Multiobjective Comprehensive Optimization of Fibre-Reinforced Concrete Mix Proportions Based on Entropy Weight Improved MOPSO in Multiscale Context

Concrete is the most widely used building material on Earth, a mixture of cement, water, sand, and stone that forms the skeleton of our modern world. Yet, the industry faces a growing dilemma: how to make this material stronger and more durable without consuming more of the planet's finite resources. One solution involves recycling old concrete, crushing it down to create new aggregate, but this recycled material is often weaker and more porous than fresh stone, leading to structures that may crack or degrade faster. To fix this, engineers have long turned to adding fibers—tiny strands of steel or plastic—to bridge cracks and hold the material together. However, simply adding more fiber is not a simple fix; different types of fibers work at different scales, from the microscopic level of the cement paste to the macroscopic level of the whole structure, and finding the perfect balance requires navigating a complex web of interactions where too much of one thing can weaken the whole.

In a recent study, researchers set out to solve this balancing act for a specific type of advanced concrete known as multiscale fiber-reinforced recycled aggregate concrete. This material combines recycled stone with three distinct types of fibers: stiff steel strands, flexible plastic fibers, and tiny, needle-like mineral whiskers. The goal was not just to test these ingredients, but to find the exact recipe that would make the concrete as strong as possible in compression, as tough as possible when pulled apart, and as resistant as possible to saltwater corrosion, all at the same time. The team, led by scientists from Hohai University and other institutions in China, realized that traditional trial-and-error methods were too slow and that human intuition alone could not calculate the best mix among the thousands of possible combinations. Instead, they treated the problem like a complex navigation task, using a sophisticated computer algorithm to search for the perfect path through the data.

The researchers began by creating a series of concrete batches, each with a slightly different amount of the three fibers. They used a statistical design method to ensure they covered the full range of possibilities without wasting time on unnecessary tests. After curing these samples for twenty-eight days, they put them through rigorous physical tests. They squeezed cubes of the concrete until they crushed to measure compressive strength, pulled cylinders apart to measure tensile strength, and subjected them to an electric current to see how quickly chloride ions could penetrate the material, a key indicator of how well the concrete would resist corrosion in harsh environments. The results showed that the amount of each fiber mattered, but so did how the fibers interacted with one another. For instance, adding more steel fibers generally made the concrete stronger, but only up to a point; if the amount of plastic fibers was too high, the steel fibers would tangle and lose their effectiveness. Similarly, the tiny mineral whiskers helped fill gaps in the material, but adding too many of them created new weak spots.

To make sense of these competing results, the team developed a new way to let the data speak for itself. In many engineering decisions, experts assign importance to different goals based on their own judgment, which can introduce bias. This study avoided that by using a mathematical concept called information entropy to weigh the importance of strength versus durability objectively. They then fed these weights into an advanced search algorithm, a digital evolution of the way a flock of birds might find food, where a group of virtual "particles" explores the solution space to find the best answer. This improved algorithm, which the researchers call EWMOPSO, was designed to find a single mix that offered the best overall performance rather than just the best performance in one specific category.

The search yielded a clear winner. The algorithm determined that the optimal mix for this multiscale concrete contained 1.06 percent steel fibers, 0.23 percent plastic fibers, and 1.39 percent mineral whiskers by volume. At this precise combination, the concrete achieved a compressive strength of 44.28 megapascals, a split tensile strength of 5.38 megapascals, and a chloride migration coefficient of 6.52 times 10 to the negative twelfth power square meters per second. These numbers represent a superior balance, outperforming the best results found in the initial set of physical experiments. The study demonstrated that by using this objective, computer-driven approach, engineers can move beyond guesswork to identify mix designs that are not only theoretically sound but also practically viable for real-world construction. The findings suggest that with the right combination of recycled materials and multiscale reinforcement, it is possible to create concrete that is both environmentally friendly and structurally superior, offering a reliable path forward for sustainable building practices.