Project Update by Keith Abey, PE, SE, Geoffrey Bee, PE, and Kush Chohan, PE, GE
The BART Berkeley Hills Tunnel is twin-bored, horseshoe-shaped, and has a cast-in-place concrete liner. It connects Oakland and San Francisco to Contra Costa County on BART’s most heavily traveled regional rapid transit rail line. It also crosses the active Hayward Fault, which produces 4 millimeters of lateral creep each year, or 8 inches (200 mm) of tunnel offset over the last 50 years. Tracks have been realigned to account for this, but as creep continues, tunnel clearances will be compromised.
McMillen Jacobs was contracted through an on-call contract under Parsons Transportation Group to explore options for improving tunnel clearances to increase the tunnel’s usable life while maintaining train operations during construction. The preferred alternative involved partial removal of the concrete liner on the tunnel side adjacent to the walkway and reinforcing with steel liner plate, to be welded to the original steel sets to create a composite system.
To verify feasibility, we used Abaqus, a general purpose nonlinear finite element modeling tool, to perform detailed 3D analysis of this clearance modification. Traditionally, structural analysis approaches combine the stiffness of the various structural members prior to analysis into an isotropic “composite” material representative of the overall system, but not of any individual structural component. Abaqus allowed us to independently account for the stiffness of the concrete liner, steel sets, rebar, and new liner plate—stiffness being dependent on the stress-strain relationship of the structural components’ materials, geometric shapes, and configurations. The global behavior of the structural system was then analyzed through the individual structural components’ constrained interactions with one another.
A time-step analysis of the tunnel captured stresses and movements during the construction sequence, including the temporary notched condition prior to placement of the new steel liner plate. This plate was incorporated into the model where it could interact with the existing steel sets, concrete liner, and reinforcing steel. The model provided insight into how forces flowed around areas of discontinuity and allowed identification and mitigation of high-stress concentrations in the modified tunnel (model geometry created in SolidWorks, then imported into Abacus for meshing).
Our Abaqus inelastic constitutive model for concrete identified concrete cracking expected during earthquake shaking for both the as-built tunnel liner condition (above right) and clearance improvement case (left two images). The racking analysis was run in both directions because of the clearance alternative’s asymmetry.
The model captured localized steel and concrete stress concentrations in each structural component with high precision. In final design, stresses from this model will be used to design the thickness of bearing plates needed to adequately distribute loads and weld sizes for stiffener plate connections.
Traditional structural modeling doesn’t account for the differing stress-strain relationships of each material, stress levels within individual system components, and localized regions of the structural system that are not as stiff (e.g., between sets). The sophisticated Abaqus program can. As software and computer hardware improve, nonisotropic modeling of structural systems will become more common.
The level of detail we provided in this model gave BART a high degree of confidence that the tunnel clearance could be improved under live track work windows while maintaining structural safety.