. standard, practice, or code for the design of most underground structures. Designers apply codes such as ACI Codes and Practices for concrete design, but these were developed for structures above ground, not for underground structures, and only parts of these codes apply to underground structures such as cut-and-cover structures There are five basic steps in the design of underground structures: 1. Define functional requirements, including design life and durability requirements. 2. Acquire and analyze geologic, geotechnical, and cultural data relevant to the design and construction of the underground facilities. 3. Determine plausible and possible modes of failure, including construction events, unsatisfactory long-term performance, failure to meet environmental requirements, and flooding; determine means of analyzing these modes of failure and acquire the necessary data. 4. Establish appropriate method(s) of construction considering the geologic and groundwater information, constructibility, and economy. 5. Establish and design appropriate initial and final ground support and lining systems, considering both ground conditions and the method(s) of construction.

Immersed and Floating Tunnels Immersed Tunnels Whenever there is a need to cross water, an immersed tunnel should be considered. Immersed tunnels may appear complex to those unfamiliar with the technology because of the operations in and over water that they entail (Figure 15B.1). In reality, though, the technique is often less risky than bored tunneling, and tunnel element manufacture can be better controlled. As a result, immersed tunnels are nearly always much more watertight and therefore drier than bored tunnels, due to the construction of the elements in a controlled dry environment. Immersed tunnels offer a number of special advantages as follows: • They do not have to have circular cross-sections unless the external pressure is particularly high. Almost any cross-section can be accommodated, making immersed tunnels particularly attractive for wide highways and combined road/rail tunnels. © 2001 by CRC Press LLC

FIGURE 15B.1 Lowering an immersed tunnel element into the excavated trench. (© Parsons Brinckerhoff, Inc., 1967. With permission.)

• They can be placed immediately beneath a waterway, in contrast to a bored tunnel. This allows immersed tunnel approaches to be shorter and gradients to be flatter — an advantage for all tunnels, but especially so for rail tunnels. A nominal cover of 1.5 to 2.0 m of backfill is usually given to provide protection against dropping anchors or sinking ships. • They can be constructed in ground conditions that would make bored tunneling difficult or expensive, such as the soft alluvial deposits characteristic of large river estuaries. Immersed tunnels have been located in both fresh and seawater, in hot or cold climates, in busy waterways, and in earthquake zones. Alignments do not need to be straight, so the tunnels can be designed to suit design speeds, existing land use, topography, and connections to the existing road system. The ideal alignments for an immersed tunnel may not coincide with ideal alignments for a bridge. Soft ground is ideal for immersed tunnels, but with a rock bed the high cost of rock excavation under water could make other tunneling methods more cost effective. Immersed tunnels are not suitable for every situation; © 2001 by CRC Press LLC

however, if there is water to cross or water can be used to float in a precast structure, they usually present a feasible alternative to bored tunnels at a comparable or better price. A catalog of existing immersed tunnels is given in Reference 1. Floating Tunnels

As water depth increases, particularly if the waterway is narrow, tunnels may become excessively long when compared to the width of the crossing. Using shallow alignments, a new method has been developed in which the tunnel is exposed within the water column, resulting in much shorter tunnels. Such tunnels are known as floating tunnels and appear to be viable using available technology; designs for several locations are well advanced although none has yet been constructed. While very short floating tunnels might not require intermediate supports, longer tunnels might be supported by columns up from the bed or suspended from pontoons on the surface. Anchors might hold down a permanently buoyant tunnel (similar to tension-leg oil platform technology). Further information on floating tunnels can be found in References 1 and 2. Although most immersed tunnels are built for water depths of between 5 and 20 m, schemes have been postulated for depths of 100 m. Such great depths could be avoided by using floating tunnel technology, though if submarines ply the waters the risk of collision might preclude use of a floating tunnel.

Cut-and-Cover Tunnels Introduction Cut-and-cover tunnels are constructed by excavating a trench from the surface and installing the structure, the “bottom-up” approach. With “top-down” construction, the walls and tunnel roof are built first and the surface reinstated, after which the tunnel section is excavated below the roof structure. The tunnel structure is usually cast-in-place concrete or erected steel structural elements. It is unusual for prefabricated elements to be used for cut-and-cover tunnel structures. The cut-and-cover method is most attractive for relatively shallow tunnel sections. Cut-and-cover construction, particularly the bottom-up method, can be disruptive to surface traffic and existing facilities. The disruption can be minimized by use of temporary decking over the cut. Trench Excavation The tunnel trench may be constructed by: • Sloping back the excavation, with little or no excavation support • Using temporary support of excavation walls, such as soldier piles and lagging or steel sheet piles that are not part of the permanent structure • Using excavation support walls that are designed to be part of the permanent structure. The first option can be the most economical, but it is often impractical due to adjacent structures and facilities. Comparing the second and third options, the increased cost and staging difficulties for building permanent excavation support walls must be balanced against the simplicity and ease of building a permanent structure within temporary walls. Top-Down Construction This method typically requires use of excavation support walls as part of the final structure (for example, concrete diaphragm walls cast in slurry-filled trenches, hereinafter called slurry walls). Slurry walls are constructed downwards from the surface; excavation proceeds down to the underside of roof level, and the roof is installed. The surface is then restored to its final condition as excavation proceeds below the finished roof. Top-down construction requires a different set of analysis assumptions and staging approaches than bottom-up construction, with or without temporary decking. For example, the staging must lay out specific glory-hole locations for all stages (glory holes provide access for construction, materials, and removal of excavated soil and rock). This type of staging planning can be more complex than cut-and-cover work with temporary decking or an open cut. © 2001 by CRC Press LLC

Groundwater Impacts It is important to evaluate groundwater impacts for cut-and-cover construction. The evaluation includes: • Analysis of determination of impacts on the water table beyond the zone of excavation • Analysis of the stability of the cut during construction • Evaluation of buoyancy under final conditions In all stages of cut-and-cover excavation and construction, the weight of the structure and backfill will tend to be less than the weight of the soil removed. The staging evaluation can be more complicated in areas with high groundwater levels.

Bored and Mined Tunnels in Soil or Rock Transportation tunnels in built-up areas are often constructed by tunneling methods such as machine boring or hand mining. Tunneling causes much less disruption at the surface and is less expensive for deep tunnels. Usually at least one diameter of soil or rock cover is required, though shallower cover can be accommodated. Depending on functional requirements, bored or mined tunnels come in almost all sizes, ranging from some 2 m in diameter for medium-sized water and sewage conveyance up to about 20 m in diameter for rail stations and some hydropower plant caverns. While rock tunnels excavated by blasting methods can be built to almost any size and shape, tunnels in soil are usually built using a shield, currently to a maximum circular diameter of about 14 m, although larger diameter machines are being designed. Most rapid transit tunnels are single-track tunnels with a diameter of about 6 m, but a few have been built as double-track tunnels with a diameter of about 10 m. Functional and environmental requirements determine basic tunnel support and lining requirements such as shape and size, smoothness and water tightness, and durability. Some tunnels through highquality rock are unlined or only furnished with nominal support consisting of rock bolts, wire mesh, or shotcrete. At the other extreme, transportation tunnels through soft ground below the groundwater table are furnished with durable, watertight linings, generally designed today as moment-resistant reinforced concrete linings with waterproofing membranes. Many sewer tunnels are furnished with corrosionresistant internal linings.

15B.2

Immersed and Floating Tunnels

Introduction Most concepts in this chapter apply to floating tunnels as well as immersed tunnels, except for comments on foundations and backfilling. The primary difference between the design of an immersed and a floating tunnel is that floating tunnels have to be designed for dynamic loads throughout their life, whereas design of immersed tunnels need only consider dynamic loads that occur until the tunnels are finally placed.

Sizing of Tunnel Sections The needs of the client, projected traffic volume, projected vehicle types, and the profiles of the tunnel will dictate the number of traffic lanes required. If uphill grades are long or steep, climbing lanes may be required for heavy vehicles, though it is usual to avoid climbing lanes within the immersed tunnel elements themselves. Due to cost, it is unusual to have full-width emergency lanes or shoulders within tunnels, nominal widths usually sufficing. Very long tunnels may have a short extra lane at intervals to permit emergency stopping. Unmountable barriers, such as Jersey barriers, are generally used to protect the walls from traffic impact. When the height of such barriers exceeds 600 mm, the lane width seems narrower and motorists tend to shy away, thus slowing traffic. © 2001 by CRC Press LLC

FIGURE 15B.2 Floating element: airport rail tunnel, Hong Kong. (© Christian Ingerslev.)

Walkways within tunnels should be discouraged, although emergency access through a central wall into an adjacent tunnel should be available. This would require an emergency walkway at least 600 mm wide on the side adjacent to emergency doors at the level of the top of the barrier and so arranged that vehicle overhangs do not endanger users of the walkway. Such emergency “cross-passages” may need to be provided at intervals of say 100 meters. In some cases, it may be desirable to provide an escape duct, usually having an air pressure slightly above that of the highway ducts. Utility ducts may be provided with space in excess of that needed to service the tunnel so that space may be rented out to others. Space above the minimum vertical clearance for traffic may be needed for lighting and signs. The clearance height for permitted vehicles is usually held as low as possible. Permitted classes of vehicles in any tunnel may be restricted by legislation or owner requirements. Having thus determined the width and height of internal spaces, preliminary calculations can be made regarding proposed methods of ventilation, jet fan sizes, or duct areas. Although normal ventilation may be designed for stalled traffic conditions, the critical case that defines ventilation may be that of a fuel fire [3]. Space within the tunnel envelope yet outside the traffic envelope may be required to accommodate jet fans or, alternatively, ventilation ducts may be needed. Air requirements must also be determined. Most immersed tunnel elements are designed to be able to just float when completed (Figure 15B.2), yet be heavy enough to stay submerged by the addition of permanent ballast. A few have been provided with temporary external buoyancy to avoid adding the ballast later. Because of this very delicate balance of being able to float yet later to stay submerged, it is very important that the internal air volume is kept to a minimum consistent with demands for the internal space. Tolerances to allow for construction variations and possible misalignment of elements are additional to other space requirements. In contrast, floating tunnels relying on buoyancy must have sufficient compartmentalized buoyancy to stay afloat in case of accidental damage, usually considered to be to two adjacent compartments (damaged on the joint). Once minimum air, traffic, electrical, mechanical, and utility duct requirements have been evaluated, temporary end bulkheads can be sized and calculations made to ensure that tunnel elements do float. Initial estimates of slab and wall thickness will be needed to do this. Space for additional ballast to be added later (or some other means) to prevent the incomplete tunnel from floating after removal of bulkheads will need to be provided. If subsequent analysis requires increases in thickness, these may have © 2001 by CRC Press LLC

FIGURE 15B.3 Steel immersed tunnel: Ted Williams Tunnel, Boston, MA. (© David Sailors, 1993. With permission.)

to be achieved at the expense of adding extra internal space to compensate for the additional weight. Haunches may be necessary to alleviate shear problems at the edges of larger spans. If shear does require reinforcement, it is better to use bent-up bars and avoid shear links. Allowance must be made for the addition of more concrete or permanent ballast in order to meet requirements for an immersed tunnel not to float under final conditions. Tunnels are usually either circular or rectangular. The composite action of the structural steelwork with the concrete infill in a steel tunnel generally requires a circular tube (Figures 15B.3 and 15B.4) for the greatest efficiency, but other shapes including rectangular have also been used. The space generated within a circular section below a two-lane roadway and above the traffic envelope can often be used to meet the supply and exhaust air requirements. Concrete can be cast into any shape, so economics can influence whether rectangular or circular sections are used. For the shallowest profiles, rectangular sections (Figure 15B.5) may provide the best alternative and may be side vented, if required. Where more than two lanes per tube are needed, concrete rectangular tunnels are usually more economical than steel tunnels. Steel immersed tunnels can be designed like a ship to require as little as 2 or 3 m of

FIGURE 15B.4 Steel immersed tunnel: Cross Harbour Tunnel, Hong Kong. (© Parsons Brinckerhoff, Inc., 1971. With permission.) © 2001 by CRC Press LLC

FIGURE 15B.5 Concrete immersed tunnel: Western Harbour Crossing, Hong Kong. (© Christian Ingerslev.)

draft at float-out, as long as the remaining concrete is placed afloat at an outfitting site with greater draft. In contrast, concrete tunnels are virtually complete at float-out and will need a draft of almost the full height.

Principles of Design Elements are designed to resist dead loads, live loads, exceptional loads, and extreme loads [4]. These should be applied in accordance with relevant codes where they consider the particular conditions of an immersed tunnel. It is important that in considering the design of any one element, all aspects of the design of that element meet the same code. In the absence of such codes, the following assumptions may be made: • Dead load includes all long-term loads and mean water level. • Live load includes creep, shrinkage, prestress, temperature, backfill, seabed erosion and siltation, traffic, variations in water level, current, storm loads, and earthquakes, each with a return period of 5 years or less. • Exceptional loads include loss of support (subsidence) below the tunnel or to one side and storms and extreme water levels with a probability of being exceeded once during the design life. • Extreme loads include sunken ships, ship collision, water-filled tunnel, explosion (e.g., vehicular), fire, the design seismic event predicted for the location, and the resulting movement of soils. Some of these loads may be affected by categories of dangerous goods permitted through the tunnel. Load combinations should be selected with regard to simultaneous probability. For example, extreme seismic events may be assumed to occur without storm loads. Structures should be designed to accommodate expected movements due to deformation of foundations without limiting normal operations. Soil pressures should take account of the soil surface profile as well as the geometry of the structure. Geotechnical considerations should also include effects due to seepage, erosion, a change from drained to undrained conditions, and cuts in soft clays. Differential settlements can be expected at interfaces between types of construction, at locations where subaqueous tunnels extend into the shoreline, and during construction. At least the following conditions should be considered during analysis and design:

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TABLE 15B.1 Load Combination Multipliers for Immersed Tunnels Load case

Normal

Abnormal

Extreme

Construction

1.4/0.9

1.2/0.9

1.05

1.1

Traffic load: Normal Exceptional vehicle Centrifugal

1.6/0 1.4/0 1.6/0

1.2/0 1.2/0 1.3/0

— — —

— — —

Braking load: Normal Exceptional vehicle

1.6/0 1.4/0

1.3/0 1.2/0

— —

— —

Wind and waves Current Water pressure allowing for tidal variation Additional water pressure due to surge

— 1.4 1.4/0.9 —

1.2 1.2 1.2/0.9 1.2/0.9

1.05 1.05 1.05 1.05

1.2 1.2 1.2 1.2

Backfill pressure: Horizontal Vertical

0.9/1.6 1.6/0.9

0.9/1.4 1.4/0.9

1.05 1.05

1.3/0 1.3/0

Creep and shrinkage Temperature effects and prestressing

1.3 1.3

1.3 1.3

1.05 1.05

1.1/0.9 1.1

Sunken ship Earthquake

— —

1.2/0 1.2

1.05 1.05

— —

Other extreme loads Imposed loads during construction

— —

— —

1.05 —

— 1.3

Loading: Dead load and road ballast

• Normal operating conditions, with the tunnel operation unaffected by environmental loads • Abnormal conditions, demonstrating that either a tunnel with live loads can remain operational under the after-effects of extreme or exceptional loads (excluding flooding) or settlement, or that with operations ceased and closed to traffic the tunnel can survive some loss of support beneath or to one side • Extreme actions with the tunnel closed, the abnormal conditions above combined with one of the extreme loads • Construction conditions, including temporary structures (e.g., sheet piles) and loads due to handling, launching, transporting (including expected wave conditions), and placing, combined with environmental and seismic loads appropriate to the season, duration of use, and location; abnormal and extreme conditions may be inappropriate

Analysis General Methods used for analysis may include usual frame and finite element methods, but where subsoils are non-uniform or where sudden changes in loading on top of the tunnel occur, such as at the banks of a river, effects may require soil-structure interaction analysis to correctly model soil behavior. Both ultimate and serviceability analysis, as appropriate, should be investigated. Effects to be considered include adequate safety against failure of complete structures and of their components, static equilibrium, buckling, water tightness, fatigue, durability, vibration, cracking, and deformations. In the absence of other data for immersed tunnels, methods may use the load factors (appropriate load combination multipliers) given in Table 15B.1. Where alternate factors are given, the most adverse combinations should be used.

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Analysis of Earthquake Effects All immersed tunnels should be designed for seismic events appropriate to their location (see Reference 1, chap. 8). Seismic events during the construction phase should also be considered. Liquefaction of soils around an immersed tunnel should be avoided, perhaps requiring special measures to be taken. An appropriate level of risk should be agreed upon with the client because cost implications may be significant. Three magnitudes of earthquake loading should be considered: • The functional evaluation earthquake (FEE), also known as the design basis earthquake (DBE), should be used first in order to design the structure for either limited or full performance. A magnitude corresponding to a return period of one to three times the design life is appropriate. • The safety evaluation earthquake (SEE) should be checked to ensure compliance with minimum performance for life safety and survivability of a design made to FEE. The SEE is the most severe seismic event considered at the location. A client-agreed-to performance level may or may not assume progressive collapse under SEE, but ductility of the structure must be ensured to prevent sudden fracture. A return period of 1000 years or more should be used. As an alternative, however, selecting the maximum credible earthquake (MCE; i.e., the maximum foreseeable earthquake) or large earthquakes that occur at a lesser frequency may sometimes be appropriate. • A smaller serviceability limit state (SLS) earthquake, corresponding to a 5- to 10-year return period, may also be included as an ordinary static live load to be combined with other live loads. For each of these magnitudes, an acceptable structural response to or performance with these loads, including the extent of cracking, movement, damage, formation of plastic hinges, etc., needs to be defined and agreed upon with the owner so that corresponding allowable design stresses and displacements can be determined. (Structural response resulting in collapse or catastrophic inundation is not acceptable.) Typical acceptable performance criteria include: Minimum performance level: • Significant damage, repairable or perhaps not • May require full closure or replacement of tunnel • Flooding on roadway not to exceed that passable by emergency vehicles and slow moving traffic • Limited lighting and ventilation Limited performance level: • Intermediate damage, repairable over 12 months • Limited emergency and public traffic possible within hours • Limited leakage • Full lighting and ventilation Full performance level: • Light damage requiring minor repairs • Public traffic immediately • Minor leaks • No significant loss of service Not all combinations of earthquake and performance levels may be useful to consider. Those that should be used for design would depend on the strategic importance of the tunnel route, the availability of alternative routes, risks that the owner is prepared to carry, and the cost. Dynamic structural response analysis and assessment of displacements using soil-structure interaction may be necessary and may need to include the effective mass of water. An effective soil drainage system can reduce soil pore pressures.

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Methods of Constructing Elements: Concrete and Steel Concrete An element is a length of tunnel that is floated and immersed as a single rigid unit. The rigidity may be temporary and later released. In other words, elements may either be monolithic or may consist of a number of discrete segments stressed temporarily together longitudinally for ease of transportation and placing. After placing, the stressing may be removed so that each segment may act as a mini-element free to move at each segment joint. Some Dutch tunnels and the Øresund tunnel between Denmark and Sweden consist of such released segments. The ability to use discrete segments can depend upon subsurface conditions, acceptable displacements, and sufficient capacity to resist seismic effects. Monolithic Elements Monolithic elements are cast in bays (equivalent to segments), typically with the floor slab cast first, followed by the walls and roof in either one or two operations (Figure 15B.5). Special efforts to reduce cracking adjacent to previously cast concrete could include low-heat concrete mixes and cooling pipes embedded in the concrete. Reinforcement is continuous across construction joints. Discrete Segments Discrete segments lend themselves to being cast in a single continuous operation, either horizontally (Øresund Tunnel) or vertically and then rotated (Tuas Bay Tunnel). Either way has the advantage of eliminating horizontal construction joints in the walls and the associated thermal cracking. If assembly can be achieved reasonably quickly, a basin or dock sized for a single element can be used. Operations can be tailored to obviate the need to store completed elements before immersion. External walls and slabs are usually one meter or more in thickness; therefore, these must be considered thick concrete, so special precautions must be taken to avoid cracking during casting. It is particularly important to avoid cracking caused by heat of hydration because such cracks will leak. Steel A steel tunnel is usually designed to be able to float initially with little or none of the internal concrete having been placed. The bulk or all of the concrete is then placed after launching, either close to the fabrication site or more usually at an outfitting site close to the immersion site. If a graving dock is used (Figure 15B.5), a compromise must be reached among the size, the number of reuses, and schedule. Testing and repair of any cracks and leaks are necessary before submerging elements. Figure 15B.4 shows the Cross Harbour Tunnel in Hong Kong on the quayside almost ready for side launching. Ease of construction can be achieved by a high degree of mechanization and line fabrication. Prefabricated forms, work shelters (heated in winter), shop welding of any steel plate, and prefabrication of reinforcement cages and prestressing cables can all be used to advantage. Waterproofing The need for waterproofing concrete tunnels is still a hotly debated issue. A barrier between concrete and saltwater, warmer waters, or corrosive waters would appear particularly beneficial. Waterproofing will also reduce the amount of water penetrating remaining cracks, particularly if the waterproofing adheres to the concrete. In case of fire, concrete that is not saturated with water is less likely to spall, as the formation of steam is less likely. Steel tunnels do not need waterproofing because the structural steel shell serves this purpose well, yielding and not cracking when overloaded, although measures to inhibit corrosion of the steel may be required.

Tunnel Joints Final Joint Some tunnels are constructed progressively from one end to the other, after which the land-side structures are completed. Others may require the last element to be inserted rather than appended to the end of

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FIGURE 15B.6 Seismic joint of BART, San Francisco, CA. (©1967 Parsons Brinckerhoff, Inc. With permission.)

the previous element. In order to achieve this, a small final gap will remain. This closure or final joint corresponds to a short length of tunnel that will need to be cast in place. Methods commonly used include tremie concrete to seal the joint and dewatering to complete the joint in the dry from the inside. Construction Joints These are horizontal or vertical connections between monolithic parts of a structure. Usually a waterstop is placed in such a joint. Typically, this would be one of the traditional types of waterstops, although hydrophilic and groutable waterstops are sometimes used. Special moveable watertight joints are required between segments of a tunnel element, designed as expansion joints, usually with shear capacity. Immersion Joints These are the joints between tunnel elements that are dewatered after elements are installed at the seabed. They may remain flexible or can be made rigid, as has been common with many steel tunnels. Flexible joints are generally sealed with a temporary immersion gasket or soft-nosed gasket in compression. The use of a secondary independent flexible seal, capable of being replaced from within the tunnel, is common practice (often an omega seal). Each seal should be capable of resisting the external hydrostatic pressure and should allow for expected future movements. Protection should also be provided against damage to seals from within the tunnel, such as impact damage or airborne contaminant damage. Seismic Joints A seismic joint, which can be an immersion joint of special design, may be required to accommodate large differential movements in any direction due to a seismic event. Such a joint is shown in Reference 5 and most likely would be located at significant changes in cross-section. Figure 15B.6 shows a typical seismic joint of BART in San Francisco. Semi-rigid or flexible joints between elements may also need to be strengthened to carry seismic loads and to prevent catastrophic inundation, typically by using stressed or unstressed prestressing components across the joints or by using bearings and shear keys. Terminal Joints (Land Connections) The terminal joints between the shore ends of an immersed tunnel and the land portions may also be immersion joints. Direct joint connections may be made to land-based structures such as cut-and-cover tunnels or ventilation buildings. These structures may be constructed either before or after placing the © 2001 by CRC Press LLC

FIGURE 15B.7 Second downtown Elizabeth River Tunnel, VA. (©1983 Parsons Brinckerhoff, Inc. With permission.)

immersed tunnel, depending upon schedule constraints and local conditions. For a bored or mined tunnel connection, the backfill around the end of the immersed tunnel would first need to be made relatively impermeable, such as by grouting, to allow boring to continue into the end of the immersed tunnel. Steel immersed tunnels, because of their shallow draft capabilities, may eliminate the need for cutand-cover tunnel construction in poor ground. After backfilling, the end of the tunnel can be exposed and open depressed highway sections constructed up against it, as was done at the Second Downtown Elizabeth River Tunnel in Virginia (Figure 15B.7). Wherever the cross-section changes significantly, seismic actions may generate significant differential movements, and the design must accommodate these. Drains, sumps, and pumping stations are required at both portals to remove rainwater that falls within the open sections and at the tunnel low points to remove wash and leakage water. Ventilation buildings, if needed, should preferably be sited on land where they cannot be hit by shipping. The end faces of the buildings may also make a suitable interface between immersed tunnel elements and on-shore techniques.

Construction Aspects Dimensional and density checking of the concrete is necessary at all stages of construction to ensure that the design weight is not exceeded, as the tunnel might then not float. It is easier to add more weight than to remove it, and weight can always be added externally. Temporary bulkheads are needed at the ends of each element, just visible in Figure 15B.2 and clearly visible in Figure 15B.7. They need to be watertight and yet reasonably simple to remove later. Bulkheads, if made of steel, are often designed for reuse. Typical foundation layers are 600 mm to 1 m thick above the bottom of the pre-dredged trench. They are mostly formed either by a screeded mattress of stone placed before the tunnel element is immersed or by jetted sand after the element is set on temporary supports — conditions to be allowed for in design. Such supports at the free end of the element are made adjustable, while the other end is first guided and then held by the previously laid element. Other types of design including injection of concrete are © 2001 by CRC Press LLC

sometimes used. Before immersing (Figure 15B.1), elements are usually held by temporary lifting hooks while ballast is added to provide the necessary negative buoyancy. Survey towers or similar devices are attached to the elements to enable monitoring of position after lowering starts, while bollards and other towing equipment are removed. Calculations to ensure stability at all stages of placement are necessary. Backfilling must be carried out in such a manner that unbalanced lateral forces do not move the element.

Protection Against Ship Traffic and Currents Immersed tunnels should be protected against falling anchors by a layer of either graded material or sacrificial concrete (see Reference 1, chap. 6, Hazard Analysis). The same reference also provides guidance on expected loads from sinking ships, although this is very much dependent on the cargo that the ships could be carrying. Typical results for actual ships passing a particular location, assuming the worst cargo, can be plotted as shown in Figure 15B.8. These results may vary further, depending upon the following: • Partially sunken vessels, which may increase these values, particularly if the vessel has a rigid stern post that can produce point loading • Critical water depths over which the vessel must pass • The water depth at the tunnel location

If storms could cause vessels to drag their anchors, it may be desirable to protect the tunnel further with rock berms over which anchors would be forced. Once clear of the tunnel, the anchors could re-engage. At the proposed site of the tunnel, the depth to the structure below the clearance envelope required for the shipping channel will vary according to the amount of over-dredge expected during maintenance and the amount of protective backfill required over the tunnel. Protection may be required for the surface of the bed in the vicinity of the tunnel to protect against scour, not only from currents, but also from propellers. At some vessel terminals where propellers are kept turning to maintain position, significant local scour can occur. Over-dredge of 1 m is not unusual, depending upon the method used for dredging. Anchor loads are usually small compared with structural capacity but may cause local surface damage if insufficient backfill is provided [1]. The type and grading of backfill layers are selected so that they do not damage the tunnel structure and waterproofing, if used, and so that the material does not get washed away under anticipated currents. It may not be necessary to completely bury a tunnel and restore the original bed levels (a floating tunnel is an extreme case). In such cases, the effects of hydraulic intrusion of a tunnel into an existing waterway regime may require study, as water flow is obstructed. For a floating tunnel, tidal and current effects may also cause dynamic and fatigue effects.

FIGURE 15B.8 Ground pressures from fully sunken ships. (Courtesy of Christian Ingerslev.)

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15B.3

Cut-and-Cover Tunnels

Introduction For structural evaluation of cut-and-cover tunnel structures, we can consider a spectrum where the cutand-cover tunnels fall midway between immersed and bored tunnels. Immersed tunnels are largely made of prefabricated structural sections. Structural analysis resembles the more traditional problem of applied loads to a structure. Construction staging must be carefully considered as the tunnel is floated and immersed. Bored tunnels can be thought of as reinforced openings in a competent subgrade material. The structural analysis is usually not a problem of applied loads to a structure, but one of considering how the soil behaves once a gap is constructed and then lined. Analysis of cut-and-cover tunnels typically will consider both of these features: • Soil-structure interaction • The traditional approach of loads applied to a structural model Recently, computer models have become available to allow for more sophisticated soil-structure interaction analysis of cut-and-cover tunnel construction. As the software becomes easier to use and more flexible, more sophisticated analyses of tunnel sections are being performed, as discussed below in the section, Analysis in Section: Typical Frame and BOEF Methods of Analysis. We can make an initial distinction between tunnels for which support of excavation (SOE) walls are temporary and those for which the cofferdam walls are incorporated in the final structure. In the past, construction walls (for example, sheet piling and lagging) were “throw-away” temporary walls. More recently, however, engineers have specified that the construction excavation walls be used as part of the final tunnel section. Examples include conventional concrete slurry walls, soldier pile tremie concrete (SPTC) walls, tangent pile walls, and secant pile walls. There are important differences between the two types in terms of construction issues, but we will focus here on structural analysis and design characteristics. Figure 15B.9 shows a schematic of the two different types of section.

Grade

Non-integral rigid wall

Grade

Integral rigid wall

FIGURE 15B.9 Typical sections for cut-and-cover tunnels.

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E = Exhaust duct S = Supply duct

TABLE 15B.2 Cut-and-Cover Tunnel Structural Analysis Approaches Type of Analysis

Description

Advantages

Disadvantages

“Traditional” analysis

Frame analysis model of tunnel section, with applied loads and assumed uniform support conditions.

Used with good results for decades; comparatively easy to formulate.

In some cases, can return conservative results, especially for complex tunnel section geometry.

Frame analysis with soilstructure interaction

Similar to the traditional method, but the effect of soil is mathematically modeled as a series of springs. Base slab springs use the Beam on Elastic Foundation (BOEF) method. Lateral springs can also be applied, partially in place of assumed soil loads.

Better modeling representation of structure; takes advantage of more realistic base slab soil support to permit smaller slabs in design.

Can be more complicated to model than the traditional method; soil springs are difficult to quantify based on soil test data.

Finite element analysis

The section soil and structure are modeled as a grid of geometric elements. This category includes many different types of analyses, depending on the mathematical model assumed for the soil type. Structural elements are usually treated as linear elastic.

Modeling representation closest to “reality,” better numerical resolution for conditions of difficult tunnel geometry and framing details.

Usually complex to set up and run; results require careful interpretation; precision of analysis method can be many times better than the data that forms the input, especially for soil model

When the SOE walls are temporary, the tunnel box is assumed to experience mostly final loading conditions; however, when SOE walls are included as part of the final structure, the design loading conditions become much more time dependent. The designer will need to consider not just final loading conditions, but also all of the states of stress experienced by the cofferdam walls as they are constructed, braced or tied back, and finally connected to the tunnel as a whole. The evaluation of impacts to existing facilities is another complication for cut-and-cover tunnel analysis that is not as much of a concern for bored and immersed tunnels. Of the three tunnel types, cut-andcover tunnels are most frequently built adjacent to existing buildings, utilities, and other facilities, so the nature of the tunneling process can lead to significant impacts to the existing structures.

Structural Analysis Typically, cut-and-cover tunnel sections have been modeled as structural frames. In general, however, we can categorize three ways to analyze cut-and-cover tunnel sections: 1. “Traditional” frame analysis. A stick figure is drawn to represent the tunnel section. Soil-structure interaction is treated as an applied load to the frame. 2. Frame analysis with a more rigorous soil-structure interaction. The soil is not just an applied load; its properties are modeled along with the tunnel. An example is treating the subgrade material as a series of springs, the “Beam on Elastic Foundation” (BOEF) approach. 3. Finite element/finite difference analysis. The continuous soil and tunnel structural material are modeled as a continuum. Table 15B.2 describes attributes, advantages, and disadvantages of the three analysis approaches. Twodimensional sectional analysis remains as good practice for most tunnel conditions, even though the most accurate tunnel model is three-dimensional. Structural analysis of tunnels in three dimensions © 2001 by CRC Press LLC

has been performed but is very complex. Also, a good case can be made for the fact that the number crunching exceeds the accuracy of its input for this type of design. Given uncertainty about the way soil behaves, its inherent lack of homogeneity, and difficulties in modeling three-dimensional soilstructure interaction, three-dimensional structural analysis and design of cut-and-cover tunnels is reserved mostly for special analysis conditions, such as rail transit station boxes with rigid end diaphragm walls.

Methods of Framing A difference between the tunnels with temporary support walls and those with support walls as part of the final tunnel section is related to the framing model for the structure. When SOE walls are temporary, the tunnel section is almost always treated as a box with fixed joints; however, when rigid cofferdam walls become part of the final structure, it can become difficult to construct fixed connections in the field. Designers, therefore, may specify partially fixed or shear connections at the roof to wall joints or base slab to wall joints. The number of different ways to model the tunnel frame increases in this case. Considering the shape of the frame, most cut-and-cover tunnel sections are rectangular, unlike immersed and bored tunnels, which are often round or oval. A rectangular cross-section is the best fitting shape for most uses of the tunnel, and it is the one requiring the least excavation for the relatively shallow cut-and-cover tunnel. However, the box shape is also the least efficient structural system for carrying compression loading, in comparison to circular bores. This structural inefficiency is often mitigated by placement of haunches (Figure 15B.10).

FIGURE 15B.10 Haunched section.

Most cut-and-cover tunnels are constructed from reinforced concrete. When using temporary SOE walls, the tunnel section is formed and cast inside, often with a layer of waterproofing completely enveloping the section. The construction procedure for the tunnel using the SOE walls as part of the structure will involve placement of keys in the cofferdam wall, where the roof and base slab can then frame in. Another method is to cast an inside wall against the face of the SOE wall. In this case, the base and roof slabs are supported by the inside wall. The SOE wall may also be structurally connected by a composite design with the inside wall. Concrete framing is most common, except for very deep or very wide tunnels that can require excessively thick concrete slabs. In these cases, one structural type that has been used frequently is steel composite concrete construction. A relatively thin concrete slab is cast with a steel beam, compositely connected with shear studs. This framing can be used in the roof. Wall members may be designed as steel columns without composite connections to the enveloping concrete, or composite action can be specified. The base slab is the least likely location for composite steel concrete members. Designers will take advantage of the comparatively thinner composite beams and columns in the roof and wall to raise the tunnel vertical profile and its fit in plan. However, space constraints are typically least severe on the bottom, and a concrete base slab helps to resist uplift through its additional weight. On the other hand, there are examples where a full steel frame, including the base member, has been built. © 2001 by CRC Press LLC

Analysis in Section: Typical Frame and BOEF Methods of Analysis Although there are many types of cut-and-cover tunnel sections, we can think of a “typical” section as having the following features: • Construction and excavation are via temporary, flexible SOE walls such as soldier piles and lagging. A mud mat is constructed at the bottom of the excavation to facilitate casting of the base slab. For some types of soil, a geotextile fabric can be placed to help stabilize the excavation. • Base slab, roof slab, and walls are reinforced concrete. • A layer of waterproofing is placed beneath the base slab, on the outside surfaces of the walls, and above the roof slab. The waterproofing is protected by a layer of lean concrete before backfilling. A typical structural analysis of this section would use a frame model. Different loadings would be calculated and applied to the model. Analysis would be performed using an indeterminate method, such as moment distribution, or with the assistance of a frame analysis computer program such as STAADIII or STRUDL. Based on the results of the analysis, the components of the cut-and-cover tunnel would be sized. Concrete slabs would be typically designed as bending members. There would be some amount of iteration to the process. The engineer, following sizing of the structure, may need to revisit the analysis with more accurate proportions for member size. In the analysis, each member must be assigned initial trial analysis properties such as sectional moment of inertia and cross-sectional area. For a concrete slab tunnel, typically a 1-foot longitudinal section is selected for modeling, and the corresponding member properties are calculated based on the assumed depth of the slab. Likewise, material properties must be calculated and assigned to the members. For example, each member in the frame analysis must receive a specification for modulus of elasticity and a value for material unit weight. Assumptions for analysis frame supports in the model are typically handled in one of two ways (Figure 15B.11): 1. Traditional frame analysis. For the simple tunnel box shown, two imaginary support points are placed in the model. An upward uniform vertical load is assumed to be placed below the base slab such that all vertical loads are balanced. The resulting reactions at the imaginary support points are zero. 2. Beam on Elastic Foundation (BOEF) method. Spring supports are specified. The value of the spring constant is determined from consideration of the underlying strata and its modulus of subgrade. As shown in Figure 15B.11, this method results in a non-uniform, base, slab pressure, in contrast to the conventional design method of balancing the vertical loads. The resulting soil pressure depends on the width of the tunnel box and the relative stiffness of the soil. If the soil were infinitely stiff, all load would be transferred to the soil directly beneath the walls of the box. If the soil behaved as a fluid, the load would be uniformly distributed below the base slab. While much of the current process for cut-and-cover tunnel analysis is a refinement of tried-and-true methods that have been used for decades, computerized design has caused some new issues to surface. One such concern is lateral load balancing. In the past, tunnels were analyzed structurally and designed by drawing a frame model, applying some assumed loads, performing frame analysis, and sizing the members. With the increased power of computer frame analysis comes realization of a curious problem: The frames tend to distort laterally. Unless the assumed lateral loads are perfectly balanced and the frame geometry perfectly symmetric, the frame models will tend to lean to one side. Past manual studies would have shown the same results if engineers had the ability to display the deformed shape of the tunnel model in a matter of seconds, as we do today. In reality, the tunnel model would not sway. The “sway” side would be pushed back by a higher soil pressure than that assumed by the preliminary analysis. For frame models, the issue can be approached in two ways: © 2001 by CRC Press LLC

Surcharge

Soil Load

Deadload

Imaginary Supports

Pore Water Pressure

Delta Load Delta Load = Deadload + Surcharge + Soil - Water Vertical Load Balancing

BOEF Support

FIGURE 15B.11 Base slab pressure: traditional and beam on elastic foundation (BOEF) analysis.

1. Add soil springs to wall members. This is a complex treatment because of difficulties in calculating properties for lateral springs and in calculating applied loads for the springs to react against. 2. Use “lateral load balancing.” Lateral loads are estimated and additional, triangular “balancing” loads are applied to the sway side. The reasoning is that the sway side would be pushed back via a passive pressure mode in the soil. While it is difficult to specify the resulting stress distribution exactly, a triangular loading approximation is reasonable. Other conditions in the frame model that need to be considered, which differ from the “typical” section described above, include the following: • Use of haunches. For the cast-in-place tunnel section, the designer may place haunches to reduce design spans and bending moments (Figure 15B.10). This is an attempt to develop a tunnel shape more in compression, as achieved by a circular bore, and less in bending, which is a disadvantage of the straight, rectangular sections. • Integral, rigid SOE walls. For this condition, a rigid, impervious SOE wall, such as a concrete slurry wall or SPTC wall, is incorporated in the final structure. For the purpose of structural modeling, the designer has to deal with the added concerns of the complex tunnel shapes, loadings on the wall segments not directly a part of the box, complicated construction sequence loadings, and other concerns. • Different material types and framing methods. These can include steel-composite concrete construction and prestressed concrete elements. • Different modeling methods. All-concrete box tunnels are usually designed with moment connections at the joints. These are not difficult to detail and construct when the box is cast-in-place within temporary cofferdam walls. The designer may wish to consider other structural models for some of the other tunnel types. © 2001 by CRC Press LLC

• Different construction staging approaches (e.g., top-down). The order of construction will impact loading and assumptions. For example, in top-down construction, permanent support of excavation walls used as part of the final structure will receive heavier bearing loads because the roof is placed and loaded before the base slab is constructed. The base slab acts as a mat for supporting vertical loads, but it is not available until towards the end of construction of the section. • Framing of ducts. In highway tunnels, ventilation supply ducts may be placed in the base slab, roof slab, or as side ducts adjacent to walls. The ducts introduce additional framing conditions and considerations. For example, ducts formed as part of the base slab can be modeled as a type of Vierendeel truss in a stick-frame model.

Loading Cut and cover tunnel loads include: • Vertical loads, roof slab: soil pressure on the roof slab from backfill, own weight of the roof, a live load surcharge, typically uniquely specified for each project; oftentimes, a future air-rights development load. • Vertical loads, base slab: hydrostatic pressure (acts up); soil pressure due to weight of tunnel above; own weight of base slab (acts down) • Lateral loads: hydrostatic pressure, effective soil pressure, lateral soil load due to surcharge loading, special loading conditions due to nearby foundations and other underground conditions Vehicle loading (transit or highway) needs to be considered, but may not contribute to the most severe tunnel loading case. The dominant loading direction on a tunnel base slab is up from hydrostatic pressure and soil pressure, so including the downward-acting vehicle loads would reduce the overall loads on the base slab. Therefore, the controlling load case is often for an empty tunnel. In congested urban areas — the sites for many cut-and-cover tunnels — the tunnel design may need to consider temporary loads from underpinning existing structures, and permanent loads from construction of future structures above the new tunnel. A good example of both concerns is the tunnel design for Boston’s Central Artery. The depressed artery is constructed directly beneath the original overhead viaduct, so bridge loads from underpinning of the elevated expressway needed to be included in the tunnel design. In addition, once construction is complete, acres of land that can be developed in downtown Boston will become available, so the tunnel design had to incorporate provisions for future building loads directly on the tunnel boxes.

Finite Element Analysis The preceding discussion focused on the use of frame models for structural analysis of cut-and-cover tunnel sections. As introduced in the Structural Analysis section above, frame models with load-balancing and frame models with soil-structure interaction assumptions represent the first two of the three analysis methods. These are the traditional approaches for this type of design and have been used since before computers; however, we can list several ways in which the frame models form an inaccurate representation of the analysis problem: • Frame models feature line elements, but in reality, elements of the tunnel section have thickness. For example, base slabs with air vents are thick and massive, and the line elements of the frame are a coarse representation of the structure. Steps can be taken to modify the frame models to account for the mass of the tunnel. • Frame models treat the surrounding soil as an equivalent applied load. In reality, the soil and structure behave together in a complex problem of soil-structure interaction. Assumed soil loads, used for decades in tunnel design, are a conservative but imprecise representation of the analysis problem.

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Another concern is the issue of construction staging. Underground structures experience several different states of stress. These are time-dependent, depending on how excavation is done, how the cut is tied back or braced, and the order in which the tunnel components are installed. For the purposes of this discussion, we will consider the finite element method and finite difference method to be the same. Although they differ mathematically, the general approach of the two is similar. They are both used to model cut-and-cover tunnel analysis by discretizing the continuous soil space and having the computer calculate most applied loads using assumptions about staging, soil properties, and boundary conditions. In general, the finite element method is an analytical tool for solving partial differential equations by first discretizing the equations in the solution domain. The solution domain refers to the physical definition of the problem. For a cut-and-cover tunnel section, the solution domain includes the structural elements of the tunnel, the backfill, the soil behind the walls, and soil beneath the excavation. The discretization is performed by dividing the solution domain into small regions of simple but arbitrary shape — the finite elements. The locations of elements are defined using nodal points (nodes). To solve the equations over the entire domain, the equations for the finite elements are summed, resulting in global matrix equations. The finite element method is almost always performed by computer because of the large number of equations and difficulties in incorporating boundary conditions. A finite element solution can be run for each construction stage. The output from the previous stage — one line of data for each node and element, plus loading and material property data — is used as the input for the current stage. Initial conditions are established by “turning on gravity”. The soil (finite elements) is then excavated and supports are installed for each stage. The finite element analysis loads the structural model based on the input soil properties and constitutive relationships. Unlike the traditional approach, no assumed applied soil loads are calculated. Although frame models have been used for cut-and-cover tunnel sections traditionally, finite element analysis provides a more rigorous analysis of the problem. A few words of caution are in order, however: • Available information for soil-structure interaction problems will often be less sophisticated than the analysis model. The finite element study assumes that the soil mass behaves in an elastic or other mathematically quantifiable way. The interpreted soil layer itself, based on investigation that can only approximate in situ conditions, is taken as a group of homogeneous layers. The computer model can, at best, include certain simplifying assumptions about the soil behavior. To complicate matters further, the stress/strain relationship at the soil-structure interface is highly indeterminate, time-dependent, and not well understood. Research has focused on ways to extrapolate laboratory conditions to mathematical models, but it is difficult to quantify such conditions as a vertical tunnel wall against different soil layers. • In reality, a model with better accuracy would include three-dimensional geometry and loading. However, whatever uncertainties are present for two-dimensional finite element studies are magnified for three-dimensional work. • Soil-structure finite element analysis is invariably more complicated and time-consuming than frame analysis. Interpretation of results requires much greater care. A highly automated approach can be difficult to run for this type of analysis because the results need to be carefully inspected. Software and interpretation methods continue to improve with time, however. • While the behavior of the soil mass is very sensitive to the way it is modeled, the ultimate design of the tunnel structure is not. Discounting a few exception cases, the finite element and frame modeling will result in a tunnel design of about the same structural dimensions. More significant differences will be apparent in the calculation of temporary support of excavation structures such as struts and tiebacks and the estimation of temporary construction soil movement. All things considered, frame analysis of cut-and-cover tunnels is still a viable, appropriate design tool. A suggested approach for structural analysis and design of cut-and-cover tunnels is as follows:

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• Prepare sections, taken at a suitable interval, and run frame analysis and design. The frame can be modified to reflect conditions such as special structural framing, vents, cofferdam walls incorporated in the final structure, and other features. • Run a few soil–structure interaction computer analyses for study of special problems. These can include construction staging, stress analysis of thick, vented members, predictions of soil movement during excavation, estimates of effects of lateral cross walls (in subway stations, for example) and other problems where the improved resolution of the finite elements outweighs the increased effort in their application. • Check the results against frame analysis for a “reality check” of the finite element runs. • Prepare a few computer frame analyses to study longitudinal conditions. While analysis in section largely governs the tunnel design, special longitudinal conditions should be studied as well. These can include framing of transverse ducts to vent buildings, lateral diaphragm walls at the ends of transit stations, and modeling of changes in foundation material in the longitudinal direction.

Buoyancy In areas with a high water table, buoyancy will be a concern. The weight of soil taken out for the cut-andcover tunnel can be less than the weight of the tunnel structure. In addition to the procedures above, buoyancy calculations involve a stability analysis. For the final condition, the weight of the tunnel section must be greater than the upward net hydrostatic pressure. It is conservative not to take advantage of side friction acting on the tunnel walls. However, in some cases, considering construction methods and the in situ soil, side friction can be used in the calculations. For tunnel sections where the excavation support wall is used as the final structure, the weight of the full wall above and below the tunnel section may be used to resist buoyancy. Calculations for buoyancy must be done for temporary construction stages as well as for the final condition. The calculations must be consistent with specified requirements for dewatering, as required, for various stages of the excavation and construction.

Evaluation of Construction Impact and Mitigation An important issue for cut-and-cover tunnel analysis and design is the evaluation and mitigation of construction impacts. By the nature of the methods used, cut-and-cover construction can be more disruptive than bored tunnels. It is important for structural engineers to be familiar with analytical aspects of evaluating soil movement and the impacts it can have on existing buildings and utilities at the construction site. Soil movement can be due to the following:

• Inward movement of excavation support walls. Walls will deflect into cut-and-cover excavation prior to installation of each level of struts or tiebacks supporting the wall. The movement is not recoverable. At each level of excavation support, a certain amount of inward movement will have been recorded, and this is the starting deflection for the next stage of excavation. Therefore, whether using a frame model with assumed applied loads or a finite element analysis, the analysis is nonlinear. • Consolidation due to dewatering. In excavations where the water table is high, it is often necessary to dewater inside to avoid instability. Dewatering inside the cut leads to a drop in the hydrostatic pressure outside the cut. Depending on the soil strata, this can lead to consolidation. Existing buildings and facilities must be evaluated for estimated soil movement during excavation. This evaluation depends on the type of existing structure, its distance and orientation from the excavation, and other parameters. The analysis is site specific, and it can be very complex. Empirical methods and screening tools are available to more generally characterize impacts. These approaches are a good way to analytically get a handle on this complex problem. Many tools available to mitigate, measure, and control adverse impacts from soil movement, including: • Design of stiffer and more watertight excavation support walls • More closely spaced and stiffer excavation support braces and tiebacks © 2001 by CRC Press LLC

• Pre-excavation soil improvement • Specification of limiting values for allowable movements of excavation support walls, soil profiles, and allowable impacts to depressing the water table during construction • Measurement of these impacts by a program of geotechnical and structural instrumentation during excavation • Requirement for mitigation plans to react to situations where movement measurements approach allowable limits

15B.4

Tunnel Linings for Bored and Mined Tunnels

This section describes basic principles for the selection and design of lining systems for bored and mined tunnels. For a greater overview of these principles, see Kuesel [7]. For detailed application in the realm of tunnels in hard ground, see U.S. Army Corps of Engineers Manual, Tunnels and Shafts in Rock [8].

Introduction The design of bored and mined tunnels differs in principle from the design of most other types of structures. Two important aspects largely govern the design of these tunnels: • More than for other structures, the design details of the tunnel structure, often even its basic shape, depend on the method and details of construction. • The principal load-carrying component of the tunnel structure is the soil or the rock mass surrounding the tunnel opening, and the structural lining serves largely to maintain the integrity of the surrounding ground mass. For these reasons the method of construction of a bored or mined tunnel must be established before its design can be contemplated, and the design must include analyses or assumptions concerning the interaction between the tunnel lining and the ground. Principles and details of tunnel linings depend very much on the functional requirements of the finished structure. The lining concept can vary from an unlined and leaky tunnel in rock, supported only by occasional initial ground support such as rock bolts, to a full concrete or steel lining designed to carry all of the rock and groundwater load and to be watertight. The lining concept may be no lining or onepass or two-pass lining. The lining concept is selected based on the following basic criteria: • • • •

Functional requirements Ground conditions Constructibility Economy

One of the most important decisions in the development of the lining concept is what to do with the groundwater, both during construction and in the permanent structure. Highway tunnels and most railway tunnels today are designed to eliminate water inflow through the crown and sidewalls of the tunnels. If the tunnels are above the groundwater table, making the top of the tunnel watertight prevents infiltration of occasional seepage water. If the groundwater is not far above the tunnel, this method will also work, provided adequate drainage is placed outside the waterproofing and through pipes in the tunnel invert. This is a so-called drained tunnel. If the groundwater table is high above the tunnel and the ground is very pervious, then a drained tunnel is not feasible and the tunnel must be waterproofed all around, and the lining must be designed for the full groundwater pressure. Tunnels conveying water for power, irrigation, drainage, or other purposes may be pressurized structures or operated with open-channel flow. These tunnels must be designed for the highest operating and transient internal pressures, compatible with the hydraulic grade-line and the hydraulic controls, in addition to the external loads. Air relief must be provided as required. The tunnel finish must match the roughness (Manning’s coefficient) assumed for the hydraulic analyses. © 2001 by CRC Press LLC

For the design of pressurized tunnels, the external load and the strength of the surrounding rock mass may be considered if the rock is competent, but often the lining must be designed for the full internal pressure. When the internal water pressure is relatively low, less than 100 to 150 psi, it is possible to design steel reinforcement in the concrete lining to accept the hoop tension. With higher pressures, it is usually necessary to use a steel lining. For the design of pressurized tunnels, see the penstock literature or, for example, the U.S. Army Corps of Engineers Manual, Tunnels and Shafts in Rock [8]. When the groundwater is aggressive or contains chemicals that cannot be permitted to flow into potable water, in case of a water-supply tunnel, the tunnel should be made watertight. Some groundwater contains chemicals that will clog up drainage facilities. In that instance, the drainage paths must be serviceable or the tunnel made watertight. Sewage tunnels with open-channel flow in warm climates will typically require protection against corrosion resulting from generation of hydrogen sulfide. Frequently, this protection takes the form of an internal PVC or HDPE membrane cast into the internal tunnel lining. Another important functional requirement deals with the tolerance of the installation of the tunnel facility. A pressurized-water tunnel can tolerate a wide placement tolerance in all directions without serious impairment of function. A tunnel with gravity flow must satisfy the vertical flow requirement but can tolerate wide horizontal tolerances. The interior of traffic tunnels (rail as well as highway or street) must meet the civil requirements of the guideway and the dynamic envelope of the vehicles. Setting a concrete form precisely within an excavated tunnel or cavern is usually much easier than producing a precise excavation in the first place; therefore, a wide tolerance can be applied to the initial excavation and still permit proper placement of the concrete. On the other hand, the one-pass lining is also the final lining and must be built precisely. One-pass linings are often designed with several inches of additional construction tolerance just to make sure the finished structure will meet the functional requirements.

Mechanized Tunneling Through Soil Modern tunnel excavation through soil is almost always done with a shield, most often a mechanized shield. A shield is a circular steel cylinder furnished with a cutting edge and jacked through the soil as the soil is excavated at the face and removed through the back. A tunnel lining is erected as the shield advances and usually furnishes the reaction for the propulsion jacks of the shield. The shield provides the initial ground support. A fully mechanized shield is much like a factory, producing a tunnel in the fashion of an assembly line. Details of the mechanized shield are selected mostly on the basis of the ground and groundwater conditions. Dry Soil In dry ground above the groundwater table, it is usually possible to excavate with an open face or with partial face support. Hand tools or more commonly a large hydraulic scraper or hoe are used to loosen the soil and scoop it onto a conveyor belt for loading muck cars. If the ground is firm, an initial lining consisting of steel ribs and timber lagging, or unbolted concrete segments, may be expanded against the soil behind the advancing shield tail. On the other hand, sand or silt material without cohesion will tend to collapse behind the shield tail, and it may be necessary to erect the initial lining inside the shield tail. In this case, the lining will usually be erected and bolted together to a diameter smaller than the diameter cut by the shield, and the resulting tail void will need to be filled, often with pea gravel and grout. Wet Soil In soft clay, the ground will tend to be overstressed in the face of an open shield and ground movements can be unacceptably large; thus, continuous support is required. This is also the case in most soils below the groundwater table. Without continuous support, the ground will tend to flow uncontrollably into the shield, driven by the seepage forces in the ground. In these cases, a shield with face pressure control is often used today. The front end of the shield is sealed off with a sturdy bulkhead and sufficient pressure © 2001 by CRC Press LLC

is maintained in the front to keep the soil and the groundwater stable. There are two types of facepressure shields: • Slurry tunnel-boring machine (slurry TBM) • Earth-pressure-balance (EPB-TBM). Slurry TBM With a slurry TBM, the sealed front compartment is filled with clay slurry, usually a bentonite slurry, pressurized to balance the groundwater pressure plus at least the active earth pressure acting in front of the face. A constant pressure is maintained either through delicate flow controls or a compressed-air buffer chamber. The earth is loosened by a rotary cutterhead and kept in suspension in the slurry. The muck-laden slurry is pumped to the ground surface, where the muck is separated and the slurry reconditioned before being returned to the tunnel face. In recent years, the slurry TBM has lost much of its market in favor of the EPB-TBM, which does not require an expensive slurry separation and treatment plant. However, the required rotary torque for a large-diameter EPB cutterhead becomes excessive, and all machines over 10-m diameter to date have been slurry TBMs. The slurry TBM also offers advantages of better face control, in particular in mixedface and bouldery ground. It also offers the opportunity to place a boulder-crushing unit at the bottom of the face to reduce large boulders to manageable sizes. Figure 15B.12 shows a typical slurry TBM. EPB-TBM With the EPB-TBM, the front compartment is kept full of soil under sufficient pressure to maintain the stability of the face and minimize ground movement ahead of the face. The soil excavated by the rotary cutterhead is removed from the bottom of the compartment through one or two screw conveyors in series, discharging onto a conveyor belt or directly into muck cars. Groundwater is prevented from flashing through the screw conveyor system by foam, sometimes supplemented by a polymer, or clay slurry added to the soil in the front compartment. The additives must add sufficient cohesion to counter the groundwater pressure along the length of the screw conveyor. The additives also help lubricate the soil mass, reduce the required torque for turning the cutterhead, and reduce wear on the components.

FIGURE 15B.12 Schematic of slurry TBM. (Courtesy of Parsons Brinckerhoff, Inc.)

© 2001 by CRC Press LLC

Linings for Tunnels in Soil One-Pass Lining Both types of face-pressure TBMs usually require the installation of a bolted, gasketed tunnel lining usually made of concrete segments. In the past, cast iron and fabricated steel segments have been popular but are now much too expensive except in special circumstances. The lining must be installed under the protection of the shield tail, and the tail void must be filled. To prevent excessive movement of soft or loose soil into the tail void, it is usually necessary to fill the tail void as the shield advances and keep the tail void under pressure equal to the ground and groundwater pressure. After the installation of the segmental lining in the tail of the shield, no additional internal lining is usually required. This type of lining is usually required when the ground conditions are sufficiently poor to require a face-pressure TBM. The one-pass lining must be fabricated and erected with great precision; once in place, misalignment can be fixed only with great difficulty. The one-pass lining must be designed for all transport and construction loads, including the forces from the shield propulsion jacks. Its adequacy to resist ground loads must also be checked. Two-Pass Lining When an initial lining can be installed behind the tail of the shield, the advance rate of tunnel excavation is usually much faster and the cost of tunneling less expensive, even if a second lining must be placed inside. The initial lining may be steel ribs with lagging or unbolted concrete segments, just adequate to permit installation of the final lining. The final lining is cast-in-place concrete with one, and sometimes two, layer(s) of reinforcement. A waterproofing membrane is usually installed before placing the internal concrete. With a two-pass lining, the initial lining is often considered part of the permanent structure, participating in carrying the loads; however, the inside final lining usually must be designed at least for the groundwater pressure.

Bored Tunnels in Rock Hard-Rock TBM Long tunnels in rock are now mostly excavated using hard-rock TBMs, which excavate a tunnel of circular cross-section. The rotary cutter head of a hard-rock TBM is fitted with disc-shaped rock cutters that roll over the face of the tunnel under great thrust, breaking the rock into slivers, advancing the tunnel by a fraction of an inch per rotation, up to tens of feet per hour. In excellent rock with few discontinuities, no immediate ground support is required. More commonly, the rock mass is fractured and initial ground support in the form of rock bolts or dowels, or even steel sets or lattice girder support, is required. Propulsion of the advancing TBM and the thrust required for breaking the rock are usually derived from large pads jacked firmly against the sides of the tunnel. Every four to six feet or so, the jacks are retracted from the walls, advanced forward toward the face, and re-engaged against the sidewall. In poor rock, or even in good rock where other parts of the tunnel are advanced through soil-like materials, the TBM may be outfitted with a shield much like a soil TBM. A one-pass or two-pass lining system can be erected in the tail of the shield, as in a soil tunnel. Figure 15B.13 shows the cutterhead of a hard-rock TBM, holing through. Roadheader Another type of rock excavator is the roadheader, which is a smaller excavator or ripper mounted on a slewing and elevating arm. The excavator is equipped with ripper or point-attack teeth that rotate around the axis of the arm or around an axis at a right angle with the arm. The roadheader cannot excavate as strong a rock mass as the hard-rock TBM, but it is able to excavate a rectangular or horseshoe-shaped opening. Figure 15B.14 shows a typical roadheader.

© 2001 by CRC Press LLC

FIGURE 15B.13 Rock TBM holing through. (© David Sailors, 1988. With permission.)

Sequential Excavation and Support for Rock Tunnels Shorter tunnels in rock, and rock tunnels of large cross-sections, are sometimes excavated by roadheader, if the rock is soft enough, but are more often excavated by blasting. This is a cyclic operation, which typically includes the following activities in sequence: 1. Drilling blast holes in a pre-designed pattern and loading them with blasting agents 2. Setting off the blast using millisecond delays so there is a series of closely timed blasts (reduces vibrations and facilitates the blasting process) 3. Removing the loosened rock, loading it into trucks or rail cars, and bringing it out 4. Scaling loosened rock from the crown and the side walls 5. Installing initial ground support, rock bolts, shotcrete, steel ribs, or other components as required 6. Repeating the cycle With small cross-sections in good rock, the full face can be blasted at one time. Often a top heading is excavated first, followed by excavation of the bench. In very poor rock, it may be necessary to excavate and support multiple headings. The final lining is usually made of reinforced concrete cast in place. Below the groundwater table, a waterproofing membrane is placed to cover the initial ground support before placing the cast-in-place lining. As discussed earlier, the tunnel lining may be designed to be undrained, with the final lining accepting the full groundwater pressure. Alternatively, drainage may be provided outside the waterproofing membrane, in which case the final lining may be designed for only a portion of the full groundwater pressure.

Selection of Lining System in a Rock Tunnel For most transportation tunnels a substantial final lining is installed. For many tunnels, however, there is a wide selection of tunnel ground support. In some cases, a different ground support system will be selected for different parts of the tunnel depending on geologic conditions and local variations in construction methodology. For example, a steel lining may be required for a portion of a pressure tunnel

© 2001 by CRC Press LLC

FIGURE 15B.14 Roadheader with double rotating cutterhead. (©2000 Sandvik. With permission.)

with high pressure and poor rock, while other parts may require no lining at all. A watertight tunnel may be required through a permeable shattered-rock zone or through seams of gypsum or anhydrite, which may expand or deteriorate, but may not be required elsewhere. If a TBM and a substantial initial lining are required in part of the tunnel, and if the lining is used to provide part of the reaction for the TBM propulsion, then a contractor may choose to continue the lining throughout, even if not required for ground support. Unlined Tunnel

In an unlined water tunnel, the water has direct access to the rock, and leakage will occur into and out of the tunnel. Changes in pressure can cause fluctuations and flows in and out of fissures that wash out fines and eventually lead to instability. For an unlined tunnel to be feasible, the rock must be inert to water, free of significant filled joints and faults, able to withstand the internal pressure in the tunnel without hydraulic fracture, and be sufficiently tight that leakage rates are acceptable. Unlined tunnels should be furnished with an invert pavement to provide a suitable surface for vehicles and help to control erosion. Norwegian hydropower tunnels in good crystalline rock are often unlined for most of their length. Shotcrete Lining A shotcrete lining will provide ground support and may improve leakage and hydraulic characteristics of the tunnel. It also protects the rock against erosion and deleterious effects of water. To protect watersensitive ground, the shotcrete should be continuous and crack-free and reinforced with wire fabric or fibers. As with unlined tunnels, shotcrete-lined tunnels should be furnished with an invert pavement to provide a suitable surface for vehicles and help control erosion. Unreinforced Concrete Lining An unreinforced concrete lining is placed to protect the rock and provide a smooth interior surface. Most shafts that are not subject to internal pressure are lined with unreinforced concrete. This type of tunnel or shaft lining is acceptable if the rock is in equilibrium before concrete placement and loads are expected to be uniform and radial. Shrinkage and temperature cracks are expected and can cause leakage. If the groundwater is corrosive to concrete, a tighter lining may be required to prevent corrosion by the seepage water. An unreinforced lining is generally not acceptable through soil overburden or through badly squeezing ground, which can exert non-uniform displacement loads. © 2001 by CRC Press LLC

The obvious attraction of the unreinforced lining is the substantially lower expense of the lining when no reinforcing steel cage is needed, even if a waterproofing membrane might be set or fibers might be used to minimize cracks. A considerable amount of information on the use of plain concrete in tunnels is available in the AFTES (French Tunnelling Association) Recommendations in Respect of the Use of Plain Concrete in Tunnels (AFTES c/o SNCF, 17 Rue d’Amsterdam, F75008 Paris France) [9]. Reinforced Concrete Lining The reinforcement in linings with only one layer of steel should preferably be placed close to the inside face to resist temperature stresses and shrinkage. Depending on the moment distribution calculated in the lining based on exterior loads, the single steel layer may move from inside to middle to outside around the ring. A lining of this type can remain undamaged at distortions of 0.5% or more, measured as relative diameter change, and can remain functional even at greater distortions. Multiple layers of reinforcement may be required due to large internal pressures or in a squeezing or swelling ground to resist potential non-uniform distortions. Non-uniform pressures requiring a second layer of steel can also occur through faults and shear zones, near the ground surface and at connections to adjacent structures. Pipe in Tunnel This method is often used in water and sewer tunnels up to a size of pipe manageable on the job or on the road, maximum usually up to about a 14-ft (4.2-m) diameter. The tunnel is driven and provided with initial ground support, and a steel or concrete pipe is installed. The concrete pipe may be a standard pipe or prestressed pipe with steel core. The pipe may be furnished with interior corrosion protection made of PVC or HDPE to resist sulfuric acids generated by hydrogen sulfide in an anaerobic condition. Plastic pipe as well as glass-reinforced plastic/plastic mortar pipes have also been used. After placing the pipe, aligning it, and securing it against flotation, the void between the pipe and the rock is filled with flowable mass concrete or, more economically, by cellular concrete. Steel Lining Where the internal pressure in the tunnel exceeds the external (confining) ground and groundwater pressure, a steel lining is usually required to prevent hydrojacking of the rock mass. With only steel reinforcement (two layers), the ability of the tunnel lining to withstand internal pressure is limited. The guideline in regard to confinement is that the weight of the rock mass above the tunnel must exceed the internal operating water pressure, with a suitable safety factor, usually 1.2. This is generally conservative with a level ground surface, but not for tunnels running in a valley wall, where the side cover may be smaller. Here, more precise in situ stress analyses must be made or in situ stress tests performed. In addition to the interior pressure, the steel lining must also be designed for the exterior pressure. Assuming that pipe leakage over the long term occurs, it is often assumed that the external water pressure is equal to the interior pressure. The critical design condition is buckling, and external stiffeners are often required. Methods of analyses of both internal and external water pressures for tunnels and shafts are found in the U.S. Army Corps of Engineers Manual, Tunnels and Shafts in Rock [8]. Concrete Segmental Lining The one-pass concrete segmental lining is usually used for lining of shield or TBM-driven tunnels through soil. Where portions of a tunnel are in soil and others in rock, it may be convenient to build the entire length of tunnel using concrete segmental lining. Particulars on the design of concrete segmental linings are provided below in the Design of Segmental Concrete Linings section.

Structural Design of Permanent Concrete Linings in Rock Rock-Lining Interaction The most important material for the stability of a tunnel in rock is the rock mass, which accepts most or all of the distress associated with the excavation of the rock opening by redistributing stresses around © 2001 by CRC Press LLC

the opening. The initial ground support and the final lining often serve primarily a confining function, in addition to providing the appropriate interior finish. A lining placed in a rock opening that has reached stability will experience no stresses other than self-weight and internal loads. On the other hand, a lining placed inside an opening that has experienced, say, 70% of its elastic (or elasto-plastic) latent displacement will experience stresses from the release of the remaining 30% of displacement. The actual stresses and distortions will depend on the modulus of the lining and of the rock mass. If the rock modulus or the in situ stresses are anisotropic, then the lining will distort as a complex equilibrium is sought. External loads on a tunnel lining may be following or non-following loads. Typical following loads are the contributions from groundwater pressure, which are independent of the displacement of the lining resulting from the loading. Other types of following loads come from squeezing or swelling ground, where only very large distortions may reduce the load intensity. The typical soil or rock load, however, is to a large measure non-following. As the crown of the tunnel lining yields away from high loads at the top, the loads are relaxed. At the same time, the lining distortion will expand the horizontal diameter of the tunnel, increasing reaction loads on the sides, thus rendering the lining loads more uniform. Cracking of Linings With non-uniform loads or distortions, moments will occur both in circular and non-circular tunnel linings. Thus, tension cracks can form, the extent of which depend on the combinations of moments and thrusts. Tension cracks in a tunnel lining usually do not form a failure mode. There is usually a compressive component so that a tension crack does not penetrate through the entire section. In fact, separated blocks in compression form a stable arch. Without through-going cracks, water tightness also is not significantly impaired. Calculated extension cracks at the exterior of the lining, facing the rock, may be fictitious because the rock outside the lining is usually in compression and shear bond between lining and rock will prevent a tension crack from actually opening. As a rule of design, the calculated crack length is usually permitted to reach one half the section thickness, whether the lining is reinforced or not. Depending on the end-use requirements of the tunnel, this can be relaxed. Cracking will also occur in linings due to shrinkage during curing, temperature variations, and the like. Because a blasted rock surface is uneven and the lining thickness therefore variable, such cracks can vary in dimension and location and often are concentrated into a few large cracks at the locations of the lesser thicknesses, rather than many small cracks. If steel ribs are used for initial ground support, cracks will occur typically at the locations of the ribs. Incorporation of expansion joints is usually not effective in controlling these types of cracks because the concrete is bonded firmly to the irregular face of the rock and initial ground support. These types of shrinkage cracks may go through the entire cross-section and may be undesirable. To control them, reinforcing steel is often placed close to the interior surface up to a percentage of 0.28% (up to 0.40% in corrosive environment) of the maximum concrete section thickness. Alternatively, polypropylene, olefin, or steel fibers have been used with success. Construction joints between concrete pours are appropriately furnished with waterstops. Lining Loads for Design It would be misleading to present an exhaustive treatment of the subject of lining loads for tunnels in rock in this brief treatise. The design loads on the final lining will vary with the rock quality as well as the proportion of the rock load assumed to be carried by the initial ground support (if any). They will also include the external water pressure, if the tunnel is watertight, or at least a part of the external water pressure if the tunnel is drained. Additional non-uniform loads can be derived from squeezing layers of rock and from irregularities in the excavated surfaces. Different assumptions are usually made for circular and non-circular tunnels and for tunnels driven by TBM as opposed to tunnels excavated by blasting, which tends to disturb the rock and add loads. Guidance to estimate the design rock loads can be found in the rock mechanics literature and in publications such as the U.S. Army Corps of Engineers manual cited previously [8]. Experienced geologists and rock tunnel engineers should be consulted when establishing these design loads. Conditions in the field should be observed to verify the estimated loads.

© 2001 by CRC Press LLC

Methods of Analysis

Closed-form solutions are available for the simple conditions of a circular elastic tunnel lining embedded in a homogeneous elastic ground, where the induced stresses are the assumed in situ stresses in the ground. The closed-form solution presented in the following is based on the following simplifying assumptions: • • • • • •

Plain strain, elastic radial lining pressures are equal to in situ stresses or a proportion thereof. Tangential bond between lining and ground is included. Lining distortion and compression are resisted/relieved by ground reactions. Vertical and lateral in situ soil or rock stresses are sv and K0sv . Modulus and Poisson’s ratio of the soil or rock mass are Er and vr . Concrete lining modulus, moment of inertia, and area are Ec , I, A, and mean radius R.

Maximum/minimum bending moment can be determined by the following equation: 2

s v ( 1 – K 0 )R M = ± ----------------------------------------------------------------------3 3 – 2v r Er R - Ê ----------ˆ 4 + -----------------------------------------3 ( 1 + v r ) ( 3 – 4v r ) Ë E c I ¯

(15B.1a)

Maximum/minimum hoop force can be determined by the following equation:

s v ( 1 + K 0 )R s v ( 1 – K 0 )R - ± ------------------------------------------------------------------------------------N = -------------------------------------------------------------------------------------3 2 ( 1 – vr ) Er R 4v r E r R ˆ 2 + --------------------------------------------------------------------------- Ê -------2 + ( 1 – K 0 ) (--------------------------------------3 1 – 2v r ) ( 1 + v r ) Ë E c A¯ ( 3 – 4v r ) ( 12 ( 1 + v r )E c I + E r R )

(15B.1b)

Maximum/minimum radial displacement equation: 3

3 s v ( 1 – K 0 )R s v ( 1 + K 0 )R u --- = -----------------------------------------------------------------± ---------------------------------------------------------------------3 – 2v r R 2 ------------- E r R 3 + 2E c AR 2 + 2E c I ---------------------------------------- E r R 3 + 12E c I ( 1 + v r ) ( 3 – 4v r ) 1 + vr

(15B.1c)

These simplifying assumptions are hardly ever met in real life and presume essentially the lining “wished in place” into the ground. Nonetheless, the equations are useful in examining the effects of variations of important parameters. The maximum moment is controlled by the flexibility ratio: 3

Er R a = ---------Ec I

(15B.2)

For a large value of the flexibility ratio (large rock mass modulus), the moment becomes very small. Conversely, for a small value (very rigid lining), the moment is large. If the rock mass modulus is zero, the rock does not restrain the movement of the lining, and the maximum moment in the lining is

M = 0.25s v ( 1 – K 0 )R

2

(15B.3)

With K0 = 1 (uniform stress field) the moment is zero, and with K0 = 0 (simple vertical loading of vertical ring) the moment is maximum. More commonly, structural finite element programs are used for analysis, where the lining ring is modeled as beam elements and the ground as springs representing the modulus of the ground. From these analyses, the sectional forces, moment, thrust, and shear are deduced. The structural analysis offers © 2001 by CRC Press LLC

FIGURE 15B.15 Installation of one-pass liner. (© Bernie Martin. With permission.)

little difficulty, but the loading assumptions and the elastic constants assumed are dependent on both the nature of the ground and the method of construction. Continuum analyses using finite element or finite difference methods, where the ground is represented by a grid of elements, more accurately can analyze variations in the ground stratification as well as steps in the construction process. Thrusts and moments in the lining elements can be derived directly. The concrete cross-section is designed for the moment and thrust force, using the standard momentthrust interaction diagram, which is described in concrete design texts. The typical analyses may be modified to fit just one layer of reinforcement, fiber reinforcement, or none at all. Sometimes a larger theoretical zone of tension in the concrete section may be accepted rather than strictly according to Code.

Design of Segmental Concrete Linings Components of the Lining The number of segments in a lining ring is decided as a compromise. A small number of segments will give the contractor fewer pieces to handle, allowing for quicker erection, and a smaller number of segment forms. On the other hand, fewer segments are heavier and more difficult to handle. With a wide-open shield, as few as three segments per ring can be handled, but this is rare. More typically, there are five to eight segments per ring, sometimes more for a very large tunnel. The last segment placed is usually wedge-shaped for ease of insertion. Each ring is between 1 and 1-1/2 m wide, matching the stroke of the shield propulsion jacks, with the narrower rings better suited for tunnels with short-radius curves. Segment rings for curved tunnels are tapered (with one side slightly wider than the other) to allow placement as secants to the curve of the tunnel. Segment joints are usually staggered from ring to ring to provide greater rigidity and redundancy. Figure 15B.15 shows the installation of a one-pass liner ring. The most important parts of the lining are the joints. A one-pass lining must be firmly fixed in a circular form. This usually requires bolts to be installed between rings and between segments in a ring. Sometimes dowels are used between rings. Joints in a one-pass lining must also usually be made watertight, which is usually accomplished by installing a recessed rubber or neoprene gasket around each segment. The rubber gasket is vulcanized and made to fit the segment precisely. The two opposing gaskets in the joint will be compressed sufficiently so that water leakage through the joint is prevented. The gasket © 2001 by CRC Press LLC

recess and the size and geometry of the gasket are designed to meet the leakage requirements, even if the segments are joined out of tolerance. Laboratory testing of gaskets in adverse installation configurations is often performed. Another type of gasket is the hydro-swelling gasket, made with rubber and bentonite or similar materials. When exposed to seepage water, this gasket will swell three to ten times and fill the available space for a watertight fit. Some important linings are fitted with a hydro-swelling gasket towards the exterior and a rubber gasket towards the interior. Several types of bolt systems are employed. The most common type consists of straight bolts and nuts with washers and grommets, requiring bolt holes and pockets cast into the segment for their insertion. Curved bolts are easier to install and require smaller bolt pockets. More common today are the straight bolts installed at an angle into an insert cast into the segment. Some designers assume that bolts are for erection only and do not require them to be considered for the permanent structure, except at transitions and other critical locations. Some contractors will retrieve most of the bolts after reuse once the lining is in place and the surrounding grout is fully cured. Design Conditions The segments must be analyzed and designed both for the ultimate functional design and lifetime criteria. It must also withstand all other events during the life of the segments: casting, de-forming at low strength, storing, transport, erection, bolting/doweling, shield jacking, forces from out-of–tolerance placement, gasket forces, etc. Reinforcement is placed to help withstand bending moments around the ring and other forces such as: • • • •

Splitting or tension across the section from the force between the segments in a ring Eccentric jacking force tending to break off a corner of the joint Forces from tightening the bolts, in particular when curved bolts are used Torsion across the segment resulting from only partial contact between adjacent ring segments, when segment joints are staggered

From the point of view of fabrication, it is an advantage if the reinforcing cage is manufactured in part from welded-wire fabric. Recently, steel-fiber reinforced concrete without other reinforcing steel has been used successfully for the manufacture of tunnel lining segments. In the long term, elements of the lining can corrode if exposed to corrosive environmental agents. For example, sulfates in the soil and groundwater can attack the concrete. Salt in the groundwater will tend to seep through the concrete and concentrate at the inside face as the water evaporates, eventually causing reinforcing steel to corrode. Remedies to improve long-term durability include at least the following: • • • • •

Use of high-density, low-permeability concrete with pozzolanic admixtures and microsilica Coating the exterior concrete face with impervious bitumen Epoxy coating of reinforcing steel after fabrication of cages Placement of thick grout or mortar backfill around the lining, designed for water tightness Use of corrosion-resistant bolts and nuts

In some instances, all of these measures have been implemented on a single project.

15B.5

Seismic Analysis and Design

Introduction Tunnels, in general, have performed better during earthquakes than have above-ground structures such as bridges and buildings. Tunnel structures are constrained by the surrounding ground and, in general, cannot be excited independent of the ground or be subject to strong vibratory amplification, such as the inertial response of a bridge structure during earthquakes. Adequate design and construction of seismic© 2001 by CRC Press LLC

resistant tunnel structures, however, should never be overlooked. Their seismic performance could be vital, particularly when they comprise important components of a critical transportation system (e.g., a transit system) for which little redundancy exists. The general procedure for seismic design and analysis of tunnel structures should be based primarily on the ground deformation approach; that is, the structures should be designed to accommodate the deformations imposed by the ground. The analysis of the structure response can be conducted first by ignoring the stiffness of the structure, which leads to a conservative estimate of the ground deformations. This simplified procedure is generally applicable for structures embedded in rock or stiff/dense soil. In cases where the structure is stiff relative to the surrounding soil, the effects of soil-structure interaction must be taken into consideration.

Performance Record During Earthquakes Seismic performance data of underground structures, including tunnels, are relatively scarce. Data reported in several studies [11–15] show: • The greatest risk to all types of tunnels (including bored and mined, cut-and-cover, and immersed tunnels) occurs when the following conditions exists:  An active fault intersects the tunnel.  A landslide intersects the tunnel.  Soils surrounding the tunnels liquefy. • Damage potential to tunnels reduces with increasing overburden, due partly to the attenuation of ground-shaking intensity with depth. • Damage is greater in soils than in competent rock. • Seismic performance of shallow cut-and-cover rectangular tunnels has been relatively poor in comparison to that of bored tunnels, as evidenced during the 1995 Kobe, Japan, earthquake [16,17]. These rectangular box-type structures are particularly vulnerable at the joints connecting the slabs with the walls/columns when subject to cyclic racking deformations imposed by the ground. • Immersed tunnels are susceptible to permanent ground deformations resulting from liquefaction induced settlements, lateral spread, and uplift (flotation), as well as slope instability (landslides) in soft cohesive soils. Joints connecting tube segments are particularly vulnerable to the relative movements between two adjacent segments during shaking (note that water tightness is one of the critical performance requirements of immersed tunnels). • Damage potential to bored tunnels due to ground-shaking effects (excluding permanent displacements due to faulting, landslides, and liquefaction) increases with ground-shaking intensity and decreases with a better tunnel lining/support system. Figure 15B.16 presents performance data of bored tunnels under the effects of seismic ground shaking alone [13]. The figure suggests that:  Ground shaking caused little damage in tunnels for peak ground acceleration (PGA) less than about 0.2 g, where g is the gravity of acceleration.  Tunnels with ductile lining (reinforced concrete or steel) tend to have performed better, with damage observed only when the PGA exceeds 0.5 g.

Design and Analysis Approach for Ground Shaking Effects General

Underground tunnel structures undergo three primary modes of deformation during seismic shaking: ovaling/racking, axial, and curvature deformations (see Figures 15B.17 and 15B.18) [12,15]. The ovaling/racking deformation is caused primarily by seismic waves propagating perpendicular to the tunnel longitudinal axis, causing deformations in the plane of the tunnel cross-section. Vertically propagating shear waves are © 2001 by CRC Press LLC

FIGURE 15B.16 Rock surface peak ground acceleration for various tunnels. (Courtesy of M.S. Power, Summary and Evaluation of Seismic Design of Tunnels, Draft Report submitted to MCEER.)

FIGURE 15B.17 Ovaling and racking deformation of tunnels [15]. (© Parsons Brinckerhoff, Inc. and Jaw-Nan Wong. With permission.)

© 2001 by CRC Press LLC

FIGURE 15B.18 Axial and curvature deformation of tunnels [15]. (© Parsons Brinckerhoff, Inc. and Jaw-Nan Wong. With permission.)

generally considered the most critical type of waves for this mode of deformation. The axial and curvature deformations are induced by components of seismic waves that propagate along the longitudinal axis. Evaluation of Axial and Curvature Deformations Free-Field Deformation Procedure This procedure assumes that the tunnel lining conforms to the axial and curvature deformations of the ground in the free-field (i.e., without the presence of the tunnel). While conservative, this assumption provides a reasonable evaluation because, in most cases, the tunnel lining stiffness is considered relatively flexible to the ground. This procedure requires minimum input, making it useful as an initial design tool and as a method of design verification. The lining will develop axial and bending strains to accommodate the axial and curvature deformations imposed by the surrounding ground. St. John and Zahran [18] developed solutions for these strains due to compression P-waves, shear S-waves, and Rayleigh R-waves. Table 15B.3 presents the solutions due to the three wave types propagating at an angle, f, in the horizontal plane with respect to the longitudinal axis of the tunnel. The strains e due to combined axial and curvature deformations can be obtained by combining the longitudinal strains generated by axial and bending strains as follows: For P-waves:

VP 2 A 2 -----Pe = ----C P cos f + Y C 2P sin fcos f

(15B.4a)

For S-waves:

VS A -----2S cos 3 f e = ----sin f cos f + Y CS CS

(15B.4b)

For R-waves:

VR 2 A 2 -----Re = ----C R cos f + Y C 2R sin fcos f

(15B.4c)

where: VP = peak particle velocity of P-waves at the tunnel location VS = peak particle velocity of S-waves at the tunnel location © 2001 by CRC Press LLC

VR AP AS AR CP CS CR Y

= = = = = = = =

peak particle velocity of R-waves at the tunnel location peak particle acceleration of P-waves at the tunnel location peak particle acceleration of S-waves at the tunnel location peak particle acceleration of R-waves at the tunnel location apparent propagation velocity of P-waves apparent propagation velocity of S-waves apparent propagation velocity of R-waves distance from neutral axis of tunnel cross-section to the lining extreme fiber

It should be noted that: • S-waves generally cause the largest strains and are the governing wave type. • The angle of wave propagation, f, should be the one that maximizes the combined axial strains.

TABLE 15B.3 Strain and Curvature Due to Three Wave Types Wave Type

Longitudinal Strain

P-wave

VP 2 e = ----C P cos f

aP 1 2 --- = ------2 sin f cos f CP r

VP e max = ----C P for f = 0°

aP 1 --------- = 0.385 ------2 for f = 35.27° CP r max

VS e = ----C P sin f cos f

aS 1 3 --- = -----2 cos f CS r

VS e max = -------2C S for f = 45°

aS 1 --------- = -----2 for f = 0° CS r max

VR 2 e = ----C R cos f

aR 1 2 --- = -----2- sin f cos f CR r

VR e max = ----C R for f = 0°

aR 1 --------- = 0.385 -----2- for f = 0° CR r max

S-wave

Curvature

R-wave: Compression component

Shear component

aR 1 2 --- = -----2- cos f CR r aR 1 --------- = -----2- for f = 0° CR r max

VP aP CP VS aS CS VR aR CR 1/r

= = = = = = = = = =

soil particle velocity caused by P-waves. soil particle acceleration caused by P-waves. apparent propagation velocity of P-waves. soil particle velocity caused by S-waves. soil particle acceleration caused by S-waves. apparent propagation velocity of S-waves. soil particle velocity caused by R-waves. soil particle acceleration caused by R-waves. propagation velocity of R-waves. curvature.

Source: Adapted from St. John and Zahrah [18].

© 2001 by CRC Press LLC

The horizontal propagation S-wave velocity, CS , in general, reflects the seismic shear wave propagation through the deeper rocks rather than that of the shallower soils where the tunnel is located. In general, this velocity value varies from about 2 to 4 km/sec. Similarly, the P-wave propagation velocities, CP , generally vary between 4 and 8 km/sec. The designer should consult with experienced geologists/seismologists for determining CS and CP . When the tunnel is located at a site underlain by deep deposits of soil sediments, the induced strains may be governed by the R-waves. In such deposits, detailed geological/seismological analyses should be performed to derive a reliable estimate of the apparent R-wave propagation velocity, CR. The combined strains calculated from Equations 15B.4a,b, and c represent the seismic loading effect only. To evaluate the adequacy of the structure under the seismic loading condition, the seismic loading component has to be added to the static loading components using appropriated loading combination criteria developed for the structures. The resulting combined strains are then compared against the allowable strain limits, which should be developed based on the performance goal established for the structures (e.g., the required service level and acceptable damage level). Procedure Accounting for Soil-Structure Interaction Effects If a very stiff tunnel is embedded in a soft soil deposit, significant soil-structure interaction effects exist, and the free-field deformation procedure presented above may lead to an overly conservative design. In this case, a simplified beam-on-elastic-foundation procedure should be used to account for the soilstructure interaction effects. According to St. John and Zahrah [18], the effects of soil-structure interaction can be accounted for by applying reduction factors to the free-field axial strains and the free-field curvature strains, as follows: For axial strains:

E l A l 2p 2 2 - Ê -------ˆ R = 1 + -------K a Ë L ¯ cos f

(15B.5a)

For bending strains:

E l I l 2p 4 4 Ê -------ˆ R = 1 + ------K h Ë L ¯ cos f

(15B.5b)

where: El Al Ka Kh L Il

= = = = = =

Young’s modulus of tunnel lining cross-sectional area of the lining longitudinal soil-spring constant transverse soil-spring constant wave length of the P-, S-, or R-waves moment of inertia of the lining cross-section

It should be noted that the axial strain calculated from Equation 15B.5a should not exceed the value that could be developed using the maximum frictional forces, Qmax, between the lining and the surrounding soils. Qmax can be estimated using the following expression:

fL Q max = ----4

(15B.6)

where f = maximum frictional force per unit length of the tunnel. Evaluation of Ovaling Deformations of Bored/Mined Circular Tunnels

The seismic ovaling effect on the lining of bored/mined circular tunnels is best defined in terms of change of tunnel diameter, DDEQ. For practical purposes, the ovaling deformations can be assumed to be caused primarily by the vertically propagating shear waves. DDEQ can be considered as seismic ovaling deformation demand for the lining. The procedure for determining DDEQ and the corresponding lining strains is outlined as follows [15]. © 2001 by CRC Press LLC

Step 1 Estimate the expected free-field ground strains caused by the vertically propagating shear waves of the design earthquakes. The free-field ground strains can be estimated using the following formula:

V g max = -------SC SE

(15B.7)

where: gmax = maximum free-field shear strain at the elevation of the tunnel VS = S-wave peak particle velocity at the tunnel elevation CSE = effective shear wave velocity of the medium surrounding the tunnel Alternatively, the maximum free-field shear strain can be estimated by a more refined free-field site response analysis (see, for example, Reference 19). The effective shear wave velocity of the vertically propagating shear wave, CSE, must be compatible with the level of the shear strain that may develop in the ground at the elevation of the tunnel under the design earthquake shaking. A rough estimate of the ratio of CSE/CSS (where CSS is the low-strain shear wave velocity of the surrounding medium) can be made as follows: • For rock, CSE/CSS @ 1.0. • For stiff to very stiff soil, CSE/CSS may range from 0.7 to 0.9 for low to moderate earthquake shaking and from 0.5 to 0.7 for strong shaking. Alternatively, site-specific response analyses can be performed for estimating CSE. Site-specific response analyses should be performed in soft soil sites. The values of the low-strain shear wave velocity, CSS, can be determined using geophysical testing techniques in the field, such as P-S logger, cross-hole, and seismic cone penetration methods, or they may be estimated from empirical correlation. Step 2 By ignoring the stiffness of the tunnel, which is applicable for tunnels in rock or stiff/dense soils, the lining can be reasonably assumed to conform to the surrounding ground with the presence of a cavity due to the excavation of the tunnel (but without the presence of the lining). The resulting diameter change of the tunnel is

DD EQ = ± 2g max ( 1 – n m )D

(15B.8)

where: nm = Poisson’s ratio of the surrounding ground D = diameter of the tunnel. Step 3 If the structure is stiff relative to the surrounding soil, then the effects of soil-structure interaction should be taken into consideration. The relative stiffness of the lining is measured by the flexibility ratio, F, defined as follows: 2

3

E m ( 1 – n l )R l F = ----------------------------------6E l I l, 1 ( 1 + n m ) where: Em nl Rl Il,1

= = = =

strain-compatible elastic modulus of the surrounding ground Poisson’s ratio of the tunnel lining nominal radius of the tunnel lining moment of inertia of lining per unit width of tunnel along the tunnel axis

© 2001 by CRC Press LLC

(15B.9)

FIGURE 15B.19 Seismic ovaling coefficient curves [15]. (© Parsons Brinckerhoff, Inc. and Jaw-Nan Wong. With permission.)

The strain-compatible elastic modulus of the surrounding ground Em should be derived using the strain-compatible shear modulus Gm corresponding to the effective shear wave propagating velocity CSE. The moment of inertia of the tunnel lining per unit width, Il,1, should be determined based on the expected behavior of the selected lining under the combined seismic and static loads, accounting for cracking and joints between segments and between rings as appropriate. Step 4 The diameter change, DDEQ , accounting for the soil-structure interaction effects, can then be estimated using the following equations:

1 DD EQ = ± --3- k 1 Fg max D

(15B.10)

12 ( 1 – n m ) k 1 = ------------------------------2F + 5 – 6n m

(15B.11)

where k1 = seismic ovaling coefficient. The seismic ovaling coefficient curves plotted as a function of F and nm are presented in Figure 15B.19. The resulting bending moment induced maximum fiber strain, em, and the axial force (i.e., thrust) induced strain, eT, in the lining, can be derived as follows:

Em g max t l 1 2 ------------e m = --6- k l ------------------R l 2E ( 1 + vm ) l I l, t

(15B.12)

Em g max 1 ---------e T = --6- k l ------------------R l ( 1 + vm ) El tl

(15B.13)

where tl = thickness of the lining. The solutions presented in Equations 15B.10 through 15B.13 assumes that a full slippage condition exists along the soil/lining interface, which allows normal stresses (without normal separation) but no © 2001 by CRC Press LLC

FIGURE 15B.20 Racking deformation for a box structure [15]. (© Parsons Brinckerhoff, Inc. and Jaw-Nan Wong. With permission.)

tangential shear force. The full-slippage assumption yields slightly more conservative results in estimating the diameter change and bending strain, but significantly lower values of thrust-induced strain than the no-slippage condition. Therefore, Equation 15B.13 should not be used unless a full-slippage mechanism is incorporated in the design. Instead, the no-slippage condition should be assumed in deriving the thrust-induced strain as follows [15]:

Em g max - --------e T = k 2 2----------------------( 1 + nm ) Rl El tl

(15B.14)

1 2 F [ ( 3 – 2n m ) – ( 1 – 2n m )C ] – --2- ( 1 – 2n m ) + 2 k 2 = 1 + ---------------------------------------------------------------------------------------------------------------------------------------------------5 2 F ( 3 – 2n m ) + ( 1 – 2n m )C ] + C --- – 8n m + 6n m + 6 – 8n m 2

(15B.15)

2

E m ( 1 – n l )R 1 C = --------------------------------------------------E l t ( 1 + n m ) ( 1 – 2n m )

(15B.16)

where C = compressibility ratio. The seismically induced strains due to the ovaling effect need to be combined with strains resulting from non-seismic loading and then checked against the allowable strain limits consistent with the performance goal established for the design of the tunnel lining. Evaluation of Racking Deformations of Rectangular Tunnels Racking deformations are defined as the differential sideways movements between the top and bottom elevations of the rectangular structures, shown as DS in Figure 15B.20. The resulting material strains in the lining associated with the seismic racking deformation, DS , can be derived by imposing the differential deformation on the structure in a structural frame analysis. The procedure for determining DS , taking into account the soil-structure interaction effects, is presented below [15]. Step 1 Estimate the free-field ground strains gmax (at the structure elevation) caused by the vertically propagating shear waves of the design earthquakes (see Evaluation of Ovaling Deformations of Bored/Mined Circular © 2001 by CRC Press LLC

Tunnels section above). Determine DFree-Field , the differential free-field relative displacements corresponding to the top and the bottom elevations of the rectangular structure (see Figure 15B.20) by:

DFree-Field = hg max

(15B.17)

where h = height of the structure. Step 2 Determine the racking stiffness, KS, of the structure from a structural frame analysis. For practical purposes, the racking stiffness can be obtained by applying a unit lateral force at the roof level, while the base of the structure is restrained against translation, but with the joints free to rotate. The structural racking stiffness is defined as the ratio of the applied force to the resulting lateral displacement. In performing the structural frame analysis, it is important to use the appropriate moment of inertia, taking into account the potential development of cracked section, particularly for the vertical walls. Step 3 Determine the flexibility ratio, Frec, of the proposed design of the structure using the following equation:

Gm w - --F rec = -----KS h

(15B.18)

where: w = width of the structure. Gm = average strain-compatible shear modulus of the surrounding ground The flexibility ratio is a measure of the relative racking stiffness of the surrounding ground to the racking stiffness of the structure. Step 4 Based on the flexibility ratio obtained form Step 3 above, determine the racking reduction ratio, Rrec, for the structure using Figure 15B.21 or the following expression [21]:

FIGURE 15B.21 Racking reduction ratio [15]. (© Parsons Brinckerhoff, Inc. and Jaw-Nan Wong. With permission.)

© 2001 by CRC Press LLC

4 ( 1 – nm ) R rec = --------------------------3 – 4n m ------------------ + 1 F rec

(15B.19)

The triangular points in Figure 15B.21 correspond to published results [15]. Data in Reference 15 were generated by performing a series of dynamic finite element analyses on a number of cases with varying soil and structural properties, structural configurations, and ground motion characteristics. As indicated in the figure, if Frec = 1, the structure is considered to have the same racking stiffness as the surrounding ground; therefore, the racking distortion of the structure is about the same as that of the ground in the free-field. When Frec is approaching zero, representing a perfectly rigid structure, the structure does not rack, regardless of the distortion of the ground in the free-field. For Frec > 1.0, the structure becomes flexible relative to the ground, and the racking distortion will be magnified in comparison to the shear distortion of the ground in the free-field. This magnification effect is not caused by the effect of dynamic amplification; rather, it is attributed to the fact that the ground has a cavity in it as opposed to the freefield condition. Step 5 Determine the racking deformation of the structure, DS, using the following relationship:

DS = RrecDFree-Field

(15B.20)

Step 6 The seismic demand in terms of internal forces as well as material strains can be calculated by imposing DS upon the structure in a frame analysis, as depicted in Figure 15B.22.

FIGURE 15B.22 Frame analysis modeling of racking deformations [15]. (© Parsons Brinckerhoff, Inc. and Jaw-Nan Wong. With permission.)

Loads Due to Vertical Seismic Motions The effects of vertical seismic motions can be accounted for by applying a vertical pseudo-static loading, equivalent to the product of the vertical seismic coefficient and the combined dead and design overburden loads used in static design. The vertical seismic coefficient can be reasonably assumed to be two thirds of the design peak horizontal acceleration divided by the gravity. This vertical pseudo-static loading should be applied by considering both up and down directions of motion. Whichever results in a more critical load case should govern. If there is a potential for a seismically loosened zone to develop above the crown of the tunnel, then the inertial effects of this loosened zone should also be included in the design, unless appropriate stabilization measures are taken to prevent it from occurring. © 2001 by CRC Press LLC

Tunnel Subject to Large Displacements As indicated above, the greatest risk to tunnel structures is the potential for large ground movements as a result of unstable ground conditions (e.g., liquefaction and landslides) or fault displacements. In general, it is not feasible to design a tunnel structure to withstand large ground displacements. The proper design measures in dealing with the unstable ground conditions may consist of the following: • Ground stabilization • Removal and replacement of the problem soils • Re-routing or deep burial to bypass the problem zone With regard to the fault displacements, the best strategy is to avoid any potential crossing of active faults. If this is not possible, then the general design philosophy is to accept and accommodate the displacements by either employing an oversized excavation, perhaps backfilled with compressible/collapsible material, or using ductile lining to minimize the instability potential of the lining. In cases where the magnitude of the fault displacement is limited, or the width of the sheared fault zone is considerable so that the displacement is dissipated gradually over a distance, design of a strong lining to resist the displacement may be technically feasible. The structures, however, may be subject to large axial, shear, and bending forces. Many factors (among others) need to be considered in the evaluation, including the stiffness of the lining and the ground, the angle of the fault plane intersecting the tunnel, the width of the fault, and the magnitude as well as orientation of the fault movement. Analytical procedures are generally used for evaluating the effects of fault displacement on lining response. Some of these procedures were originally developed for buried pipelines [20]. Continuum finite-element or finite-difference methods have also been used effectively for evaluating the tunnel-ground-faulting interaction effects.

Shaft Structures and Interface Joints The seismic considerations for the design of vertical shaft structures are similar to those for the lined circular tunnel structures, except that ovaling and axial deformations in general do not govern the design. Considerations should be given to the curvature strains and shear forces of the lining resulting from vertically propagating shear waves. Force and deformation demands may be considerable in cases where shafts are embedded in deep, soft deposits. In addition, potential stress concentrations at the following critical locations along the shaft must be properly assessed and designed for: • Abrupt change of the stiffness between two adjoining geologic layers • Shaft/tunnel or shaft/station interfaces • Shaft/surface building interfaces

Flexible connections to accommodate the potential differential movements are the recommended design strategy between any two structures with drastically different stiffness/mass in poor ground conditions.

Defining Terms advance rate: the amount of progress that a tunnel-boring machine makes — the distance it covers in a day, usually measured in feet or meters; also used for tunneling by other means. backfill: any material such as sand, gravel or crushed stone, grout, or concrete used to fill the remainder of an excavation after a tunnel or other underground structure has been constructed within the excavation. ballast: a stabilizing weight (stones or concrete), either temporary or permanent, often added to immersed tunnel elements while floating, being immersed, or in their final position. bentonite: a clay mineral that can absorb large amounts of water. When mixed with water, it forms a slurry used to support deep trenches or bore holes against collapse until they can be filled with concrete.

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bottom-up: a method of construction in which a tunnel is built within an excavated trench in a conventional way or sequence: base slab first, then the walls, and finally the roof. The completed structure is then backfilled and the ground surface reinstated. cofferdam: a temporary structure, constructed in water and pumped dry; used to keep water out so that work can be performed in dry conditions. controlled blasting: use of patterned drilling and optimum amounts of explosives and detonating devices to control blasting damage cross-passage: a short passage or tunnel connecting two adjacent tunnels, often used to allow people to escape from one tunnel to another in an emergency. crown: the top of a tunnel. cut-off wall: an underground wall, either temporary or permanent, used in tunnel excavations to prevent the passage of groundwater. decking: a plank cover over a work area that serves as a temporary surface for pedestrian and vehicular traffic (including construction equipment); usually made of wood, concrete, or steel. dewatering: the removal of groundwater from the area to be excavated. drawdown: a lowering of the normal groundwater level (water table) as the result of dewatering. drill-and-blast: a method of mining in which small-diameter holes are drilled into the rock and then loaded with explosives. The blast from the explosives fragments and breaks the rock away from the face so the rock can be removed. Repeated drilling and blasting advance the underground opening. face: the soil being excavated directly in front of the tunnel-boring machine or the surface at the head of a tunnel excavation. A mixed face is a condition with more than one type of material, such as clay, sand, gravel, cobbles, or rock. ground reinforcement: structural elements installed in the ground by drilling and insertion, including rock dowels or anchors, often grouted in place. ground support: installation of any type of engineering structure around or inside the excavation, such as steel sets, wood cribs, timbers, or lining. heading: a smaller tunnel used when a larger tunnel is excavated in several stages. Smaller headings are used when full, all-at-once tunnel excavation would not be prudent. Sometimes multiple headings are used simultaneously to increase the number of excavation faces and compensate for slower excavation rates. invert: the bottom of a tunnel. lining: a temporary or permanent structure made of concrete or other materials to secure and finish the tunnel interior or to support an excavation. mole: slang term for a tunnel engineer; also used to describe a tunnel-boring machine (TBM). open cut: a method of construction in which the excavated trench is left uncovered while the tunnel is constructed. overburden: the soil between the ground surface and the roof of a tunnel. pilot tunnel: an exploratory tunnel, usually smaller and driven ahead of the main tunnel. portal: the entrance to a tunnel. sandhog: slang term for a tunnel worker. shaft: a vertical excavation, often used to provide access to a tunnel from the surface. shield: a structure used in soft ground to provide support at the face of the tunnel for the soil above the tunnel, to provide space for erecting supports, and to protect the workers excavating and erecting supports. shotcrete: concrete pneumatically projected at high velocity onto a surface; pneumatic method of applying a lining of concrete. soft ground: soils and weak rock that can be easily removed. TBM: tunnel-boring machine; a machine that excavates a tunnel by drilling out the heading to full size in one operation.

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top-down: a method of construction in which the tunnel walls are built first, using special machinery, within a narrow trench. Next, the roof is built in a shallow excavation, and the ground surface is reinstated. The rest of the tunnel is then excavated and constructed underneath the roof. underpinning: the installation of new supports beneath the foundation of a building or other structure to protect it from settlement caused by adjacent tunneling or other construction; sometimes used in place of an old foundation that was removed.

References [1] International Tunnelling Association Immersed and Floating Tunnels Working Group, State-ofthe-Art Report, 2nd ed., Pergamon Press, Oxford, 1997. [2] International Tunnelling Association Immersed and Floating Tunnels Working Group, State-ofthe-Art Report, 1st ed., Pergamon Press, Oxford, 1993. [3] Bechtel/Parsons Brinckerhoff, Memorial Tunnel Fire Ventilation Test Program, Comprehensive Test Report, prepared for Massachusetts Highway Department, November 1995. [4] Ingerslev, L.C.F., Developments in immersed tunnels, in Options for Tunnelling 1993, Burger, H., Ed., Elsevier Science Publishers B.V., Amsterdam, 1993. [5] Ingerslev, L.C.F., Concrete immersed tunnels: the design process, in Immersed Tunnel Techniques, The Institution of Civil Engineers, Telford, 1989. [6] Bickel, J.O. and Kuesel, T.R., Eds., Tunnel Engineering Handbook, 1st ed., Van Nostrand-Reinhold, New York, 1982; Bickel, J.O., Kuesel, T.R., and King, E.H., Eds., Tunnel Engineering Handbook, 2nd ed., Chapman & Hall, London, 1996. [7] Kuesel, T.R., Tunnel stabilization and lining, in Tunnel Engineering Handbook, 2nd ed., Bickel, J.O., Kuesel, T.R., and King, E.H., Eds., Chapman & Hall, London, 1996. [8] U.S. Army Corps of Engineers Manual, Tunnels and Shafts in Rock, EM 1110-2-2901, 1997. [9] AFTES (French Tunneling Association), Recommendations in Respect of the Use of Plain Concrete in Tunnels, AFTES (c/o SNCF, 17 Rue d’Amsterdam, F75008 Paris France), 1998 (English transl. 1999). [10] AFTES (French Tunneling Association), The Design, Sizing and Construction of Precast Concrete Segments Installed at the Rear of a Tunnel Boring Machine (TBM), AFTES (c/o SNCF, 17 Rue d’Amsterdam, F75008 Paris France), 1997 (English transl. 1999). [11] Dowding, C.H. and Rozen, A., Damage to rock tunnels from earthquake shaking, ASCE J. Geotech. Eng. Div., 104(GT2), 1978. [12] Owen, G.N. and Scholl, R.E., Earthquake Engineering of Large Underground Structures, prepared for the Federal Highway Administration, FHWA/RD-80/195, 1981. [13] Power, M.S. and Rosidi, D., Seismic Vulnerability of Tunnels and Underground Structures Revisited, North American Tunneling Conf., 1998. [14] Sharma, S. and Judd, W.R., Underground opening damage from earthquakes, Eng. Geol., 30, 1991. [15] Wang, J, Seismic Design of Tunnels: A Simple State-of-the-Art Design Approach, Parsons Brinckerhoff Monogr. No. 7, 1993. [16] O’Rourke, T.D. and Shiba, Y., Seismic Performance and Design of Tunnels, Annual Report, NCEER Highway Project, sponsored by U.S. Department of Transportation and Federal Highway Administration, 1997. [17] Nakamura, S., Yoshida, N., and Iwatate, Y., Damage to Daikai Subway Station during the 1995 Hyogoken-Nambu Earthquake and Its Investigation, Japan Society of Civil Engineers, Committee of Earthquake Engineering, 1996. [18] St. John, C.M. and Zahrah, T.F., A seismic design of underground structures, Tunneling and Underground Space Technology, 2(2), 1987. [19] Idriss, I.M. and Sun, J.I., SHAKE91: A Computer Program for Conducting Equivalent Linear Seismic Response Analyses of Horizontally Layered Soil Deposits, Center for Geotechnical Modeling, Department of Civil and Environmental Engineering, University of California at Davis, 1992.

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[20] ASCE Committee on Gas and Liquid Fuel Lifelines, Guidelines for the Seismic Design of Oil and Gas Pipeline Systems, Technical Council on Lifeline Earthquake Engineering, ASCE, New York, 1984. [21] Penzien, J., personal communication.

Further Reading [1] ASCE, 1993. Steel penstocks, in Manual on Engineering Practice, No. 79, American Society of Civil Engineers, New York. [2] Hoek, E. and Brown, E.T., 1980. Underground Excavations in Rock, Institution of Mining and Metallurgy, London, 527 pp. [3] Peck, R.B., 1969. Deep excavations and tunneling in soft ground: state-of-the-art report, paper presented at the 7th Int. Conf. on Soil Mech. and Fnd. Engr., Mexico City, pp. 225–290.

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