The study, published in Case Studies in Construction Materials, was led by Yi Ding, with co-authors Xinru Wang, Man Xu, and Huiwen Tian. Their work addresses a deceptively simple question: how do you calculate the shear strength of a squat wall when part of it is made not of ordinary concrete, but of ultra-high performance concrete, or UHPC — a fiber-reinforced cementitious material that can reach compressive strengths above 130 megapascals, roughly double or triple that of conventional structural concrete? The answer, they found, requires rewriting one of the key equations that engineers use to size these walls, because the new material fundamentally changes how forces flow through the structure.

UHPC is not just stronger concrete in a loose sense. It is engineered through optimized particle packing — arranging fine sand, cement, and admixtures so that almost every void is filled — and through the addition of steel fibers that bridge cracks and hold the material together after it fractures. In the team’s earlier laboratory tests, shear walls in which UHPC was cast only in the boundary elements, the heavily loaded vertical zones at the edges of the wall, showed remarkable improvements. Compared with identical walls made entirely of normal-strength concrete, the UHPC-reinforced versions carried 6.79 to 20.64 percent higher peak loads, showed 2.54 to 24.11 percent greater ductility, and dissipated 44.88 to 57.65 percent more cumulative energy under simulated earthquake loading. Just as striking, the steel fibers restrained crack growth so effectively that the walls avoided the catastrophic spalling, bar buckling, and longitudinal bar fracture that rendered the conventional walls essentially unrepairable after testing.

But predicting how strong such a hybrid wall should be turned out to be a genuine theoretical challenge. The researchers first benchmarked three established calculation methods against their experimental data from thirteen full-scale wall specimens, which included rectangular and barbell-shaped cross-sections, UHPC distributed at various heights and widths, and axial load ratios of 0.25 and 0.45. The Chinese standard JGJ 3-2010 overestimated strength by an average factor of 1.51, the American standard ACI 318-19 by 1.56, and even the best-performing option — the softened strut-and-tie model developed by Hwang and colleagues — overshot by 1.38 on average. None of these methods was designed with a material as strong and as crack-resistant as UHPC in mind, and none accounted for how locally concentrating that material in the boundary elements redistributes the internal load paths.

To understand the failure mechanism directly, the team built highly refined three-dimensional finite element models in the LS-DYNA simulation environment. Concrete and UHPC were represented with the Karagozian and Case material model, a sophisticated constitutive framework that captures strength surfaces, damage evolution, and failure, with parameters specially calibrated for UHPC’s much higher strength. Steel reinforcement was modeled explicitly with beam elements, and the interface between UHPC and normal concrete was treated with shared nodes, reflecting the experimental observation that the two materials remained fully bonded without separation. After validating the modeling approach against independent low-rise wall tests by other researchers — achieving peak load prediction errors within 5 percent — the team turned the simulation loose on squat walls with an aspect ratio of 1, the regime where shear dominates.

The simulations revealed the failure sequence in vivid detail. At first cracking, tiny macroscopic fractures appeared precisely at the horizontal interface where the UHPC boundary element meets the normal-strength concrete web, marking the point where tensile strain first exceeded the material’s limit. As lateral drift increased, the outermost longitudinal bars in the boundary elements reached their yield stress — around 509 megapascals on the tension side and 501 on the compression side — while diagonal cracks spread through the web. By peak load, these diagonal cracks had carved the web into a lattice of small zones, and the concrete between them consolidated into a set of diagonal compression struts. The wall ultimately failed by crushing along its principal diagonal strut, exactly the mechanism that the strut-and-tie theory describes: steel bars acting as tension ties, concrete acting as compression struts, and the two working together in a self-equilibrating truss embedded within the wall.

That confirmation opened the door to the model’s central innovation. In the classical strut-and-tie framework, the depth of the diagonal compression strut is tied to the height of the compression zone at the base of the wall, and existing formulas for that height were derived from elastic theory for ordinary reinforced concrete columns. The researchers found that casting UHPC into the boundary elements shifts the compression zone significantly — but because squat walls are disturbed regions where the familiar assumption that plane sections remain plane breaks down, they could not simply adjust the flexural theory. Instead, they ran sixty parametric simulations, sweeping aspect ratios from 0.5 to 1.5, concrete strengths from C30 to C80, UHPC strengths from 120 to 180 megapascals, UHPC widths from 10 to 40 percent of the wall width, UHPC heights from 30 to 100 percent of the wall height, and axial load ratios from 0.05 to 0.45.

The parametric results distilled into a remarkably clean relationship. The height of the compression zone increases linearly with the normalized axial load — heavier vertical compression pushes the crushing zone deeper into the wall — but decreases with the width of the UHPC region following a power law, because the stronger material concentrates compression into a narrower band. The team encoded both effects in a single equation, bounded by sensible limits, and embedded it in a five-step design procedure that retains the familiar machinery of the softened strut-and-tie model: determine the geometry, select the dominant tie mechanism based on the strut’s inclination angle, compute the strut-and-tie coefficient that captures how distributed reinforcement enhances capacity, evaluate the softened concrete strength along the strut, and finally project the diagonal crushing capacity into the horizontal shear strength. Notably, the team deliberately kept the concrete softening coefficient conservative rather than increasing it for UHPC, even though studies of full-section UHPC walls suggest the material’s tensile toughness could justify a higher value — a choice made to avoid overestimating strength in a safety-critical application.

The validation was the most convincing part. Across sixty-eight walls — fifty-nine from the new simulations and nine from independent experimental programs by three other research groups — the proposed model achieved an average predicted-to-actual strength ratio of 1.03 with a standard deviation of 0.20. The existing methods fared considerably worse: JGJ 3-2010 averaged 1.19 with a standard deviation of 0.27, ACI 318-19 averaged 1.11 with 0.31, and the original Hwang model averaged 1.14 with 0.22. In other words, the new model is both nearly unbiased and the most consistent, which is precisely the combination a design engineer wants. The model did show characteristic blind spots: it underestimated precast walls in which UHPC also filled lap-splice zones and vertical columns, because those extra contributions lie outside its scope, and it overestimated two specimens that failed not by strut crushing but by fracture of longitudinal bars at a weak post-cast interface — a different failure mode entirely.

The authors are candid about these limits, noting that the model applies to cast-in-place walls where UHPC sits primarily in the boundary elements and works in reliable composite action with the surrounding normal concrete, and that further validation is needed for other UHPC configurations and interface conditions. Even so, the significance is hard to overstate. Squat shear walls are among the least forgiving elements in seismic design, and the ability to exploit UHPC’s extraordinary strength and crack-bridging fibers in exactly the zones where they matter most — without paying the cost of casting an entire wall in the premium material — could reshape how engineers protect tall buildings in earthquake-prone regions. A formula that turns laboratory performance into trustworthy numbers is the bridge between a promising material and a safer built environment, and this study has just laid a carefully calibrated plank across it.

Subject of Research: Shear strength prediction of squat UHPC-reinforced concrete shear walls under seismic loading

Article Title: A strut-and-tie model for predicting shear strength of squat shear walls reinforced with UHPC under seismic loading

Article References: Ding, Y., Wang, X., Xu, M., & Tian, H. (2026). A strut-and-tie model for predicting shear strength of squat shear walls reinforced with UHPC under seismic loading. Case Studies in Construction Materials, 25, Article e06575. https://doi.org/10.1016/j.cscm.2026.e06575

Image Credits: AI Generated

DOI: 10.1016/j.cscm.2026.e06575

Keywords: UHPC, shear walls, strut-and-tie model, seismic design, finite element analysis, squat walls, concrete structures, earthquake engineering, boundary elements, shear strength, structural engineering, LS-DYNA