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

The research team, led by Bowen Zhang, Zhi-Qi He, Jiatong Chen, and Wenjie Li, conducted eighteen local compression tests on UHPC specimens designed to represent prestressed anchorage zones. The specimens varied systematically across four key parameters: steel-fiber volume fractions of 0.5, 1.0, and 2.0 percent; bearing area ratios of 3, 5, and 7; three forms of indirect reinforcement, namely spiral reinforcement, reinforcing mesh, and none at all; and three anchorage plate configurations, including flat plates, embedded plates, and no plate. The main group of specimens was arranged in an L9 orthogonal experimental matrix, allowing the relative influence of the primary variables to be ranked without running a full factorial program, while targeted comparison groups isolated the effects of plate type and reinforcement ratio.

The material itself was a dense cementitious composite of ordinary Portland cement, silica fume, slag powder, fine quartz sand, water, superplasticizer, and straight copper-coated steel fibers 14 millimeters long and 0.20 millimeters in diameter, with an aspect ratio of 70. Measured axial compressive strengths ranged from 88.0 to 108.7 megapascals, with converted cube strengths between 122.2 and 151.0 megapascals. Direct-tension tests revealed mean tensile strengths of 3.89, 6.34, and 8.15 megapascals for the three fiber contents, a clear demonstration of how dramatically steel fibers transform the tensile character of an otherwise brittle matrix. All specimens were tested in a 500-tonne hydraulic compression machine under carefully controlled stepwise loading, with local plate indentation separated from overall specimen compression through a dual displacement measurement scheme.

Every specimen failed by splitting rather than compressive crushing, and the failure process unfolded in three recognizable phases: crack initiation, stable crack propagation, and rapid splitting collapse. Initial vertical hairline cracks appeared at loads ranging from roughly 30 to 90 percent of the ultimate capacity, most often in the upper or upper-middle regions of the specimens. Close-up examination of the fracture surfaces revealed that most steel fibers were pulled out of the matrix rather than ruptured, confirming that fiber bridging and pull-out resistance were the dominant mechanisms transferring tensile stress across cracks after the matrix had split. Specimens with lower fiber contents developed fewer but wider cracks, typically one or two dominant vertical splits, while higher fiber contents produced finer, more distributed cracking patterns.

Strain gauges on the indirect reinforcement told an equally revealing story about when different load-resisting mechanisms activate. At low load levels, reinforcement strains remained small, indicating that the UHPC matrix and its embedded fibers carried the transverse tensile demand on their own. Only as loads approached roughly 60 to 80 percent of ultimate capacity did reinforcement strains accelerate sharply, coinciding with visible cracking and lateral expansion. Specimens with 2.0 percent fiber volume kept reinforcement strains well below the monitoring reference even near failure, suggesting that abundant fibers reduce the confinement burden that transverse steel must carry. In other words, fibers and reinforcement work in sequence rather than in parallel: fibers manage microcracks and early post-cracking stress transfer, while spirals and meshes restrain macrocrack opening and lateral dilation later in the loading history.

Range analysis of the orthogonal test matrix produced a striking hierarchy of influence. The bearing area ratio, which controls the intensity of stress concentration and the geometry of load diffusion beneath the plate, was by far the dominant factor, with a range value of 65.8 megapascals in mean bearing stress. Fiber volume fraction ranked second at 49.0 megapascals, while the form of indirect reinforcement trailed at just 15.9 megapascals. The anchorage plate configuration mattered in nuanced ways: flat plates increased ultimate capacity by 15.4 percent in one matched comparison but simultaneously reduced initial stiffness and cracking load, whereas embedded plates consistently improved stiffness and cracking resistance, raising cracking loads by as much as 71.4 percent, without reliably increasing ultimate strength. Changing the reinforcement ratio between 1.5 and 3.0 percent produced no monotonic trend in either cracking or ultimate load, underscoring that its effect is conditional on the surrounding fiber and plate-transfer state.

To place these findings in context, the team compiled a database combining their eighteen tests with published UHPC and reactive powder concrete data, yielding 51 unreinforced and 34 reinforced records. When existing design provisions were evaluated against this database, their limitations became evident. AASHTO LRFD 2017 came closest on average, with a mean calculated-to-test ratio of 0.947 for unreinforced specimens, but the French UHPC standard NF P 18-710 tended to overestimate capacity with a mean ratio of 1.154, and the Chinese bridge code JTG 3362-2018 overestimated reinforced specimens at 1.092. The Chinese steel-fiber design standard JGJ/T 465-2019 performed worst, overestimating capacity by roughly 30 percent with standard deviations above 0.20, indicating that its fiber and confinement terms fail to capture the distinctive splitting resistance and fiber-bridging behavior of UHPC.

In response, the researchers developed two prediction models grounded in the observed mechanics. The first is a modified confinement-based model that expresses bearing capacity as the sum of a fiber-enhanced UHPC contribution and an additional confinement term from indirect reinforcement. A steel-fiber characteristic parameter captures the reinforcing efficiency of the fibers, while a regression-derived coefficient reveals that the confinement contribution of transverse steel actually decreases as fiber content rises, vanishing entirely beyond a fiber characteristic parameter of 1.38. The model achieved calculated-to-test ratios of 0.993 with a standard deviation of 0.081 for unreinforced specimens and 1.013 with a standard deviation of 0.105 for reinforced ones, outperforming existing literature models in both accuracy and scatter.

The second model takes a more theoretical route, treating local bearing failure as a plasticity problem. Using a modified Mohr-Coulomb criterion with a nonzero tensile cutoff to represent fiber-bridged post-cracking strength, the team idealized the failure zone as a wedge mechanism combining a shear-compression plastic flow zone with a tensile splitting zone. An upper-bound virtual work solution, calibrated with a reduction factor of 0.172 against 25 unreinforced database records, reproduced measured capacities with a mean ratio of 1.00 on the calibration set. The authors are candid that this wedge model, with its rigid-plastic idealization and simplified geometry, is best suited for mechanism interpretation and analytical assessment of unreinforced zones rather than direct design use, while the confinement-based model serves as the practical design tool within the calibrated parameter ranges.

The implications reach well beyond the laboratory. Prestressed bridge girders, stay-cable anchorages, and other heavily loaded UHPC components can now be designed with equations that explicitly recognize how steel fibers and transverse reinforcement share the job of resisting splitting, and how plate geometry reshapes the load-transfer path. The study also flags its own boundaries: the models are calibrated only within the tested ranges of fiber content, bearing area ratio, and reinforcement ratio, and further validation is needed for full-scale members, different anchorage systems, larger specimen sizes, and alternative fiber types. Still, by demonstrating that anchorage-zone failure is a progressive compression-splitting-confinement process, the work gives engineers a mechanically honest foundation for pushing one of construction’s strongest materials closer to its true limits, potentially enabling lighter, more slender, and more durable prestressed structures at a time when infrastructure demands are growing faster than conventional materials can comfortably answer.

Subject of Research: Experimental and analytical evaluation of the local bearing capacity of ultra-high-performance concrete prestressed anchorage zones

Article Title: Experimental study and analytical evaluation of local bearing capacity of UHPC anchorage zones

Article References: Zhang, B., He, Z.-Q., Chen, J., & Li, W. (2026). Experimental study and analytical evaluation of local bearing capacity of UHPC anchorage zones. Case Studies in Construction Materials, 25, Article e06508. https://doi.org/10.1016/j.cscm.2026.e06508

Image Credits: AI Generated

DOI: 10.1016/j.cscm.2026.e06508

Keywords: ultra-high-performance concrete, UHPC, anchorage zones, local bearing capacity, steel fibers, prestressed concrete, splitting failure, confinement, plasticity wedge model, bridge engineering, bearing area ratio, indirect reinforcement