An Open-Source OpenSeesPy Framework for Simplified Micro-Modeling and OMA-Based Model Updating of Masonry Infill Walls under Cyclic Loading

Imagine you are building a house of cards, but instead of flimsy paper, you are using heavy bricks and a steel skeleton. In the real world, most buildings aren't just empty steel frames; they are filled with brick walls that act as partitions. These walls are like the "meat" of the building, while the steel frame is just the "bones." When an earthquake shakes the ground, these brick walls and steel bones have to dance together. Sometimes they hold hands tightly, and sometimes they slip apart. If engineers get the steps wrong, the building might wobble too much or even collapse. To understand this dance, scientists use computer programs to simulate earthquakes. They want to know: How strong is the wall? How does it crack? And how does it vibrate when the ground shakes? The tricky part is that the wall behaves very differently when it's being gently poked versus when it's being slammed hard.

This paper is like a digital detective story where the authors build a virtual version of a brick wall inside a steel frame to see how it reacts to shaking. They used a free, open-source computer program called OpenSeesPy, which is like a giant digital LEGO set for engineers. Instead of buying expensive, locked-down software, they wrote their own code to simulate the wall. They tested two different ways of looking at the wall: first, they pushed it back and forth to see how much force it could take before breaking (like a strongman contest), and second, they listened to how it hummed when the air around it vibrated (like tapping a wine glass to hear its ring). The big surprise they found is that the wall's "stiffness"—how rigid it feels—changes completely depending on how hard you push it. When the wall is just humming softly, the bricks and the steel frame are barely touching, almost like they are strangers. But when the wall is being pushed hard, they lock together like best friends. This discovery is crucial because it means you can't use the "soft" humming sound to predict how the wall will handle a "hard" earthquake.

The Digital Brick Wall: A Two-Part Adventure

The authors, Şevket Ateş and Adamou Marou Seyni Samberou, decided to build a virtual replica of a real experiment they had seen in a lab. They wanted to make sure their computer model was so accurate that anyone else could download it, run it, and get the exact same results. They didn't just want to guess; they wanted to prove it.

Part 1: The Strongman Contest (Cyclic Loading)
First, they set up a simulation where they pushed the wall back and forth, mimicking the shaking of an earthquake. They used a "simplified micro-model," which is a fancy way of saying they treated the bricks as solid, unbreakable blocks and focused all the action on the "glue" (the mortar) between them. Imagine the bricks are like rigid ice cubes, and the mortar is like a sticky, stretchy tape. When the wall shakes, the ice cubes don't break; instead, the tape stretches, snaps, and rubs against itself.

They pushed the wall until it reached a peak force of about 96 kN (kilonewtons). Their computer model predicted 97.4 kN. That is incredibly close—only 1.5% off! The model also showed the wall cracking in the exact same pattern as the real-life test: the mortar joints opened up, the bricks slid past each other, and the wall started to separate from the steel frame at the corners. It was a perfect match. However, they hit a snag: the computer program got confused when the wall started to break apart too quickly (a "snap-back" instability). To fix this, they had to slow down the simulation, like playing a video in slow motion, to get the full picture of the wall's failure.

Part 2: The Humming Glass (Operational Modal Analysis)
Next, they switched gears. Instead of pushing the wall, they listened to it. They wanted to see how the wall vibrated when it was just sitting there, humming along with the tiny vibrations of the earth (called ambient vibration). They measured three specific "notes" or frequencies the wall made: 12.62 Hz, 25.02 Hz, and 38.36 Hz.

Here is where the mystery deepened. When they tried to use their "strong" wall model (the one that worked for the earthquake) to predict these soft humming sounds, the computer said the wall should be vibrating at over 130 Hz. That's way too high! It was like trying to tune a heavy cello to sound like a tiny violin. The model was too stiff.

To solve this, they played a game of "digital tuning." They adjusted the numbers in their computer code, specifically the stiffness of the "glue" between the wall and the frame, and the weight of the testing equipment attached to the wall. They used a mathematical method called "least squares" to find the perfect settings.

The Big Discovery: The Wall Has Two Personalities
After some digital tweaking, they found the magic numbers. The updated model matched the real humming sounds almost perfectly, with errors of only +2.4%, -5.8%, and +12.1%. But the real magic was in what those numbers told them.

They discovered that when the wall is just humming softly (at micro-tremor levels), the connection between the brick wall and the steel frame is essentially unlocked. The "glue" is so loose that the stiffness is about 100,000 times weaker (five orders of magnitude) than when the wall is being pushed hard during an earthquake.

Think of it like a door. When you gently push the door, it swings freely on its hinges because the latch isn't engaged. But when you slam the door, the latch clicks in, and the door becomes a solid, unmovable barrier. The authors found that the "soft" vibrations only see the door swinging freely, while the "hard" earthquake forces see the door slammed shut.

Why This Matters

This paper proves that you cannot use the "soft" humming of a building to predict how it will handle a "hard" earthquake. If engineers try to use the gentle vibration data to design a building for a major quake, they might think the building is much weaker than it actually is when the shaking gets intense.

The authors also solved a small puzzle about the size of the bricks. The original lab reports had conflicting measurements (some said the bricks were 100 mm thick, others said 130 mm). By testing both sizes in their computer model, they proved that the 185 mm thickness (which comes from the 130 mm brick laid flat) was the only one that matched the real-world humming sounds.

In the end, this study gives the engineering world a free, open-source tool that anyone can use to simulate brick walls. It shows that while the wall looks like one solid thing, it actually has two very different personalities depending on how hard you push it. And the best part? You don't need to buy expensive software to see it; you just need to download their code and run the simulation yourself.