Computer Calculations Speeds Tunnel Lining Design

Computer Calculations Speeds Tunnel Lining Design
CE 6/94

Civil Engineering, Volume 6/94

ABSTRACT

A computer program handles the computations and simplifies a method that sets forth in a single diagram the vast amounts of information involved in concrete tunnel-lining design. The method was used to design tunnel linings for the Dallas Area Rapid Transit system.

Deep under the heart of Texas, engineers have designed linings for a twin-bore commuter tunnel and station by using the principle of capacity limit curves (CLCS). The computations provide vast amounts of information about lining thrust and moments that can be set forth in a single curve. Simplifying matters for tunnel designers even more, the CLc design process has been converted into a computer program.
Developed by the Dr. G. Sauer Corp., Herndon, Va., in 1983 for high-speed rail projects to meet the German building code DIN 1045, the process is also applicable to American Concrete Institute's ACI 318.1 and other relevant codes. It displays, graphically and numerically, the bearing capacity of a given cross section under given loading conditions. This allows optimization of structurally required reinforcement or verification of selected reinforcement.
The cLc design process has been used for U.S. tunnel projects such as Lehigh Tunnel No. 2 in northeast Pennsylvania; the Washington, D.C. Metro; and more recently the Dallas Area Rapid Transit (DART). The underground portion of DART'S Light Rail Starter System includes two single-track tunnels (each about 17,000 ft long and 21 ft 6 in. in diameter), several ventilation structures and an underground station known as CityPlace. Although the station is located entirely in unweathered rock and a majority of the tunnels in unweathered Austin chalk, there are variations from soft ground to mixed conditions.
During design, Sauer served as subconsultant to the consulting team headed by Huitt-Zollars, Dallas, that included Sverdrup Corp., St. Louis, and HOK Architects, Kansas City, Mo. The team prepared two tunnel-design alternatives that DART offered to bidders: a conventional circular section suitable for tunnel-boring machines, and a design using the new Austrian tunneling method (NATM). The conventional alternative was similar to the other, as both use shotcrete for initial tunnel support followed by a cast-in-place concrete lining in soft ground. To adjust to ground conditions, four basic ground-support categories with varying initial-support measures were defined in both alternatives.

Calculation Tunnel Forces
In recent years, tunnel design has required more computational power to simulate the stress redistributions caused by excavation and support processes in the ground, and to design the linings in accordance with those redistributions. The computations must deal with various factors: geology and hydrological conditions, overburden depth, size and shape of the tunnel, method of excavation, and method of support. Varying lining thicknesses and loading conditions require multiple computation cross sections. Finite element and finite difference methods, spring-beam models, and similar techniques produce a vast number of bending-moment and thrust combinations to be considered in the design.
The automated CLC design method grew out of extensive experience with the NATM, which uses a cast-in-place unreinforced inner concrete lining and a rather thin flexible shotcrete lining as initial support. Researchers developed a new German code for plain structural concrete that was incorporated into the building code DIN 1045 in 1984. In contrast to ACI 318.1 (for structural plain concrete), which uses factored loads in section 9.2 but limits the stresses to "permissible stress," Germany's code is based on the ultimate-strength design method for both reinforced and plain concrete, similar to AcI 318.1.
DIN 1045 allows for limited cracking of the unreinforced concrete section within stability and safety requirements. The result is a thinner, more economical lining design. The cLc concept can be applied to any building concrete code, but in doing so designers must remember that most codes are written for aboveground structures, and they must consider the assumptions made in each code and its intended use. Design codes for aboveground structures typically lack the contributing support function of the ground and the effect of the excavation method, which are both important to lining capacity, and therefore lining cost.
The principle of CLCS is to plot computed-thrust (N) and bending-moment (M) combinations vs. all possible combinations of maximum allowable section forces.

THE DART TUNNEL NEAR CITYPLACE STATION,
 WHICH IS BEING CONSTRUCTED IN COOPERATION WITH OWNERS OF A NEW OFFICE TOWER.
PHOTO COURTESY HDR ENGINEERING, OMAHA, NEB.

The resulting graph shows N on the x-axis and M on the y-axis. Similarly, all possible ultimate section forces, derived from the state of strain at ultimate strength and divided by the safety factors (SF), are shown on the same graph.
Section-force combinations outside the curve cannot be endured by the given cross section with a satisfactory SF. DIN 1045 distinguishes safety factors to reflect failure of the cross section with advance warning (SF of 1.75) or without (SF of 2.1). Therefore, SFS are given as a function of the state of strain. The SF for plain concrete vs. reinforced concrete is constant. The concrete crete section in tension cannot be incorporated in the design, and the crack may reach to the neutral axis.
The CLC computer program allows verification of the load-bearing capacity of a given cross section along an entire tunnel section in a single diagram. Evaluating the remaining bearing reserves becomes especially important during excavation when geologic conditions differ from the designload assumptions. By plotting the section forces derived from actual loads onto the existing CLc diagram, an engineer can check sufficiency of the cross section without further calculations.

Optimizing Rebar
In concrete designs for regular building construction, reinforcement is adjusted segmentally along the length of a structural member according to computed section forces. It is common practice in tunnel designs, however, to base the reinforcement on the most unfavorable loading condition and to use constant reinforcement along the perimeter and constant lengths of equal lining thickness. Constructability and practicability issues also influence design.
These restrictions are also important in the cLc optimization process, where the essential parameters are concrete and metal strengths, thickness of the concrete lining, and amount of reinforcement.
In a simplified example of such optimization, lining thickness and concrete-design strength are assumed to be constant. The first task shows whether the given bending-moment and thrust combinations are beyond the capacity of plain concrete. If necessary, the next step is to calculate the one- or two-sided (double-layered) reinforcement. At least one pair of the given.

UPDATE ON DART

When bids were opened for the first underground segment of the Dallas Area Rapid Transit (DART) Light Rail Starter System, S.A. Healy Co., McCook, Ill., won the contract for $86.8 million, startlingly below the engineer's estimate of $122.4 million.
The contract, known as NC-113 covers 3.2 mi of the 20 mi system, extending north of the central business district. It includes twin bore tunnels about 17,000 ft long and a transit station 120 ft below ground. Healy engineers banked on favorable tunnel-boring-machine (TBM) conditions-the good-quality, homogeneous Austin chalk is competent with unconfined compressive strengths between 1,500 and 2,000 psi. Healy's recently completed sewer tunnel in similar chalk at Austin had remained self-supporting after little or no initial support; similar bores in Dallas showed the same competence, with little ground-water seepage, despite being below the water table.
The Light Rail Starter System, currently on schedule to begin passenger service in mid-1996, is the latest of many efforts to add rail service to the mix of buses and vans that cover the city of Dallas and 13 surrounding municipalities (CE August 1993). Various plans dating back to 1983 called for light rail on the median of the North Central Expressway, then rails carried in boxes at the sides of a depressed expressway, and finally the underground station and tunnels independent of the expressway route.
DART's design team had only a few months between the June 1991 tunnel decision and the December 1991 bid date, but was able to use data compiled for previous schemes, particularly the ventilation structures in the box plan and a drainage tunnel that was being bored nearby. The team, headed by Huitt-Zollars, Dallas, includes subconsultants Sverdrup Corp., St. Louis; HOK Architects, Kansas City, Mo.; the Dr. G. Sauer Corp., Herndon, Va.; and HDR Engineering, Omaha, Neb.
The CityPlace station, one of 21 on the 20 mi of light rail, is being constructed in cooperation with owners of a new office tower, which shares the station's name. The owners expect to finish a second tower before the end of the century that will also be tied into the station. Initial support of the station bores is by dowels or nontensioned rock bolts and a 4 in. layer of fiber-reinforced shotcrete under the membrane. Final support is a 10-12 in. concrete liner.
At the south end, the last 240 ft of mined tunnels merge into 270 ft of cut-and-cover construction and the 1,500 ft of contract NC1A, also cut-and-cover. These sections, largely through silt and sandy soils, are waterproofed and lined with 12 in. cast-in-place concrete. At the south portal, the line rises to street level, where the light-rail cars will run along the central business district. At the north portal, the cars will rise to street level near Mockingbird Lane.
For the tunnels, Healy brought a 22 ft diameter Robbins from the hard-rock Rogers Pass railway-tunnel site in Canada and renovated it, changing the cutter head to 21 ft 6 in. The northbound tunnel took 66 mining days, from September 1993 to January 1994. Healy removed 220,650 cu yd of rock from the total TBM length of 16,410 ft. Work on the southbound tunnel, which is the same length, began in October 1992, but was not completed until August 1993 because of delays due to water problems and pockets of gas.
In the running tunnels, about 95% of the surface is finished with 2 in. or 4 in. fiber-reinforced shotcrete. The cast-in-place concrete liner, varying from 9 to 12 in., was specified for about 2,000 ft of the total project. Membrane waterproofing was required in the station and certain areas of the tunnels-mostly at the south portal.
The entire Light Rail Starter System, budgeted at $841 million, is expected to be in full service by the end of 1996. Eventually, a commuter rail line between Dallas and Irving, Tex. will be coordinated with service in Fort Worth, Tex. and the Dallas-Fort Worth International Airport via existing rail lines. RR section forces should lie on the cLc. This state is found by an iterative procedure that varies the rebar area until the difference between the given and allowable section forces becomes zero for any component.
For double-layered reinforcement, the minimum of the reinforcement sum is introduced as a criterion for the optimization process in which the symmetrical reinforcement leads to an upper limit. The tracing process is continued from this symmetrical optimum to reach reinforcement amounts of the unsymmetrically reinforced section. This is done by varying the difference in reinforcing-steel areas until the sum becomes a minimum.

Calculating for DART
Sauer performed the structural-design computations for DART's running tunnels and underground station known as section Nc-1B. For the two tunnel alternatives alone, 10 computation cross sections were established to account for varying ground support and site specifics such as adjacent underground storm sewers, narrow pillar configurations between the tubes, and piles supporting the roadway bridges above.
Sauer engineers worked with the finite element program ABAQUS 4.8, which features material-behavior models required in soil and rock excavations using extended Mohr-Coulomb and Drucker-Prager failure criteria. Eight-noded plane strain elements represent the ground; three-noded curved beam elements represent the concrete and shotcrete linings. A fine-mesh grading resulted in 18 beam elements for the shotcrete and another 18 beam elements for the concrete lining. The program output of two integration points for each element gave 36 thrust-moment combinations each for shotcrete and concrete.
In the NATM soft-ground tunnel design,the shotcrete is reinforced with lattice girders set at each excavation round and spaced about 39 in. (1 m) apart, as well as with two welded-wire-fabric layers facing the inside and the rock side. Therefore, the design task consists of verifying the capacity of the reinforced cross section. Fig. 1 shows that the 7.9 in. (200 mm) reinforced concrete design section bears capacity reserves. The final lining computations conservatively assume that ground water will deteriorate the shotcrete, so all ground loads are transferred onto the final concrete lining. The cl.c curve for the unreinforced 9.8 in. (250 mm) thick inner cast in-place section (Fig. 2) also bears capacity reserves. 

Erich Bauer is with the University of Graz, in Graz, Austria. Vojtech Gall and Gerhard Sauer, M.ASCE, are with the Dr. G. Sauer Corp., Herndon, Va.