| Those who have ridden in trains passing through tunnels at high speeds may have noticed a popping in their ears similar to what happens when driving down a mountain road or being on a high-speed elevator. These effects are the result of air pressure transients, which are caused by the action of the train forcing air through the tunnel at high pressure and velocity.
These pressure effects are of particular interest to designers of underground rail systems because, if not controlled, they can result in passenger discomfort, damage wayside facilities and limit train operating speeds. When relatively high train speeds are desirable, some level of passenger awareness of air pressure changes and even some discomfort are unavoidable, so the designers’ objective is to find a level of pressure change that will not deter ridership, yet will allow trains to travel through tunnels at reasonable speeds.
A Primer on Air Pressure Transients
As a train enters a tunnel, a large volume of essentially motionless air is rapidly displaced. The piston-like action of the train creates regions of compression and rarefaction along the train. The train’s nose in particular is subject to high initial air pressures. As the train moves along, air pressure in the various regions changes continuously, often quite rapidly. This rate of pressure change is of greatest concern. The most severe cases occur at critical events such as nose and tail passage of entry portal, vent and blast structure passage and sometimes at exit portal passage. Highest interior pressures are felt just behind the nose of the train and occasionally just ahead of the tail. Highest exterior pressures are felt just to the side of the nose of the train. Analysis of pressure transients tends to concentrate on these regions.
The primary determinates of high pressure changes are train speed and the blockage ratio, which is the ratio of the train cross sectional area relative to tunnel cross sectional area, with faster speeds and higher blockage ratios having greater impact. Two obvious solutions are to increase tunnel size or reduce speed through tunnels. Both options would reduce pressure transients, but neither is practical. Increasing tunnel size is prohibitively expensive, and reducing speed adversely affects schedule and profitability. An effective mitigation strategy is to provide blast relief shafts. These vertical shafts leading from the tunnel to the atmosphere above work by damping pressure waves as they travel down the tunnel.
Many tunnels have ventilation shafts for smoke control in the event of fire. Because they are similar in structure to blast relief shafts, they can also serve to relieve pressure effects. Careful analysis is required to locate the shafts in an arrangement that maximizes their effectiveness for both purposes. In many cases, careful location of vent shafts can even eliminate the need for further pressure transient mitigation.
PB Automated Analysis Procedures
Quantitative analysis of air pressure transients is needed to evaluate both their impacts and possible mitigation strategies. The analysis methodology we used was taken from the Subway Environmental Design Handbook (SEDH)1, which uses incompressible, one-dimensional flow theory and traveling wave theory to approximate pressure wave effects and establishes maximum acceptable pressure levels for passengers and wayside facilities.
Unfortunately the methodology is very cumbersome and can require hundreds of separate, often complex, calculations to analyze even simple rail systems. This complexity has deterred most who have seen it from considering the SEDH methodology to be a practical tool.
Figure 1: Comparision of results of Subway Environmental Design Handbook and PB's automated Mathcad System |
We undertook the task of automating the SEDH methodology for California’s Bay Area Rapid Transit (BART) Airport Extension Project in 1996. We considered several analysis programs, including spreadsheet. It was clear, however, that a spread-sheet type program would not be ideal because of the complexity of the calculations and the difficulties involved in following the flow of operations and checking for errors. Ultimately, we selected Mathcad for many reasons:
• All equations are presented in standard math format.
• Reviewers do not have to be proficient in Mathcad to understand the flow of operations.
• Calculations are easy to read and errors are easy to locate.
We verified the program’s accuracy by checking it against published examples in SEDH. The results showed near perfect correlation with given pressure levels, as shown in Figure 1. Results have also been compared to actual pressure measurements taken on trains passing through BART tunnels with very good results. Over the years, the Mathcad program has been continuously refined and improve d. The current product is more flexible, easier to follow, and more user frie ndly.
Case Study: BART’s Warm Springs Extension
We recently had the opportunity to apply our program’s capability in pressure transient analysis on yet another BART project, the Warm Springs Extension. This project includes a 1320-m (4,600-foot) -long section of rail under Lake Elizabeth in the south bay area toward San Jose. The structure will comprise two tunnel sections, one for each direction.
Figure 2: Maximum speed allowable verses ventiliation shaft distance from portals |
Because of the geography of the area and the distance between stations, BART design criteria called for relatively high-speed service. Normal operating speed was anticipated to be 112 kph (70 mph), although some trains would travel 128 kph (80 mph) on occasion to make up schedule delays. We were to determine the most efficient way of accommodating desired speed without adversely affecting passenger comfort or train operations. From experience, we recognized that the geometry of the trains and the size of the tunnel shafts made these speeds impossible without a mitigation strategy.
Our evaluation of unmitigated pressure effects as a base showed that pressure transients would be more than twice allowable levels. Numerous mitigation strategies were evaluated for their effectiveness. Certainly blast or ventilation shafts would be required, and they would need to be carefully located.
Blast shafts were not wanted because of cost. The tunnel smoke control strategy called for at least one and possibly two ventilation shafts. It was BART’s practice and preference to have two. Because most of the tunnel would be under a regional park, there were only a few places where the shafts could be located.
Two alternatives were developed for initial analysis.
• A one-vent alternative with the shaft located 565 m (1,850 feet) from the south portals.
• A two-vent alternative with one shaft 440 m (1450 feet) from the north portals and the other 215 m (700 feet) from the south portals.
Evaluation of both alternatives showed that one-shaft would result in unacceptable pressure levels on passengers. The two-shaft strategy presented problems, but they were manageable. We felt that the system could be made to work without adding blast shafts.
Our first task was to determine the optimum locations for the ventilation shafts. It was known that worst case pressure transients tended to be associated with nose and tail passage at entry portals and passage of vent shafts, with the location of the first ventilation shaft being most critical. Several iterations were performed with shafts at various distances from portals. A graph showing maximum speed allowable verses vent shaft distance from portals (Figure 2). The graph showed that the ideal location would be 200 m (650 feet) from entry portals. This was only 15 m (50 feet) from the preferred location in the northbound direction.
Our data showed that northbound trains could travel at 112 kph (70 mph) without exceeding pressure criteria. This was acceptable to our client. Unfortunately, the highest allowable speed in the southbound direction was determined to be only 94 kph (59 mph). Our analysis showed that a vent shaft located such a great distance from a portal provided benefit that was only nominally better than having no shaft at all.
As it happened, a station was to be located just over 610 m (2,000 feet) from the north portal. Civil design rules limited train speed to 80 kph (50 mph) until the last car has left the station. Still, at normal rates of acceleration, train speed would reach and exceed the maximum allowable a few hundred feet before the portal. We determined that a delay in acceleration of just a few seconds would keep speed to acceptable levels in the critical sections of the tunnel. Speed could then continue to increase to normal operating level without any adverse effect. This strategy will be incorporated into train control rules.
BART management had also expressed interest in running trains at 128 kpg (80 mph) on occasion to make up schedule delays. Doing so would cause unacceptable pressure effects under normal conditions, exceeding criteria by about 36 percent. This level of pressure change was well within safety limits, although it would likely cause minor temporary discomfort for some passengers. Research has shown, however, that when pressure effects are infrequent, they are unlikely to deter ridership or adversely affect health.
In the end, we determined that BART’s comfort and operating criteria could be met with only minimal effect on schedule and at no additional constructed cost. By understanding the mechanics of pressure transients and with the ability to predict them accurately, effective mitigation strategies can be incorporated into the process. |
