Good morning. This is Back of the Envelope, where I share bite-sized SE stuff I learned recently.

Today, I am going to talk about an interesting study I came across regarding the Fukae bridge collapse during the Kobe 1995 earthquake.

The study was interesting not because of the reason the bridge collapsed, but because of the “counterintuitive” concept the researchers have discovered that could’ve prevented the collapse.

Alright, deep breath. Back to the Fukae bridge study.

(Estimated read time = 3 minutes and 6 seconds)

Kobe 1995

The Great Hanshin earthquake (also known as the Kobe earthquake) happened in Japan on January 17, 1995.

It measured 6.9 on the moment magnitude scale and lasted for about 20 seconds.

Lots of damages – one of which was the collapse of an elevated expresway, as shown in the picture above.

The Collapse

Since then, many studies have been done to determine the reason for the collapse. Mainly it was because:

1. The structure was designed in the 70’s. The earthquake accelerations turned out to be much higher than the designed level.

2. Most failures occurred 2.5 m (8.2 ft) above the pile cap. This was the location where the third row of longitudinal reinforcement was terminated. The result was brittle shear failure rather than flexure.

(source: “Fukae bridge collapse (Kobe 1995) revisited: New insights”)

“Fukae bridge collapse (Kobe 1995) revisited: New insights”

The 2020 study done by Sakellariadis, Anastasopoulos, and Gazetas, re-examined the collapse by incorporating nonlinear soil-foundation interaction using sophisticated finite-element and nonlinear methodology.

What they found was that the original 17-pile foundation group plus the pile cap was so stiff that the energy dissipation was forced to occur only on the structure itself.

(source: “Fukae bridge collapse (Kobe 1995) revisited: New insights”)

This is pretty consistent with most of our current design approaches (i.e., overdesigning the foundation to prevent settlement and forcing the nonlinear behavior to occur in the structure’s weak spots).

The researchers then thought, “Hey what happens if we go to the opposite end of the spectrum and under design the foundation?”

So they modeled a structure supported on shallow footing (not embedded in soil). And as expected, there was lots of rocking and settlement but only little damage to the structure.

(source: “Fukae bridge collapse (Kobe 1995) revisited: New insights”)

So they thought, “Ohh, let’s check out some intermediate alternatives between the two extremes!”

And that’s what they did. Additional 4 models were analyzed:

• Capped 9-Pile group (Reduced capacity compared to the original)

• Unconnected piled raft (This is new to me but essentially, a thin layer of soil is introduced below the pile cap to allow more “sliding,” forcing plastic hinging at the piles)

• Embedded footing (Same as shallow footing but embedded into soil)

• Shallow footing with confining ring (Also new to me but basically an unconnected “ring” around the footing to restrict shearing but promote rocking)

The result:

(source: “Fukae bridge collapse (Kobe 1995) revisited: New insights”)

• delta_str = max drift due to structural damage

• delta_theta = drift due to foundation rotation

• theta_res = residual value of foundation rotation

• w = foundation settlement

Summary of the structural damage at 8.5 m (26.2 ft):

(source: “Fukae bridge collapse (Kobe 1995) revisited: New insights”)

• delta_str = max drift due to structural damage

• delta_r = structural drift ratio

What does this all mean?

Essentially, foundation design is a tradeoff between settlement and structural damage.

• Over-design the foundation = significant structural damage but little settlement.

• Under-design the foundation = repairable structural damage but significant settlement.

As the author puts it:

In other words, for a structure that can tolerate settlement, not over-designing the foundation could potentially improve its seismic performance significantly.

Something to think about.

And that is all – thanks for reading 😊

Andy Lin
Back of the Envelope/Structural Engineer HQ