Conference Agenda

It is generally accepted that engineering structures, whether bridges or aircraft, should be designed to have failure probability no higher than 10−6 per lifetime. The current probabilistic and computational predictions cannot satisfy this goal. While sophisticated probabilistic models have been developed to deal with the randomness of loads, the problem is the uncertainty of material failure, which has been relegated to empirical understrength (or capacity reduction) factors. Historically, the design equations of all design codes have been “marginal” equations, which is our name for the equations set at the lower margin of the test data cloud (depending on structure size, 25% to 40% below the data mean in the case of RC beam shear). Unfortunately, the offset of the mean and the variance of the database are not declared in the design code and have remained buried in the code committee documents. Furthermore, probabilistic modeling of the mechanics of failure process that determines the structural strength has been absent and the probability distribution function (pdf) required to extrapolate to 10−6 has been chosen arbitrarily – often as the lognormal pdf, which gives the lowest (and thus least safe) estimate of the understrength factor. This pdf, which represents the least safe assumption possible, is shown to be physically impossible for a database with one-and-the-same concrete while playing some role in a database comprising concretes of very different strengths. All of these problems have rendered the current failure probability estimates of concrete structures virtually meaningless when computational stochastic mechanics software is used. There is a looming crisis and concrete design code clarifications are urgently needed. Related to this is the previous conclusion that the blind prediction competition of a single large test, in which only the required strength of concrete is revealed (which is all that is required in the design code), has been misleading. The sine qua non of the remedy is that the offset of the data mean from the code equation and the coefficient of variations of the data set must accompany each design code equation. A realistic probability distribution (or, at least, its acceptable forms) should also be suggested. To this end, a proof that the lognormal distribution, though often used in practice, can never characterize structural failure probability. More genrerally, it is proven that no distribution with positive skewness is possible. At 10−6 this makes a difference as big as 1 : 2 to 1 : 3 in terms of the standard deviation. A complete remedy would require revising all the load and understrength factors of the design code and rescaling the design equations to the database means.

Crack width control is essential for the serviceability of reinforced concrete (RC) structures, yet current design models rely on simplified assumptions that fail to capture strain localization and material heter-ogeneity. This study investigates uncertainty in crack width predictions using a finite-element model based on smeared crack and fracture mechanics approaches. The model incorporates the crack band concept to ensure mesh-objective energy dissipation and addresses limitations of experimental measurements, such as single-face observations and the exclusion of microcracks. Validation against experimental results of RC elements sub-jected to bending and direct tension examines the influence of mesh size, bar modeling, and concrete heteroge-neity represented by random fields. The verification demonstrates that 3D modeling with embedded bars and an imposed minimum crack band size significantly improves prediction accuracy, achieving model uncertainty close to unity for maximum crack width. The findings provide practical guidance for applying smeared crack models in the serviceability verification of RC structures.

Concrete is widely used but limited by its brittle behaviour and low tensile strength. Fibre-reinforced concrete (FRC) improves crack resistance, ductility, and tensile performance, yet its microstructural mechanisms remain insufficiently understood. This study uses the DEM code YADE to model concrete as a two-phase material and analyse the pull-out behaviour of fibres. Fibres were represented with real geometry, either rigid or deformable. Simulations were compared with experimental data, highlighting the role of interface stresses, and fibre deformability. The results demonstrate DEM’s effectiveness in capturing fibre-concrete interaction.

In this contribution, a model-based investigation is conducted to correlate fiber orientation measures with the post-cracking strength of Fiber-Reinforced Concrete (FRC), thereby providing guidance for the engineering design of FRC structures. For this, a multi-level model for the analysis of FRC structures is used, which allows to assess the influence of a chosen fibre type, content, and orientation on the structural response. Using data from segmented CT images, the effects of the fiber orientation, fiber content and embedment length on the fiber bridging stress are quantified. After providing an overview of models describing the fiber orientation state and their relation to experimental measurements, the model is validated by the re-analysis of 3-point bending tests, using the fiber orientation state from segmented CT images as explicit model input. Additionally, assumption-based predictions using different orientation tensors are carried out to discuss the influence of incomplete information. A parametric study quantifies the discrepancy between post-cracking strengths obtained
from standard FRC characterization tests and the post-cracking strength expected in the to-be-designed structural member due to differences in fiber orientation. The results demonstrate how the fiber orientation state governs the post-cracking performance and provide practical guidance for incorporating orientation effects in the design of FRC structures.

Corrosion-induced cracking is a leading cause of durability loss in reinforced concrete structures exposed to chloride environments. Existing numerical models often assume uniform rust expansion or treat chloride diffusion and mechanical cracking as sequential processes, limiting their ability to capture spatially heterogeneous corrosion patterns. This work presents a finite element framework that couples chloride transport with mechanical model describing cracks together with concentration triggered rust expansion and crack-enhanced diffusion. Using the thermal analogy in Abaqus with user subroutines, the approach enables non-uniform corrosion to develop naturally in response to local chloride concentration. A smooth activation function captures the progressive filling of the porous zone before expansive pressure develops. The framework implements bidirectional coupling where mechanical cracking accelerates chloride ingress through crack width dependent diffusion, creating a self-accelerating deterioration process. The model was validated against experimental results from accelerated corrosion tests, successfully reproducing both non-uniform rust distribution and characteristic crack patterns. While the formulation assumes two-dimensional sections and neglects electrochemical kinetics, satisfactory agreement with experiments demonstrates that essential features of chloride-induced deterioration can be captured using this simplified approach.

This paper validates a computationally efficient 2.5D approach for modelling cohesive discrete cracks in concrete at the mesoscale. The proposed method relies on extracting a series of planar, two-dimensional slices from a full three-dimensional geometry and coupling them through horizontal and vertical springs that transfer force interactions between adjacent layers. The main objective of this approach is to effectively reconstruct the essential three-dimensional mechanical response while maintaining the computational efficiency of two-dimensional analyses. The validation is performed using two benchmark configurations: a dogbone-shaped tensile specimen and a notched three-point bending beam, both featuring stochastically generated mesostructures with ellipsoidal aggregates. Key model parameters are systematically examined, and mesh-sensitivity analyses ensure solution objectivity. The study conducts comprehensive performance comparisons between isolated 2D models, the proposed 2.5D layered approach, and full 3D simulations to evaluate crack-propagation patterns, force–displacement and computational efficiency. The results demonstrate that the 2.5D approach achieves an optimal balance between accuracy and computational cost, making it a practical alternative to full three-dimensional simulations for mesoscale concrete fracture analysis.

Numerical modeling plays a key role in assessing the safety and performance of reinforced con-crete nuclear containment buildings (NCBs). However, uncertainties arising from material heterogeneity, boundary imperfections and modeling assumptions can significantly affect predictive accuracy. This paper pre-sents a Bayesian updating (BU) framework for reducing such uncertainties in finite element simulations. The methodology employs a Markov-Chain Monte-Carlo (MCMC) algorithm to infer posterior parameters distri-butions based on experimental evidence. Its implementation is first illustrated through a simply supported beam under a central load, highlighting the influence of the algorithmic settings (number of chains, sample size, proposal scale, and measurement noise) on posterior convergence and uncertainty reduction. The framework is then applied to the PACE-1450 mock-up, a reinforced concrete representative structural volume of NCBs, using a surrogate model to assimilate observed crack counts. Results show significant variance reduction for key parameters, an improved agreement with experimental data and an enhanced predictive capability of damage-based numerical models.

With the publication of the second generation of EN1992-1-1, many changes are introduced in the shear design of concrete elements. Among those, the implementation of prestress in the shear resistance in the cracked regions of prestressed elements without transverse reinforcement has changed, since this is now calculated according to the Critical Shear Crack Theory. To verify the new design proposals, a series of prestressed beams are tested, complemented by a virtual simulation of the experiments. In this work, the shear resistance of one prestressed beam is simulated numerically and compared with the experimental outcome. The beam is modelled using the Lattice Discrete Particle Model, an advanced
non-linear discrete element method that explicitly models the aggregates and the cement-mortar matrix.
This makes it particularly well-suited for applications where the material heterogeneity and cracking
behaviour play a dominant role, such as in shear failure. Because of the heterogeneous modelling, the model is a mesoscale model and needs thorough calibration. To this extent, experimental characterisation tests are carried out to quantify the key mechanical properties of the concrete. These properties include the bending and splitting tensile strength, compressive strength, Young’s modulus and fracture energy. These characterisation tests are also simulated virtually to perform the calibration of the mesoscale parameters. Finally, a large-scale beam test is modelled and the load-displacement diagram is compared with the virtually obtained diagram. Together with the global behaviour, the local cracking behaviour is compared by experimental measurements and the final numerical and experimental cracking pattern is compared. Additionally, the obtained shear resistance is compared with the analytically obtained resistance predicted by the CSCT. These results contribute to the validation of the design provisions of Eurocode 2 and showcase the ability of LDPM to simulate experimental outcomes.

Optimization of structural elements in reinforced concrete design is central to modern engineering efforts to reduce self-weight while maintaining or improving strength and ductility, especially in seismic-prone regions. This study presents a comprehensive confinement analysis of Hollow Circular Concrete Sections (HCS) as compared to their Solid Circular Section (SCS) counterparts. Employing a computationally efficient, non-linear finite-layer framework, it develops a numerical procedure that evaluates confined strength using incremental–iterative moment-of-area computations based on a secant-stiffness formulation embedded in a custom finite-layer model.

The study systematically investigates various HCS geometries with different inner-to-outer diameter ratios, longitudinal and lateral reinforcement arrangements, and concrete strengths ranging from 3.4 to 5.4 ksi. The confinement effects are analyzed using a modified Mander-type concrete model adapted for hollow geometries, with attention to stress distribution across the annular cross-section. Axial–moment interaction diagrams are produced for a wide range of experimental configurations, allowing direct performance comparison.

Results show that, with proper detailing, HCS can achieve confinement performance comparable to that of equivalent SCS, particularly when tri-axial reinforcement is used. Overall, the study demonstrates the potential of hollow concrete columns as a sustainable and high-performance alternative to traditional solid members, paving the way for advanced structural typologies in both high-rise and infrastructure applications.

Concrete cover spalling caused by reinforcement action is characterised by a pressure acting on the internal surface. The plasticity theory exhibits limitations when used for predicting the mechanical response during crack propagation since concrete exhibits tensile softening, which may be taken into account by implementation of so-called effectiveness factors. Therefore, this contribution proposes an analytical methodology with the goal of predicting post-peak softening until the concrete cover spalls. A continuum Finite Element model is used to analyse crack propagation, the kinematics of the system and the propagation of the principal tensile stress along the relevant cracks. Subsequently, an analytical model is developed, where cracks are explicitly considered following Baˇzant’s crack band theory, which propagate towards the surface. Stresses, strains and crack widths are defined according to the deformed state of the spalling concrete body. By expressing that the system should be in static equilibrium for all deformed states, the internally applied pressure is expressed as a function of the deformed state. Eventually, the pressure - displacement diagram is plotted and compared with experimental results from the literature. It is shown that the peak pressure can be reasonably well predicted and that it is possible to capture post-peak softening by applying simple methodologies. Further improvements are possible to be explored in future work.

Numerical modeling of reinforced concrete (RC) elements is well established, but hybrid rebar–
fiber-reinforced concrete (RFRC) systems introduce additional challenges due to high nonlinearity from complex material behavior and fiber-rebar interaction. With Eurocode 2 (2027) incorporating fiber-reinforced concrete provisions, reliable constitutive models are essential. This study evaluates modeling strategies for RFRC beams in Abaqus using the Concrete Damaged Plasticity model. Two post-cracking tensile laws are examined: the Eurocode 2 Annex L formulation and an inverse-analysis model derived from notched beam tests. Rebar–concrete interaction is modeled using both embedded constraints and cohesive zone approaches. Moel validation is performed against four-point bending tests from an ongoing program on minimally reinforced beams with three polypropylene fiber volume fractions. Results show that the Annex L model provides reasonable predictions for polypropylene fibers. Both interaction approaches capture global structural behavior with respective advantages in computational efficiency and deformation accuracy, although the final failure response remains mesh-sensitive when strain-based material criteria are used.

Italian transportation networks include several existing bridges, built since the early ‘60s, usually characterized by simply supported prestressed concrete (PC) beams with post-tensioned steel tendons. Nowa-days, a considerable number of such bridges are becoming obsolete due to deterioration caused by environmen-tal exposure during their service life. In particular, bridge beams with dapped-ends are more prone to reinforce-ment corrosion due to the geometry of the nib, which can lead to a significant reduction in load-bearing capacity. In the present study, a numerical modelling approach is presented to evaluate the reduction of the load-bearing capacity of an existing Italian bridge by including defects and corrosion-induced effects varying over time on post-tensioned tendons. To this purpose, Non-Linear Finite Element Analyses (NLFEA) of an existing PC bridge beam have been performed. The corrosion over time of post-tensioning wires is considered by modifying their constitutive laws (in terms of residual stress vs strain) to reproduce the time-dependency of the load-bearing capacity of the bridge beam. The results demonstrate that numerical models can serve as digital twins of existing structures suitable to implement the effects of the spatial and temporal variability of corrosion process in the response prediction of existing structures.

Flat slab punching of reinforced concrete structures is still a field of ongoing research. A huge amount of experimental data is available. Accompanying numerical 3D-simulations applying sophisticated concrete
models are computationally expensive and generally calibrated from the few respective experimental results. This prevents a generalization. An alternative approach is followed with this contribution. The computational costs are substantially reduced with a parametrized axisymmetric finite element modeling and a simplified material model for concrete. Only uniaxial compressive strength is required as input. Nevertheless, triaxial behavior and decisive nonlinear effects are considered. The application of the parametrized model is demonstrated with a representative example with detail results described. Furthermore, the model simplifications allow to perform simulations for 227 quite heterogeneous data sets collected from a wide range of experimental investigations. With respect to ultimate failure loads the simulation results in the mean show a good agreement with the experiments although with number of outliers. The model sets a base for gradual improvements by introducing further parameters step by step.

Understanding the phenomena that play a crucial role in the support of (precast) elements is crucial for the production and application of concrete elements. A lively debate is still ongoing about how it should work and how it seems to work in practice, where neither supports the other. Numerous examples of well-performing elements exist where the 10Ø or 100 mm criterion is not fulfilled, and exceptions are intro-duced by product standards, illustrating our lack of understanding. In the context of the introduction of a new national annex to EN 1992-1-1 (2023) in Belgium, a research project was launched to provide complementary information. A new analytical model and a new test setup have been developed, leading to a better understand-ing. Results of the tests support the proposed model based on a slip modulus. Based on the outcomes, signifi-cantly reduced anchoring lengths can be used.

This paper presents a thermodynamically-based lattice discrete particle model (LDPM) for simulating concrete fatigue from material to structural scale. The constitutive model is rigorously derived from thermodynamic potentials with explicit damage evolution driven by cumulative plastic strain at inter-aggregate level. The model is calibrated through comprehensive uniaxial compression simulations on prisms, accurately reproducing S-N curves, Sparks-Menzies relations, and realistic hysteretic behavior. At the structural level, the model predicts progressive damage evolution and stress redistribution in prestressed beams under subcritical cyclic loading. Key findings include: (i) the perfect alignment of material-to-structural fatigue results with the Sparks-Menzies relation provides theoretical justification for extrapolating laboratory fatigue relationships to engineering applications; (ii) damage dissipation emerges as a scale-invariant fundamental material property, offering a physically grounded alternative to empirical design approaches. The presented thermodynamic framework enables structural fatigue prediction based on material-level calibration, reducing reliance on costly full-scale testing while providing insights into concrete fatigue mechanisms.

The reliable validation and verification of simulation models is a key challenge in computational engineering, especially for complex materials and multi-physics problems. Existing approaches are often computationally intensive and tailored to specific setups, making generalization and objective comparison across models and codes difficult. This paper presents a concept for a reproducible and extensible benchmarking platform designed for any FEM or CFD-based simulation setup, with concrete modeling as a motivating example.
The platform aims to facilitate data exchange between experimentalists and simulation researchers, enable transparent comparison of models and implementations, and support referencing models with quality criteria in engineering standards. Key components include a machine-readable database structure for experimental metadata, standardized calibration procedures, and quality metrics that account for uncertainties. The platform supports integration of open-source constitutive model libraries into commercial codes, promoting interoperability and community-driven benchmarking. A federated database infrastructure enables sharing and publication of experimental and simulation results, with full provenance tracking to ensure reproducibility. Interactive visualization tools allow users to query, explore, and compare models and results. While the conceptual framework is well developed, a complete implementation is still in progress. Community contributions are needed to realize a broad set of benchmarks and develop tool-agnostic, machine-readable model definitions. The proposed platform aims to advance reproducibility, transparency, and robustness in computational modeling and simulation practice across engineering domains.

This paper presents development of a 3D nonlinear FE model of a concrete biological shield (CBS) in a nuclear power plant using WWER 440/213 nuclear reactor. Such structure is exposed to several nonmechanical effects, primarily the neutron radiation causing the radia-tion-induces volumetric expansion (RIVE). This causes internal stresses within the structure and years of op-eration lead to cumulation of this effect, finally developing into cracks. Crack propagation then disrupts the structure's soundness and may lead to reduced shielding property. RIVE is introduced to the analysis as an isometric eigenstrain, varying along the height, depth and in circumference along the inner surface. The results focus on determining crack initiation and propagation. The primary vertical crack appears after approx. 6 years of operation and reaches width of 0.3 mm after approx. 12 years. After considered lifespan of 60 years, the primary crack reaches width of 4.6 mm.

For retrofitting purposes, there is a demand to reinstate or increase the capacity of damaged or non-damaged columns. In addition to confinement techniques, section extensions to columns are often employed. Adhesion and mechanical anchoring over the interface are required to achieve the column's full capacity. During the hardening process of the concrete, shrinkage of the newly cast extensions results in supplementary loading of the existing part of the column. The present work, based on the principles of composite action, considers one-directional enlargements, focusing on the normal forces in the column components and the shear flow acting on the interface. Additionally, fire action on an existing column that is enlarged on two opposite sides, is considered. It is demonstrated that optimizing bar locations in the new parts leads to a significant increase in fire safety.

This paper investigates the vulnerability of reinforced concrete (RC) frame structures under extreme loading conditions such as blast and high-velocity impact events, emphasizing complex responses and secondary failure mechanisms. Explosions in close proximity generate intense shock waves that damage vertical load-bearing elements, particularly columns, leading to loss of load path continuity and potential progressive collapse. The study focuses on catenary mechanisms that temporarily redistribute loads but induce excessive tensile forces, accelerating failure. Traditional design approaches based on predefined threat scenarios are critically compared with more general, threat-independent frameworks such as dynamic column removal, which promote robustness through redundancy and alternative load paths. While threat-dependent methods provide accuracy for specific cases, they may overlook unforeseen failure modes, whereas threat-independent approaches aim to ensure resilience against a wider range of hazards. A numerical case study of a short RC frame using the Applied Element Method quantifies structural response under different damage scenarios, including sudden column loss and blast loading. The comparison of results highlights differences between threat-dependent and threat-independent frameworks, emphasizing the role of initial damage characteristics and secondary mechanisms in collapse progression. The findings underline the need for robustness-oriented design methodologies that address uncertainties in loading scenarios and enhance the capacity of RC frames to resist and adapt to extreme events while preventing progressive collapse.

Rockfall protection systems are essential for safeguarding infrastructure and human activities in mountainous regions, where falling rock masses pose persistent hazards that can cause severe damages. Structural mitigation measures, such as energy-dissipating barriers, are commonly installed near roads, buildings, and industrial facilities to reduce impact forces. These systems function by either absorbing the kinetic energy of falling blocks through deformation or resisting impact via mass and frictional dissipation. Two main energy dissipation strategies characterize these systems. Flexible barriers, such as net fences, absorb energy through large deformations and are widely used for their adaptability and effectiveness across varying block sizes. However, they require sufficient clearance between the barrier and protected infrastructure, which limits their application in narrow corridors. To overcome this constraint, rigid systems, such as L-shaped reinforced concrete walls, have been developed. For high-impact energies, a cushion layer of granular material is often added to the upslope face of the wall. However, this solution requires a large footprint, which is not always feasible, and in steep areas, the added weight can even lead to overall slope instability. Therefore, for expected impact energies up to approximately 800 kJ, a rigid system alone can represent an effective and economical solution. These structures rely on mass and bending resistance to dissipate energy without requiring buffer space, making them suitable for constrained environments. Nevertheless, their long-term reliability under diverse impact conditions remains an open question. This study introduces a time-integrated reliability analysis of rigid rockfall protection systems, focusing on performance under variable loading over extended periods. The approach incorporates the frequency–magnitude distribution of rockfall events, acknowledging that smaller blocks occur more frequently than larger ones. Variability in block mass, impact velocity, and kinetic energy is modelled within a probabilistic framework that accounts for uncertainties in material properties and structural response. The analysis is applied to a real-world slope with documented rockfall activity, evaluating the reliability of a concrete wall system under cumulative low-energy impacts and rare high-energy events. Using limit state functions, failure probabilities and critical performance thresholds are estimated. Results emphasize the importance of integrating temporal and probabilistic dimensions into design, showing that rigid barriers, while effective in constrained spaces, exhibit reliability sensitivity to impact frequency, energy dissipation capacity, and degradation over time.

The connection between flat reinforced concrete slabs and columns represents a critical design challenge in structural engineering, particularly in buildings, due to the substantial concentration of shear stresses that can lead to punching failure. This localized, brittle failure mechanism occurs abruptly, without prior warning, and carries a considerable risk of structural collapse. Despite extensive research aimed at understanding the mechanics governing punching shear failure and developing dependable design methodologies, such as the Critical Shear Crack Theory (CSCT), a unified understanding of the underlying phenomena remains elusive. This investigation makes use of the Finite Element Method (FEM) in conjunction with material models based on fracture mechanics to simulate punching shear failure in reinforced concrete slabs. While this methodology has been previously explored, challenges persist, particularly in accurately representing the overall response of the problem and the failure mechanisms involved. The objective of this work is to evaluate various modelling approaches to establish a numerical model capable of accurately reproducing this phenomenon, thereby offering insights into the intricate fracture mechanisms that drive the failure process. The numerical simulations draw upon experimental data from Kinnunen and Nylander’s seminal work, specifically referencing specimens IA15a, IB15a and IC15a. These slabs are circular, with a diameter of 1840 mm, are supported by a 150 mm diameter column, with both the column height and slab thickness being 150 mm, and incorporate different reinforcement strategies. While IA15a slab presents an orthogonal reinforcement, IB15a is reinforced with ring reinforcement and IC15a with a combination of ring and radial reinforcement. The experimental setup involves applying load from below the specimen using a hydraulic jack, while the slab’s perimeter is constrained vertically by twelve spreader beams. The FEM models employ an isotropic damage formulation to describe concrete behaviour, where damage reduces the material’s stiffness and is determined using an equivalent strain value based on the Rankine criterion. Steel is represented by a perfectly plastic material, adhering to the von Mises plasticity condition. A key focus of this study is the examination of the concrete-steel interface behaviour. Two distinct model versions are prepared for each of the three slabs: one of them assume perfect bonding between steel and concrete and do not allow debonding, while the other one permits perfect slippage between concrete and steel. The numerical findings underscore the critical importance of accurately modelling the concrete-steel interface. Notable differences in the load-displacement diagrams between those models where slippage is not allowed and those where it is allowed, emphasize the significant influence of bond-slip behaviour in accurately capturing the punching shear response of reinforced concrete slabs. This research contributes to a deeper understanding of punching shear failure and supports the development of more reliable numerical tools for structural design.

Explicitly modeling embedded fibers in a concrete matrix subject to cracking, spalling, and localized crushing presents significant challenges. On top of that, a mesh conforming model of steel fibers embedded in a concrete matrix is computationally expensive. In this study, a hybrid contact model is used to generalize fiber-matrix coupling and remove the necessity of an excessively small mesh. The generalized model simulates the movement of embedded steel bars in a predefined tunnel within a discrete-mesoscopic matrix. There are limited reports on this slideline model, but a universal calibration, parameter fitting, and investigation of geometrical configurations are lacking. To address this and reveal the merits and limitations of the slidelineassisted coupled contact model, cases of steel fiber aligned pullouts are contrasted against the conventional mesh-conforming approach and experimental evidence. Future studies will extend these investigations to include inclined pullout cases, leading to a scalable fiber-lattice explicit coupling model to simulate SFRC composites.

In order to model concrete cracking, a phase-field model is retained which converges toward cohesive fracture when its regularisation length goes to zero. The damage threshold in stress-space is adapted from experimental failure surface. In addition, damage in compression is introduced to bound the stress re-sponse. The model is deliberately kept as simple as possible to preserve its robustness. Two test-cases are computed in order to assess its capabilities. The first one consists of a shear-mode pull-out test. It is focused on robustness in the presence of other sources of nonlinearity (finite strain plasticity, contact boundary condi-tions). The second one consists of a reinforced concrete beam submitted to four-point bending. It is character-ised by multi-cracking and enables a comparison with experimental results.

Concrete is one of the most commonly utilized building materials and has a significant environmental footprint due to its production process. Over the past decades, considerable progress has been made in developing high-performance and ultra-high-performance concretes (HPC/UHPC) and incorporating fiber reinforcement in structural concrete, resulting in improved strength and durability and opening the possibility of creating slenderer structures, leading to significant material savings. However, adequate models and design approaches must accompany these material improvements to fully realize the potential benefits. This work focuses on the material behavior aspect of high- and ultra-high-performance fiber-reinforced concrete (HPFRC/UHPFRC), investigating damage processes and mechanisms occurring at small scales, which are not readily observable during loading tests. To this end, it presents a framework based on image-derived mesoscale models generated from X-ray computed tomography (CT) scans of laboratory-scale specimens. These models incorporate realistic pore and steel fiber distributions, enabling detailed simulations of crack initiation and propagation processes that are not directly accessible in experiments. A finite element model utilizing zero-thickness cohesive interface elements is applied to simulate the cracking of fiber-reinforced concrete specimens. The zero-thickness interface elements are equipped with a cohesive-frictional traction-separation law. The steel fibers are considered explicitly and modeled as elastoplastic Timoshenko beam elements. The embedment of fibers into the cement matrix is facilitated via a penalty-based coupling algorithm that enables flexible placement of fibers without needing to conform with the background mesh. The bond between the cement matrix and fibers is modeled via an elastoplastic bond-slip law, whose parameters are calibrated based on single-fiber pullout experiments. The capabilities of the proposed framework are demonstrated by the reanalysis of an experimental scenario involving UHPFRC beam subjected to 3-point bending and comparison of the results with the available experimental data.

Elastoplastic constitutive models encompassing non-associated plastic flow are widely used for modeling the pressure-sensitive mechanical behavior of cohesive-frictional materials, such as concrete and rock. Although the potential instabilities of such models are well established in the literature, they remain a common—and often overlooked—source of numerical difficulties in simulations of cohesive-frictional materials. In the present contribution, we investigate the destabilizing effect of hyperbolic plastic potential functions, which were recently identified as a potential source of constitutive instability. To this end, we derive regions of critical constitutive states on the yield surface for non-associated Drucker-Prager plasticity with a hyperbolic plastic potential function. Moreover, a recently presented analytical solution for non-associated Drucker-Prager plasticity subjected to oedometric extension is extended to account for hyperbolic plastic potential functions. The results indicate a broadening of the region of critical constitutive states near the vertex of the yield surface, revealing a destabilizing effect of the hyperbolic plastic potential function. Moreover, softening in oedometric extension is observed where it would not occur with classical non-associated Drucker-Prager plasticity, further highlighting this destabilizing effect. These findings suggest that the near-vertex behavior of elastoplastic constitutive models plays a key role in the emergence of potentially unstable constitutive behavior linked to numerical difficulties in simulations of cohesive-frictional materials.

The paper contains a survey of several equivalent strain definitions and their use in the localizing gradient damage (LGD) model. When the conventional gradient damage (CGD) model with a constant internal length scale is applied, an artificially widened damage zone may appear. In the LGD model, the localization zone is controlled by a gradient activity function. As damage grows, the variable internal length scale decreases and the nonlocal interaction is reduced. Both versions of the model are implemented in the FEAP package, and the advantages of the LGD model are demonstrated. A range of equivalent strain measures is considered, and the resulting equivalent strain envelopes are illustrated with reference to the Kupfer test. The simulation of an eccentrically notched beam in three-point bending is also carried out. A mesh-sensitivity study is presented, indicating that the numerical response stabilizes and converges for sufficiently refined meshes. Generally, selected equivalent strain definitions are investigated in the numerical analysis, and they reproduce the experimental results reported by Garc´ıa-A´ lvarez et al.Moreover, the Häußler-Combe and Pröchtel definition provides the closest agreement and leads to representative crack patterns in concrete.

Concrete fatigue controls long-term safety and serviceability, yet prediction is hampered by heterogeneous mesoscale mechanisms (microcracking, frictional sliding, damage accumulation) and their interaction under monotonic, cyclic, and high-cycle loading. We present a unified discrete mesoscale model in which rigid particles (aggregates) interact through vectorial interface laws coupling pressure-sensitive plasticity and damage derived from thermodynamic potentials. Normal response combines compression plasticity with tensile softening damage; tangential response employs coupled damage–plasticity with kinematic hardening, enabling hysteresis, stiffness degradation upon unloading, and fatigue damage growth below peak load. A mild shear–normal damage coupling reflects loss of tensile integrity after extensive sliding. The formulation yields an energy-consistent decomposition (elastic strain energy, plastic work, plastic free energy, damage dissipation) used to interpret fatigue degradation. Validation covers: (i) non-proportional compression–torsion (vertex effect), (ii) biaxial tension/compression, and (iii) notched three-point bending under monotonic, post-peak cyclic, and subcritical fatigue regimes. Simulations reproduce peak loads, unloading stiffness reduction, crack evolution, lifetime trends, and show that plastic dissipation is amplitude-dependent while damage dissipation is nearly amplitude-insensitive and correlates with failure. This supports damage energy as an objective indicator for remaining fatigue life.

Bonded anchors are widely used fastening elements in civil and structural engineering applications,
particularly where high-strength connections are required for structural safety and performance. These
anchors are essential in various construction scenarios, such as the retrofitting of existing structures or the installation of structural components. To further enhance the load-bearing capacity of these systems, post installed supplementary reinforcement (PISR) bars can be introduced. This reinforcement strategy is particularly effective in improving performance under tensile and shear loading conditions. In order to accurately assess and predict the load-bearing capacity of such reinforced bonded anchor systems, we investigate a novel numerical modeling approach based on a phase-field damage-plasticity framework. The method builds upon the Concrete Damage Plasticity (CDP) model originally developed by Grassl and Jir´asek (2006), incorporating a recent phase-field extension. This extension is crucial in addressing the issue of mesh sensitivity commonly encountered in conventional damage models. The phase-field approach allows for a smooth and continuous representation of crack initiation and propagation, thereby enabling the simulation of complex failure patterns. The proposed model is implemented within an explicit finite element (FE) framework, using the commercial software package Abaqus/Explicit. This platform allows for efficient simulation of nonlinear material behaviors under various loading scenarios. Our numerical implementation ensures stable and accurate results even for complex three-dimensional geometries and highly nonlinear problems involving contact and bonded interfaces. To evaluate the robustness and accuracy of the proposed modeling strategy, we conduct a comprehensive numerical
study that includes a wide range of test cases and reinforcing conditions. The simulation results are benchmarked against experimental data. The findings demonstrate that the proposed phase-field damage-plasticity approach exhibits excellent predictive capabilities. It accurately captures both the global structural response and the localized damage evolution of the bonded anchor systems with and without supplementary reinforcement. Overall, the study highlights the effectiveness and versatility of the proposed computational framework. The combination of the CDP model with the phase-field method offers a powerful tool for analyzing and designing reinforced fastening systems in complex and demanding engineering applications. Accordingly, this approach is well-suited for investigating structural elements subjected to various loading conditions.

This work presents an analytical micromechanical model for quasi-brittle materials featuring coupled, directiondependent friction and cohesion. Building on mean-field homogenization, the formulation addresses key limitations of existing models by introducing an implicit solution procedure and an energy-based damage law based on a total, rather than partial free energy derivative. Along with a newly proposed damage resistance function ensuring linear softening under tension, the model captures complex emergent behaviors from a simple set of parameters. Numerical examples show that hardening under compression, anisotropic crack evolution, and confinement strengthening effects are all qualitatively reproduced from the prescribed tensile behavior without any additional parameters. They also demonstrate the model’s ability to handle complex stress-states in a stable and physically meaningful way.

This article presents a recently developed mixed finite element method for modeling brittle and quasi-brittle fracture in large structures, involving contact and large deformations. The proposed formulation includes four independently approximated fields: stresses, logarithmic stretches, rotation vectors, and displacements. The first two are associated with conserving linear and angular momentum, respectively. While, the other two fields are associated with the constitutive and the consistency equation between displacements and deformation. The relationship between the rotation vectors and the rotation tensor is established by an exponential map. The stresses are approximated in the Hdivspace, and the remaining three fields are approximated in the L2 space. This formulation results in a very sparse system of equations that can be efficiently solved in parallel using hybridization with a block solver, thereby enabling highly scalable and robust solvers. The system hybridization involves ’breaking’ the Hdiv space, such that continuity of normal fluxes, i.e. tractions, is no longer enforced apriori. A hybridized field is also introduced on the mesh skeleton faces and contact surfaces. Such a field acts as a kinematic Lagrange multiplier enforcing continuity of normal tractions. Moreover, the hybridized Lagrange multiplier field is conveniently used to enforce contact conditions, and introduce displacements discontinuities. Furthermore, since the Hdivspace provides traces of fluxes on faces, the mixed element enables efficient calculation of face crack release energy. Since this methodology enables crack propagation on fixed mesh technology, along with being based on an energy-based crack propagation criterion, it inherits the robustness of the phase field while being as efficient as methods which resolves crack discreetly. In an algebraic sense, since all fields in the interior become fields in the L2 space, and fields on skeleton faces are in H1/2 space, the system of equations is extremely sparse and can be solved using a Schur complement, eliminating interior fields.

This paper proposes a new three-dimensional cyclic constitutive model for reinforced concrete structure based on the explicit finite volume method. These developments are based and largely inspired on Sellier’s model (Sellier et al., 2013a; Sellier & Millard, 2019) which is a plastic-damage model that already integrates several essential phenomena such as crack opening and reclosure, shear failures and the behavior of reinforcements. However, to ensure optimal efficiency under cyclic loading, improvements will be made to the compressive behavior of concrete as well as on the cyclic behavior of reinforcements. It was decided to implement this enhanced model on a program based on the explicit finite volume method because this method allows the efficient resolution of highly nonlinear systems. However, strict criteria must be defined to guarantee the stability and convergence of the calculations. To validate these developments, the model results will be compared with experimental tests carried out at the specimen and structure scales.

A gap test an experimental and numerical test, which is designed to show that the effective mode I fracture energy depends strongly on the crack-parallel normal stress. Talking about the fracture energy one should distinguish between the initial and the total fracture energy. According to Nguyen et al., the initial fracture energy is the area under the initial tangent of the traction–separation curve while the total fracture energy represents the area under the traction–separation curve. Alternatively one can estimate the total fracture energy as the area between the up-and-down curve and the horizontal yield line in the load-displacement diagram. Authors of this paper tried to recreate numerically the gap test with a concrete specimen and to calculate the total fracture energy. They used the concrete damaged plasticity model in Abaqus software. Results presented in this paper are continuation of the authors’ work, presented previously at the FraMCoS 2025 conference.

An extension of a recently proposed cohesive zone model that combines mixed-mode fracture with regularized friction for quasi-brittle materials is presented. This interface material model is characterized by mixed-mode fracture in tension-shear, and by cohesion and Coulomb friction in compression-shear. In previous work, the discontinuity arising in the traction-separation relation due to the introduction of friction has been smoothed through a time-independent function. In this contribution, to remove the step dependence resulting from the previous formulation, a time-dependent regularization is proposed. Similarities and discrepancies between the two procedures are discussed.

Carbonation tests of hardened cementitious materials are time-consuming even under accelerated conditions, presenting significant challenges for the design of experiments. It is widely acknowledged that utilizing a low CO2 concentration (< 3%) is critical to accurately replicate natural carbonation conditions. Hence, a model is called for to estimate the carbonation front during accelerated carbonation tests of the designed composition a priori. In this paper, we first introduce a Finite Element Method (FEM) implementation in COMSOL Multiphysics that models a one-dimensional (1-D) reactive-transport process for OPC-based materials. Secondly, an equivalent FEM model is implemented in MARS (Modeling and Analysis of the Response of Structure). After benchmarking this model against the COMSOL model, we establish a novel three-dimensional (3-D) meso-scale model using the dual-lattice Multi- physics Lattice Discrete Particle Model (M-LDPM) framework. A CO2 concentration of 1% is applied in both implementations, with a constant temperature field of 20 ◦C and a relative humidity of 65% to simulate accelerated carbonation tests in an environmental chamber. It is shown that the meso-scale model can predict the average carbonation depth while retaining the heterogeneity of concrete and, thus, the spatial variability in the carbonation front. Advantages and disadvantages of both implementations are discussed, providing insights into their applicability in simulating real-world carbonation processes that can help researchers in their design of experiments.

Reinforced concrete (RC) bridge deck slabs in cold regions are simultaneously subjected to freeze–thaw cycles (FTC) and fatigue loading, leading to premature deterioration. However, this issue is rarely considered in their design. This study employed multi-scale numerical simulations to investigate the fatigue performance of frost-damaged RC slabs. The proposed model was validated against experimental results, which successfully reproduced the coupled deterioration process involving pore ice pressure and wet fatigue. Based on the validated model, parametric analyses were performed to examine the influences of the water-to-cement (W/C) ratio, air content, and freezing temperature on the fatigue life of RC slabs. The results show the quanti-tative effects of a W/C ratio decrease, an air content increase, and a freezing temperature increase on the fatigue life of RC slabs. Meanwhile, inadequate concrete quality may cause severe damage under FTC. Finally, a strain energy-based damage factor, 𝐾_𝑈, is proposed to quantify material degradation under combined environmental and mechanical actions. 𝐾_𝑈 effectively captures the coupled deterioration mechanism and provides a rational and practical indicator for the durability assessment and maintenance management of RC bridge decks in cold climates.

Alkali-activated materials based on ground granulated blast furnace slag (GGBFS) are investigated as low-carbon hydraulic binders for immobilizing long-lived, low-activity nuclear waste (LL-LA) containing graphite. This study presents a multiscale approach to characterize the early-age behavior of sodium hydroxide-activated GGBFS mortars and ordinary Portland cement (OPC) mortars incorporating graphite. At the mesoscale, a Representative Volume Element (RVE) models the matrix and graphite inclusions, enabling the calculation of thermo-elastic deformations, hydration-induced chemical shrinkage, and the evolution of elastic modulus with hydration degree. At the macroscale, a 3D finite element simulation evaluates thermal gradients and early-age deformations, highlighting greater endogenous shrinkage and lower initial stiffness in alkali-activated mortars compared with OPC. The presence of non-hydrating, highly conductive graphite significantly alters heat dissipation, thereby reducing early-age stresses. This methodology provides a robust framework for optimizing the performance of confinement matrices for nuclear waste applications.

The production of ordinary Portland cement (OPC) results in some 8% of the world green house gas emissions. Partially replacing OPC with supplementary cementitious materials such as limestone and calcined clay is a promising approach for developing more sustainable alternatives. In this study, we model the compressive strength development of pastes made with limestone Portland cement (LPC) and limestone calcined clay cement (LC3) binders. We investigate whether or not the stiffness of microscopic binder constituents play a crucial role in the strength predictions, and we give polynomial formulae for approximating the tensorial strength model. To this end, three binders are investigated: one type each of OPC, LPC, and LC3. For the blended binders, the cement replacement ratio amounts to 30 %. The limestone-to-calcined clay ratio is set to 1.0. The water is dosed at an initial water-tobinder mass ratio of 0.45. Strength modeling is performed using a multiscale strength model which is based on methods of continuum micromechanics. The model is extended to account for inert limestone and calcined clay inclusions. Volume fractions are calculated using Powers’ hydration model. Elastic phase constants are taken from the literature. Qualitative input for the multiscale model is visualized using material organograms: spherical residual binder particles are embedded in a continuous matrix of hydrate foam, which itself consists of isotropically oriented hydrate gel needles in direct interaction with spherical capillary pores. A sensitivity analysis regarding the stiffness of binder particles is carried out. It is found that the strength predictions are virtually independent of the stiffness differences within the binder powder. This provides the motivation for developing a surrogate model which approximates the tensorial strength predictions by polynomial equations, based solely on the strength of the hydrate gel needles, the hydrate foam-related volume fractions of the capillary pores, and the cement paste-related volume fraction of the binder constituents.

The time-consuming nature of conventional shrinkage tests—which often extend over a year to approach ultimate shrinkage values and enable reliable extrapolation to structural scales—necessitates the development of accelerated approaches. This study investigates the shrinkage and moisture loss of specimens smaller than the recommended 75 × 75 mm or 100 × 100 mm prisms. In the experimental part, prismatic specimens of several sizes are prepared conventionally by casting or wet-cutting from a larger block of self-compacting concrete to mitigate the wall-effect caused by the mold. In the first 100 days of the experiment, behavior contradicting engineering expectations was observed, showing that the cut-out specimens tend dry and shrink faster and more. One-way coupled hygro-mechanical model was developed for both types of specimens. If the cut-out specimens are assumed as homogeneous, themodeling approach can accurately capture moisture loss, shrinkage evolution, and the development of internal relative humidity. The data support the credibility of the non-linear shrinkage coefficient recently introduced in the MPS theory. However, accurately reproducing the trends observed in the cast specimens remains challenging with the present modeling approach, indicating complexities that warrant further investigation.

The objective of this work is to develop a carbonation model for concrete incorporating recycled concrete aggregates (RCA), with the aim of predicting and assessing the progression of carbonation. The broader goal is to evaluate the relative influence of key parameters on carbonation and, more importantly, to determine the overall impact of replacing natural aggregates with recycled ones. Understanding carbonation is essential, as it is a critical precursor to reinforcement corrosion-one of the primary degradation mechanisms in concrete structures. The numerical model has been developed based on various approaches from the literature. It was first implemented at a macroscopic scale, then extended to a multiscale framework to account for the intrinsic heterogeneity of concrete. This heterogeneity is represented through a representative volume element (RVE), which includes the mortar paste, aggregates, and the adherent mortar surrounding them. The model considers several coupled processes, as well as the chemical reactions resulting from the carbonation process within the concrete matrix. The implementation was carried out using the nonlinear finite element software LAGAMINE, developed at the University of Liege.

After a somewhat loosely written introductory section, in which various opinions and statements only partly based on traceable facts were presented, this paper mainly intends to show that accurately defining a solution strategy is the basis for establishing trust in nonlinear failure analysis of concrete structures. The paper describes what is meant by such a solution strategy, how the concept of a solution strategy has been incorporated into a recent standard by which the practical use of non-linear finite element analyses has come a step closer, and refers to a recent blind prediction contest example to illustrate a major pitfall.

This study examines the impact of fluid flow and aggregate fragmentation on the dynamic behavior of concrete under uniaxial compression at varying strain rates. Concrete was simulated as a four-phase material consisting of aggregate, mortar, ITZs, and macropores. The concrete mesostructure was obtained from laboratory micro-CT tests. 2D simulations were carried out. A novel, fully coupled DEM/CFD technique, based on a pore-scale thermal-hydro-mechanical model, was employed to predict the effects of strain rate, fluid flow, and aggregate fragmentation on the response of both partially and fully fluid-saturated concrete.

This study investigates the influence of indenter geometry and loading conditions on the determination of viscoelastic parameters of hydrated cement pastes through nanoindentation. Experimental tests with various tip shapes (spherical, Berkovich, cube corner) and load levels were combined with finite element modeling to analyze the stress–strain fields beneath the indenter. The results show that sharp tips generate extremely high stresses and significant plastic strains, violating the assumptions of linear viscoelasticity. In contrast, blunt or spherical tips produce stress levels within the linear regime, allowing reliable evaluation of creep compliance and viscoelastic constants. Analytical models based on the Vandamme approaches were used to interpret the holding segments of indentation curves. The study establishes limits for the applicability of linear creep models at the microscale and provides methodological guidance for obtaining intrinsic viscoelastic properties of cement hydrates for use in multiscale modeling of concrete behavior.

Micromechanical models provide powerful tools for estimating the bulk properties of complex, heterogeneous materials like recycled aggregate concrete (RAC). This is achieved by considering their hierarchical microstructure, from the nanoscale of hydration products to the macroscale of the concrete composite. However, these models inherently rely on various input parameters, each carrying uncertainties that stem from experimental variability, natural fluctuations, or measurement inaccuracies. A rigorous quantification of these uncertainties and an assessment of their propagation through micromechanical models are essential for robust predictions of compressive strength in cementitious materials, with a particular focus on the critical role of the Interfacial Transition Zone (ITZ).
This study leverages a semi-analytical micromechanical multiscale model, which explicitly accounts for the spatially varying properties of ITZ. Unlike conventional approaches that simplify the ITZ as a uniform layer, the adopted model integrates non-uniform characteristics (thickness, porosity distribution) based on experi-mental insights derived from techniques like nanoindentation and SEM-EDX analyses. To quantify the inherent uncertainties associated with RAC, particularly those arising from varying recycled aggregate properties, hy-dration processes, and internal curing phenomena, a variance-based global sensitivity analysis is incorporated.
To overcome the significant computational expense using detailed micromechanical models, a key strategic component of this investigation involves developing an efficient surrogate model which helps to drastically reduce computational effort without significantly compromising accuracy. Furthermore, an assessment of the model uncertainty is integrated, potentially by comparing predictions based on alternative constitutive assump-tions or hydration models, providing a holistic evaluation of prediction capability.

A new 2D framework to simulate concrete at the mesoscopic level of observation is proposed. First, a 3D specimen with randomly generated ellipsoidal aggregates is created. Then a set of parallel cutting planes is defined. For each plane a 2D model with a mesostructure is extracted from the full 3D specimen. Topology of a chosen master plane is iteratively compared with the topology of all remaining planes. A similarity function is derived for all integration points in the FE mesh of the master plane to evaluate differences at the mesostructure between two cuts. Together with out-of-plane weighting function it is used to modify the original constitutive law at an integration point at the master plane in order to mimic 3D mesostructure. Two benchmarks are simulated: tension of a dog-bone specimen and a three-point bending test of a notched beam and the influence of selected parameters is analysed.

The interfacial transition zone (ITZ) in cement-based composites is a thin region surrounding aggregates, typically 20–50 μm thick, characterized by higher porosity and lower stiffness than the bulk paste. Its properties are governed by mix composition, aggregate characteristics, and curing conditions, making it a
critical factor influencing stiffness, crack initiation, and durability. This study quantitatively evaluates the mechanical influence of ITZ characteristics using image-based modeling. High-resolution X-ray micro-computed tomography (micro-CT) was employed to characterize ITZ geometry and property gradients near aggregate boundaries. These experimentally derived characteristics were implemented into finite element (FE) models, representing the ITZ as a zone with distance-dependent material properties. Parametric simulations examined the effects of ITZ on damage propagation. A bio-inspired modification was further investigated by coating aggregates with a bacteria-induced calcium carbonate layer through microbially induced calcium carbonate precipitation (MICP). The biomineralized coating produced a denser and more homogeneous ITZ, improving bond strength and reducing microcracking. Digital simulations confirmed enhanced load transfer and delayed crack initiation in MICP-modified specimens. The integration of microstructural imaging, biomineralization, and numerical modeling provides an effective approach to design durable and sustainable cementitious materials.

The incorporation of renewable materials such as mineral additions and recycled aggregates in mortars and concretes formulations reduces greenhouse gas emissions and promotes low-carbon construction. These substitutions significantly affect the hydration mechanism and modify the physical, mechanical and durability properties of mortars and concretes. In the present work, experimental and micromechanical investigations are conducted on recycled mortars incorporating ground granulated furnace slag (GGBFS) and recycled sand. Various mortar mixtures are designed involving different replacement ratios of Portland cement and natural sand by GGBFS and recycled sand . Microstructural and macroscopic properties are therefore investigated thanks to experimental setups such as nano and micro indentation, thermogravimetric test analysis and mechanical testing (compressive strength and elastic modulus). On the other hand, a modeling approach is proposed based on a simplified representation of the representative volume element (REV) of low carbon mortars and fed with data collected on the microstructure. Slag blended cement hydration model including kinetic aspects is therefore developed using Avrami and Knudsen kinetic laws [1] for respectively clinker and slag hydration mechanisms. The influence of parameters such as the replacement ratio of Portland cement by slag, the water-to-binder ratio, the portlandite consumption is captured using stoichiometric relationships between the reactants and the products. Volume fractions of hydration products in slag blended cement pastes at different curing ages are also estimated and discussed in this work. Finally, the overall elastic properties of REVs of recycled mortars are computed so as the compressive strengths at different curing ages using the downscaling principle and the well-known Drucker-Prager failure criterion [2]. Compared to the experimental results, the established model is found to predict accurately the macroscopic elastic modulus and the compressive strengths of mortars containing slag and recycled sand at different curing ages.

Concrete carbonation reduces the pH of the cementitious matrix, which can potentially lead to reinforcement corrosion. In urban tunnels, where CO₂ concentrations are elevated, accurately assessing the progress of carbonation is essential for planning maintenance and repair actions. This study presents a predictive model for concrete carbonation in such environments, based on established formulations and calibrated through a dedicated laboratory experimental campaign. The model effectively estimates carbonation depth and porosity
evolution, providing a reliable tool for service-life assessment of concrete in urban tunnel conditions.

Creep and shrinkage are essential characteristics of the material behaviour of concrete. To study the influence of real environmental conditions on the time-dependent material behaviour, back in 2017, a longterm testing campaign on large-scale specimens was initiated by the Research Unit Structural Concrete at TU Wien, and the measurements are still ongoing. The long-term testing campaign consists of 12 large-scale specimens, which are stored outside and they are exposed to real environmental conditions. The measurements of more than eight years indicate the influence of environmental conditions on the time-dependent behaviour. Furthermore, a pronounced influence of the production date (the season of the year in which the concrete elements are cast) is observed. A theory capable of implementing the influence of the changing environmental boundary conditions is needed to capture this influence in the model. The extended micro-prestress solidification theory (XMPS) provides an appropriate framework for capturing this influence. Therefore, the paper presents a fourstep approach to model the influence of environmental boundary conditions on the temperature, moisture and hydration field. To clarify the question posed in the title, the measurements of more than eight years are compared with the prediction of the model using the measured environmental boundary conditions. The comparison shows, that the measured behaviour of the concrete specimen is replicable with the model if the environmental boundary conditions are appropriately implemented. Furthermore, the influence of the coupling between the hydration field, temperature field and moisture field is studied, and the comparison with the measured data shows that the full coupling between these fields leads to the best model prediction.

Extending French nuclear power plants to 60 years requires verifying the long-term integrity of concrete containment buildings under Severe Accident (SA) conditions, namely, exposure to 150°C and 90% RH. An autoclave with an internal hydraulic jack was used to reproduce SA conditions, axial delayed strains were measured, and the in-situ Young’s modulus of concrete cylinders was determined. In parallel, a simplified thermo-hydro-mechanical (THM) model is developed assuming the gas phase is only composed of water vapor. The TH part includes temperature-dependent sorption and the change of porosity, density, and permeability. The mechanical model adopts Burger’s rheology to predict basic creep, drying creep, shrinkage, transient ther-mal deformation (TTD), and Young’s modulus degradation. A 2D homogeneous axisymmetric finite-element model is used to simulate the creep test. Experiments and simulations show rapid strain changes within the first 24 h, followed by a steady state, indicating that most strains accumulate early during SA exposure.

Cement-based materials such as concrete are among the most common in civil engineering applications. The complexity of its response can mainly be attributed to its heterogenous nature. Sound knowledge of features such as the wall effect, and their relation to the internal structure, remain critical to the accurate representation of concrete behaviour in computational models. The presence of the wall effect on the material meso-structure has previously been demonstrated both experimentally and numerically, though only limited work addressed its effect on the material properties. The current contribution aims at performing such investigations by means of the Lattice Discrete Particle Method (LDPM). It is a powerful discrete mechanical model that effectively can simulate the heterogenous nature of concrete on the meso-scale. Recently, the framework was enhanced by a two-phase formulation, thereby allowing to introduce meaningful variability in elastic material properties linked to the heterogeneous mesostructure. This paper demonstrates the capabilities of the model in reproducing the wall effect in concrete.

The Koralm tunnel is a railway tunnel in the south of Austria. The segmental tunnel lining rings in construction lot KAT3 consist of seven prefabricated reinforced concrete tubbings. So-called measurement rings are equipped with 38 embedded vibrating wire strain gauges. They measure the normal strain in circumferential direction. The present work is focused on the strain data from nine measurement rings. They are located close to each other in a geologically interesting area near the Lavanttal fault system. The evaluation of the monitoring data includes computation of the normal stresses in both the circumferential and driving directions, as well as quantification of the utilization degree of the tubbings. This is done by considering the long-term viscoelastic behavior of mature concrete within the framework of a hybrid, i.e. computational-experimental, approach developed by Razgordanisharahi et al. [12]. Thereby, normal strain histories measured inside the tubbings are translated into stress histories using an integro-differential viscoelastic model. It is based on the assumptions of a plane strain state in the tunnel cross-section planes and a plane stress state in the planes parallel to the tangential plane of the midsurface of the tunnel lining. The utilization degree of concrete surrounding the vibrating wire strain gauges is determined using the Drucker-Prager failure criterion. The largest utilization degree determined in any tubbing is taken as the utilization degree of that tubbing. The central result of the present work is the visualization of the development of the utilization degrees in the nine measurement rings over the first two years after the start of structural monitoring. At the end of the evaluation period, the largest utilization degree of the measurement rings is approximately 42 %.

Impressed current cathodic protection (ICCP) is one of the typical methods to protect reinforced concrete from corrosion damage. However, continuous application of current will induce acidification near the anodic region and cause degradation of ICCP system. In this study, the chemical characteristics of cement-based matrix at anodic region under the effect of ICCP are evaluated by an integrated numerical platform. Validation is first conducted based on the available experimental data, then parametric study is done to investigate the key factors influencing matrix deterioration. Finally, possible countermeasures to mitigate anodic deterioration are raised. From this study, it is found that the pH value of pore solution at anodic region gradually decreases as the current applies, resulting in the decline of matrix conductivity as well as the protection efficiency, which becomes the main reason for the ICCP degradation.

This research proposes a deep learning-based semantic segmentation method using U-Net to de-tect internal cracks in concrete cores extracted from in-service structures, employing X-ray Computed Tomog-raphy (CT). A major challenge in deep learning-based crack detection is the extreme class imbalance in the dataset. In the dataset used in this paper, the crack class accounts for only 0.5% and the void class for 0.7%, while coarse aggregates, mortar, and background dominate the composition. To address this imbalance, multi-class classification approach was adopted, and a novel Class-frequency-aware Focal Loss (CFL) was proposed. CFL applies nonlinear weighting according to the occurrence frequency of each class, thereby enhancing learn-ing for minority classes. In the results, multiclass classification outperformed binary classification, and the proposed CFL achieved notable improvements in F1-score. However, the high detection sensitivity of CFL was found to be accompanied by an increase in false positives in regions such as mortar areas.

EDF’s long-term energy strategy involves extending the lifetime of its nuclear reactors, potentially
beyond 60 years. A key element in this objective is ensuring the durability of the concrete containment
building (CCB), which is essential for reactor safety. While most ageing studies focus on concrete and steel, the role of surface coatings is often neglected. These coatings, applied to limit leakage, significantly affect the drying process by acting as moisture barriers. This reduces drying shrinkage and creep, which are key contributors to long-term deformation. This study evaluates the impact of coatings on the CCB through a comparative numerical analysis. Two configurations were considered: one not accounting for coatings in its model and one modeling them. Thermo-hydric simulations providing temperature and moisture fields up to the 8th ten-yearly inspection on the CCB (VD8) were used in long-term mechanical computations. The results show that coatings can reduce drying rates, tensile stresses, and creep-related deformations, leading to a more stable long-term behavior of the containment.

This research includes experimental and analytical studies that revealed the mechanisms of the shear stress distribution along the adhesive-concrete interface of epoxy adhesive anchor fixed with a short embedded length (L=50 - 100 mm) and different diameter of the fixing hole (D=14 - 40 mm). The averaged shear rigidity was calculated with FEM that could be a representative value of all the adhesive layers and their adjacent interfaces. The achieved shear rigidity was used to compose a macro model based on the shear-lag theory. Its model enabled to make simulations with varied shear rigidity of the adhesive layer, finally finding the relationship between the interface properties and the shear stress distribution at the interface.

The Italian infrastructural heritage is rather dated, with a large number of reinforced concrete and prestressed concrete bridges built between the ‘50s and the ‘80s, having already exceeded their expected service life. In many countries, the qualitative assessment of bridge vulnerability often relays on defect-based indexes derived from visual inspections. Many of these defects are related to reinforcement corrosion, which can be-come important in case of aggressive environments and/or insufficient maintenance. This study focuses on the numerical investigation of the effects of increasing corrosion levels on the seismic capacity of an existing via-duct pier in a marine environment. The time-dependent failure mode, with the possible change in the location of the plastic hinge, and/or the occurrence of brittle mechanisms related to rebar buckling or to an anticipated rebar rupture caused by a progressive steel embrittlement, are analysed through finite element analyses.

<p>This study investigates the effectiveness of iron-based shape memory alloy (Fe-SMA) U-shaped stirrups for shear strengthening of reinforced concrete (RC) beams in combination with near-surface mounted (NSM) carbon fibre reinforced polymer (CFRP) laminates. A three-dimensional multidirectional fixed smeared crack model was used for numerical simulations. The model&rsquo;s accuracy was first verified using experimental data from RC beams strengthened solely with NSM CFRP laminates. Subsequently, Fe-SMA stirrups were incorporated to evaluate their performance under service and ultimate limit states. The effects of prestress level and activation sequence on Fe-SMA stirrups were examined to identify an optimal hybrid configuration. Results show that using 𝜌𝑠𝑤=0.64% U-shaped Fe-SMA stirrups prestressed to 80% of its yield stress, combined with 𝜌𝑓𝑤 = 0.11٪ NSM CFRP laminates, increased shear capacity by 100% compared to the reference beam and by 28% relative to beams strengthened only with NSM CFRP. Moreover, applying the estimation of the coef-ficient of variation (ECoV) method reduced the predicted load capacity by 30&ndash;38%.</p>

With the rapid advancements in experimental techniques and the growth in the amount of available data, especially when using digital image correlation and tomography, modelling is facing the challenge of transforming this enormous amount of knowledge into analytical equations that govern the material response. Classical constitutive equations may struggle to capture complex material responses, which is among the reasons why data driven approaches emerged. In this study, we apply a data-driven scheme to the modelling of failure of a quasi-brittle material such as concrete and discuss the difficulties induced when modelling localized failure. For the sake of simplicity, we consider a one-dimensional problem. Synthetic data sets are generated from a bi-linear damage model and exhibit strain softening. As expected, the one-dimensional example of a bar subjected to tension demonstrates that the obtained solutions are sensitive to the finite element discretization. A localization limiter is needed and the implementation of a non-local (integral) model circumvents the difficulty. There is, however, a notable observation in this case: optimal sets of strain, stress, and non-local history variable lie consistently outside the data set and do not converge within the data set upon mesh refinement. Several possibilities for solving this problem are considered, from the enlargement of the data set with non-local effects to the introduction of an additional constraint e.g., following the Lip-field approach. The latter method preserves locality of the constitutive response and it is found to be very easy to implement.

Concrete cracking is analyzed using nonlinear fracture-mechanics-based constitutive models within a finite element framework. In such simulations, the predicted behavior of reinforced concrete is high-ly sensitive to the assumed crack spacing or crack band size, particularly when relatively large finite elements are employed. To alleviate this limitation, the present study introduces an approach in which artificial neural network surrogate models are used to estimate the crack spacing in reinforced concrete structures. Model uncertainties in terms of mean and maximum crack width are evaluated against a database of laboratory tests. The influence of reinforcement layout, geometric simplifications and mesh discretization on these uncertain-ties is examined. Overall, the proposed modelling strategy introduces an advanced tool for assessment of crack widths and mainly crack spacing in reinforced concrete structures at the serviceability limit state.

Reinforced concrete structures traditionally rely on Bernoulli-Euler beam theory, which assumes linear stress distribution. However, in D-regions areas near support or geometric discontinuities these assumptions break down, and more advanced methods are required, Strut and Tie method (STM) is one of the most popular. STM models rely heavily on mechanical judgment of the engineer, to determine optimal configurations, creating barriers to efficient design. This study examines machine learning algorithms to predict internal forces in deep beams with consider as D-regions. A hybrid ML/AI data bases were evaluated using standard formulation, and validated for three ML/AI approaches, linear regression, with and without polynomial expansion (2nd and 3rd order), and Artificial Neural Networks (ANN). The most advanced linear regression model and the ANN model achieved excellent accuracy, which is appropriate for structural design. The results demonstrate that machine learning can effectively automate STM analysis for deep beams, eliminating expert-dependency and enabling efficient structural design more types of D-regions.

Reliable prediction of fatigue lifetime is essential for ensuring the durability of structures subjected to cyclic loading, particularly when non-uniform load histories are involved. Such scenarios pose a significant challenge, as load sequence effects strongly influence fatigue behavior while making conventional highcycle fatigue simulations computationally demanding. This study introduces a physics-based machine learning (ϕML) framework for efficient prediction of fatigue lifetime under variable loading conditions. The approach employs a feedforward neural network in which experimentally observed fatigue characteristics are embedded as physical constraints within a customized loss function, enhancing generalization and physical consistency. The network is trained using simulation data generated by an anisotropic continuum damage model for fatigue. Model calibration and validation are performed using experimental fatigue data of concrete cylinders under uniaxial compression, with the training data capturing the effect of different loading sequences. The ϕML model shows superior performance compared to purely data-driven neural networks, particularly when only limited data are available. A general prediction algorithm based on the trained ϕML model is then applied to complex loading scenarios involving multiple load transitions. The obtained results reproduce experimentally observed reductions in fatigue lifetime with increasing load jumps, demonstrating the model’s robustness and interpretability. Overall, the proposed ϕML approach offers a computationally efficient and physically consistent framework for fatigue life prediction and holds strong potential for integration into digital twin systems for real-time structural health monitoring.

Addressing age-related deterioration of road bridges requires efficient crack detection methods to replace traditional visual inspections. This study proposes a deep learning-based approach for detecting pavement cracks in RC bridges using UAV-captured visible images. The method addresses the challenge of varying illumination conditions by implementing a two-stage process: (1) scene classification to distinguish noisy areas, sunlit pavement areas, and shaded pavement areas, and (2) specialized crack detection models trained for specific lighting conditions. U-Net architecture is employed for both scene classification and crack detection models. Image processing techniques are applied in L*a*b* color space to enhance model performance. The approach is validated on three in-service RC bridges. Results demonstrate high-precision scene classification and improved crack detection accuracy when using lighting condition-specific models. The highest detection accuracy is achieved when the lighting conditions used for model training match those of the target detection areas, confirming the effectiveness of condition-specific training approaches.

This study compares LSTM neural networks and physics-based heat balance models for predicting concrete dam surface temperatures under shadow effects from surrounding terrain. Three-dimensional shadow modeling is integrated with UAV-LiDAR point cloud data to quantify shadow-induced radiation variations. Monitoring data from 2023-2024 are analyzed to evaluate physical consistency and spatial generalization capability. Strong correlation (R²=0.562-0.587) between radiation reduction and temperature changes is demonstrated by the heat balance model. In contrast, near-zero correlation (R²=0.0001-0.0083) is observed in LSTM predictions. Spatial analysis reveals identical predictions (r=0.9999) across different monitoring locations by LSTM, indicating that spurious temporal correlations are learned rather than causal shadow mechanisms. These findings demonstrate that high accuracy metrics cannot guarantee physical correctness in data-driven models. Physics-based or hybrid approaches are recommended for structural health monitoring applications requiring spatial generalization beyond train-ing data locations.

Projectile penetration into multi-layer composite targets involves highly non-linear and dynamic physical processes, including stress wave propagation, material failure, large deformations, and interactions between different material layers. These phenomena are governed by partial differential equations (PDEs) representing conservation laws and constitutive behaviour under high strain-rate conditions. Solving these equations accurately is essential for understanding and predicting impact behaviour. However, conventional numerical methods such as finite element (FE) approaches, though accurate, can be computationally expensive and timeconsuming. This limitation becomes critical when performing multiple simulations across input parameters such as impact velocity, material properties, projectile geometry, and boundary conditions. This work introduces a Physics-Informed Neural Network (PINN) framework to model projectile penetration in multi-layer composite structures. Unlike traditional data-driven machine learning models that require large amounts of labelled data, PINNs embed the physical laws of the problem directly into the learning process. The governing PDEs and relevant initial and boundary conditions are incorporated into the loss function. This allows the network to learn physically consistent solutions without relying on labelled simulation or experimental data, making the method particularly useful when data collection is limited or computationally costly. Physics-based feature engineering is applied to improve the PINN’s learning capability. Features informed by impact mechanics are inputs to the neural network. These physically meaningful inputs help the network better understand the structure of the solution space and enhance generalization across a range of impact scenarios. The model is trained to satisfy all relevant physical constraints, ensuring that the solution respects the underlying mechanics of high-velocity penetration events. An adaptive loss balancing technique is employed to improve the stability and efficiency of the training process. During training, the different components of the loss function—representing the PDEs, boundary conditions, and initial conditions—may evolve at different rates, leading to imbalance and slower convergence. The adaptive approach dynamically adjusts the weighting of each component, ensuring that all physical constraints are learned effectively and in proportion. This technique improves convergence behaviour and leads to more accurate and robust solutions. The proposed PINN framework is validated with the experimental results under various impact conditions. These include different projectile velocities, shapes, and layered target configurations. The results show that the PINN can accurately predict key physical quantities such as the depth of penetration. The model strongly agrees with experimental results and generalizes unseen scenarios well. Once trained, the model can deliver real-time predictions, offering a fast and efficient alternative to traditional simulation methods for repeated evaluations or parametric studies. Integrating physical knowledge into the neural network architecture makes the PINN a promising tool for simulating complex impact problems computationally efficiently. This approach offers significant advantages in the study and design of advanced protective systems across a range of engineering applications, including defence, aerospace, and civil infrastructure.

Steel-plate concrete (SC) structures are increasingly adopted for protective infrastructure due to
their superior energy absorption and robustness under extreme loading. However, the influence of internal connectors under high-velocity impact remains insufficiently understood. This study evaluates the effects of shearstud spacing and tie-bar configuration on the impact resistance of SC panels using a detailed three-dimensional LS-DYNA model. The Karagozian & Case (K&C) concrete model with a user-defined dynamic increase factor calibrated from SHPB tests was employed to capture strain-rate-dependent concrete behavior. Steel faceplates and connectors were modeled with rate-sensitive plasticity and explicit steel–concrete interaction. Parametric analyses revealed that closer connector spacing enhances composite action but may intensify localized damage near the impact zone, whereas tie-bars improve through-thickness confinement and reduce global bulging. Numerical trends showed good agreement with available experimental results. These findings will directly inform an upcoming gas-gun experimental program and support improved design strategies for SC structures under extreme impact loading.

This study presents a poromechanical approach for analysing fire-induced fractures and mass transport phenomena in reinforced concrete (RC) structures. The model integrates multiphase flow and gaseous kinetics within the multi-scale simulation platform, enabling coupled evaluation of vapour pressure, cracking, and moisture migration under extreme thermal conditions. Comparisons with the diffusion model demonstrate that the poromechanical model captures localized rapid transport along cracks and provides more realistic pre-dictions of thermal damage. The poromechanical model is further applied to assess the post-fire performance of scaled cylindrical RC walls representing the reactor pressure vessel pedestal in a nuclear power plant. Sim-ulation results show that rehydration during post-fire curing contributes significantly to strength recovery after 400 °C heating, while severe degradation occurs at 800 °C heating. The proposed poromechanical model offers a rational and safety-oriented tool for evaluating RC structures under high-temperature exposure.

Delayed Ettringite Formation (DEF) is a concrete swelling pathology where early age elevated temperatures cause sulfate release, which can later precipitate as ettringite in the presence of moisture, leading to serious structural damage. Many structures built in the late 1990s now show symptoms, yet predicting their residual capacity and the reaction’s evolution remains difficult. French guidance recommends thermo-hydro-chemo-mechanical (THCM) modelling when crack growth is rapid or long-term performance assessment is needed (Godart & Divet 2018). Sellier & Multon (2018) then proposed a model to simulate the effect of DEF on concrete structures, but it faces large input uncertainties because key data are often unavailable years after construction. This study aims to identify the most influential input parameters for simulating DEF-affected concrete structures via a comprehensive sensitivity analysis on a bridge pier.

Solid reinforced concrete structures, such as pile caps and anchor blocks, are characterised by complex threedimensional stress states. Today, a widely adopted design tool that can reliably determine the stress field in solid reinforced concrete structures under serviceability limit state conditions is lacking. Current design practice often relies on hand calculations, such as the strut-and-tie method or even simple linear elastic models. Consequently, the design and verification of these structures are both very time-consuming and tend to be conservative. This leads to designs with excessive material usage and low utilisation. While advanced non-linear finite element methods offer detailed analysis of these structures, their practical application is often limited by numerical instabilities and the need for many material parameters, which may not be practical during the initial design phase. Finite element limit analysis provides a more efficient alternative, using rigid plastic models and convex optimisation. However, though suitable for ultimate limit state calculations, such models are incompatible with serviceability requirements, where an accurate representation of the cracking phase is needed. In this paper, a design-oriented tool for analysing solid reinforced concrete structures is introduced. The method uses the principle of minimum complementary energy and convex optimisation in a finite element framework to determine the structural response for a simulated elasto-plastic material model. The reinforcement can be modelled as smeared or as discrete bars embedded in the tetrahedral elements. The method is validated against a simple example with an analytical solution and against existing numerical methods. Finally, the method is applied to a complex example, demonstrating numerical stability and efficiency in capturing the structural response for a non-linear material model.

While state-of-the-art constitutive models are able to reproduce the mechanical behavior of concrete under compressive and tensile loading with satisfactory accuracy, more complex failure modes caused by shear or mixed-mode loading often result in inaccurate predictions in numerical simulations. Although numerous constitutive models have been developed in recent decades, the systematic validation and objective performance assessment of such models have received comparatively little attention. The present contribution assesses the predictive capabilities of state-of-the-art constitutive models under shear-dominated and mixed-mode failure. A gradient-enhanced extension of the Microplane M7 model, originally proposed by Caner and Bazant (2013), is compared to two established approaches: a gradient-enhanced extension of the Concrete Damage-Plasticity model by Grassl & Jirasek (2006) and the gradient-enhanced Microplane Damage-Plasticity model by Zreid & Kaliske (2018). The predictive accuracy of these models is assessed using three-dimensional implicit finite element simulations of benchmark tests involving notched prismatic specimens subjected to torsional, antisymmetric four-point, and combined shear-tensile loading. Special focus is placed on the models’ ability to predict the load-bearing capacity and post-peak behavior, including crack initiation and propagation. The results show that two of the three investigated models provide accurate predictions of shear-dominated concrete failure, while the third exhibits limitations under such loading conditions, indicating that further refinement remains necessary.

This study presents a series of non-linear finite element analyses (NLFEA) conducted in conjunction with an experimental campaign on prestressed concrete beams made continuous by a cast-in-situ diaphragm and deck slab. Due to the lack of experimental data for this beam typology and its intricate structural
behavior, these specimens provide an ideal test-case for an unbiased numerical study. The analyses include blind predictions, post-dictions, and sensitivity studies on six specimens. Sensitivities are explored by varying finite element discretization, constitutive models, and solution procedures. A brief overview of the experimental program is provided, and a reference model is established as the basis for the numerical study. NLFEA results are compared with experimental findings, and model uncertainties are quantified. Blind prediction outcomes demonstrate that the reference model can accurately estimate ultimate failure load and failure mode, where the post-dictions result react rather insensitive to updated material properties. However, the numerical response is significantly influenced by element size and the adopted smeared crack formulation (rotating versus fixed crack approach). It remains unclear whether this size dependence arises from specific modeling choices or structural details unique to the experiment. Further investigation into this topic is needed and is part of ongoing research activities.

In the present study, a mathematical framework for modeling the behavior of concrete under large deformations is developed. To capture the full degradation process of concrete, an over-nonlocal damage-plasticity theory based on an implicit gradient formulation is employed. Specifically, the coupling between plasticity and damage enables the description of both irreversible deformations and the softening characteristic of concrete, while the nonlocal formulation eliminates localization and mesh dependency, ensuring a realistic prediction of the material response. In addition, a finite element formulation is derived, incorporating the equilibrium equations along with an additional field associated with the Helmholtz-type equation of the gradient-enhanced model. The evolution equations are numerically integrated using a strongly objective algorithm, and the stress-update procedure is presented. Finally, the predictive capabilities of the proposed framework are demonstrated through simulations of reinforced concrete specimens, focusing on the loss of stability and failure of reinforced columns under compressive loading.

This study presents a 2-D numerical framework to simulate the behavior of reinforced concrete
(RC) beams, both unstrengthened and externally strengthened with fiber-reinforced polymer (FRP). The approach is based on an alternative Finite Element Method (FEM) that uses positions instead of displacements as primary unknowns, allowing for a natural treatment of geometric nonlinearity. The Mesh Fragmentation Technique (MFT) is adopted to capture the nonlinear behavior of concrete by inserting High Aspect Ratio (HAR) solid elements between bulk elements. Crack initiation and propagation are modeled through a continuous damage model applied only to the HAR elements, keeping the bulk elements linear elastic. A position-based HAR interface element is also introduced to model the interaction between concrete and reinforcements. A J2 continuous damage model describes the bond-slip behavior and degradation between concrete, steel bars, and external FRP sheets or plates. The main contributions include the integration of the MFT with HAR interface elements to represent both crack growth and bond deterioration, combined with the extension of these concepts to a position-based FEM for general nonlinear analyses. The results confirm that the proposed framework accurately reproduces the response of RC beams and captures FRP debonding due to intermediate crack formation.

Unreinforced masonry (URM) walls are highly sensitive to non-proportional loading histories, particularly when foundation settlement precedes lateral loading. In such cases, pre-damage induced by settlement can significantly affect the subsequent structural response and cannot be adequately represented using
proportional loading assumptions or equivalent reduction factors. A Total Sequentially Linear Analysis (Total SLA) framework is developed to investigate the combined effects of boundary conditions, geometry, and settlement-induced pre-damage on the pushover response of URM walls. The numerical model represents masonry units as linear elastic continua and concentrates nonlinearity within zero-thickness interface elements governed by discrete damage modes. Settlement and pushover are applied sequentially within a unified event-driven formulation, allowing damage states to be inherited across loading stages. The results show that the initial elastic response is largely insensitive to the top boundary conditions, whereas significant differences emerge during the softening phase. Fixed-top configurations exhibit a more gradual degradation of stiffness. Cantilever and free-top conditions, in contrast, show sliding-dominated behavior. Settlement causes irreversible damage, reducing both stiffness and peak capacity during subsequent pushover loading. The effects are amplified in walls with openings. These results demonstrate that neglecting load-path dependency may lead to inaccurate predictions of stiffness degradation and peak capacity in URM walls.

This study examines the microstructural and mechanical behavior of composite specimens comprising 3D-printed concrete and ordinary mortar. CT-based pore analysis was carried out for the printing, mortar, and bonding regions, and the low-order probability function was applied to quantify pore distribution and continuity. Directional tensile strength and stiffness were further evaluated using a phase-field fracture model. The printing region showed an anisotropic pore network with relatively low continuity parallel to the layer stacking, while the mortar region displayed isotropic characteristics. The bonding region exhibited an intermediate pore distribution but was notably affected by continuous pores oriented perpendicular to the stacking direction, leading to reduced interfacial bonding strength. Overall, the findings highlight how interfacial morphology governs the mechanical response of printed–mortar composite systems.

Additive Manufacturing (AM) methods like Fused Deposition Modelling (FDM) in 3D printing present the opportunity to construct geometrically complex polymeric reinforcements for cementitious composites. However, FDM 3D printed material can be highly anisotropic such that printing path-dependent models using the Lattice Beam Model (LBM) have been developed. These explicitly model the inter-layer and intralayer bonds that exist in FDM 3D printed reinforcements by assigning experimentally obtained interface properties that significantly differ from the bulk material. To illustrate the aforementioned methodology, it is used to numerically investigate particularly complex types of FDM 3D printed reinforcement for cementitious composites subjected to bending. These have a Poisson’s ratio that is tailored in accordance with the stress-strain distribution, such that their cross-sections change over the height of the beams. Three Tailored Poisson’s Ratioreinforcement (TPR) designs are modelled considering printing path-dependent anisotropy as a result of the FDM 3D printing technique. Subsequently, preliminary simulations of these reinforcements submerged in cementitious matrix to form a composite are discussed. The lattice models show that incorporating the anisotropy present in FDM 3D printed reinforcement is important, because simulations assuming isotropic properties result in significant overestimation in strength and completely change the fracture behaviour.

3D concrete printing (3DCP) brings automation to construction, reduces material usage, increases design flexibility, and eliminates the need for formwork. However, it is a complex process governed by numerous interdependent parameters that are often tuned through trial-and-error. This can lead to unforeseen failures during printing, such as instability or plastic collapse of the material. Computational modeling offers a means to predict and prevent such failures by enabling virtual design assessment, process optimization, and evaluation of how variations during printing influence the final structure. The structural failure during printing is primarily governed by the material response of fresh concrete, making the choice of constitutive model critical. Plasticity-based models are commonly employed to assess buildability, yet most approaches neglect the nonlinear behaviour observed experimentally for fresh concrete before failure. This simplification often leads to underestimation of deformations and overprediction of structural stability. In this work, a numerical framework is developed to investigate how nonlinear isotropic hardening influences the failure behaviour of printed structures. The model is based on a von Mises plasticity formulation with a saturation-type hardening law and is implemented in an updated Lagrangian finite element framework with the Jaumann stress rate to capture geometric nonlinearity. The printing process is simulated through a pseudodensity-based layer activation method, while time-dependent material parameters are incorporated to account for structural buildup and aging. A systematic parameter study is performed on printed cylinders with varying diameters and hardening parameters to investigate how geometry and material hardening jointly influence buildability. The results show that the number of printed layers before failure depends strongly on the hardening rate, particularly for slender, instability-prone geometries, while stable configurations are largely unaffected.

A lack of reliable predictive models for early-age behaviour is impeding the widespread adoption of 3D concrete printing (3DCP), a new construction technique that is gaining popularity. The layer-by-layer deposition method presents special difficulties regarding changing mechanical characteristics, heat effects, and moisture loss. In this work, the time-dependent response of printed concrete is simulated using a Multiphysics Finite Element Model (MFEM) framework. By connecting the development of shrinkage and strains with the progression of hydration, the model integrates mechanical behaviour with hygro-thermal-chemical (HTC) analysis. This model that has been calibrated against published calorimetry data is used to capture the kinetics of hydration. Eigenstrains are used to model important early-age processes, such as drying shrinkage, autogenous shrinkage and total shrinkage. The framework facilitates process parameter optimisation and provides predictive insights into early-age behaviour. Experimental validation and extension to long-term durability modelling will be part of future research.

Mixing time is a critical parameter in printcrete (3D printed concrete), directly influencing mixture homogeneity and printability, which in turn govern construction efficiency and overall cost. This study proposes a computational framework for determining the optimal mixing time based on a non-contact monitoring system. The homogeneity was quantitatively characterized by analyzing surface texture images, from which a texture index was computed as the standard deviation of grayscale values to evaluate degree of homogeneity. Simultaneously, printability was assessed via rheological properties, with key parameters derived through a linear calibration model linking mixer torque to offline rheometric data. By integrating target thresholds for both homogeneity and rheological performance, the optimal mixing time was identified using a non-contact monitoring system. The proposed method was applied to a printcrete mixture incorporating a polycarboxylate ether superplasticizer and an aluminum sulfate-based accelerator. Results demonstrate that the approach reliably determines stage-specific mixing times, ensuring consistent printability and mechanical performance.

In this contribution we discuss the differences and similarities of two extensions of damageplasticity approaches for concrete: (localizing) gradient-enhancement and the phase-field approach to fracture. Due to the similarities of their governing equations, we first present a general framework encompassing both approaches. In a second step we elaborate on their numerical implementation, and show that the same type of finite element—characterized by one scalar field, i.e., the phase field or the nonlocal damage driving force, in addition to the displacement field—can be used for both approaches. However, the consistent tangent operators on finite element level differ slightly. The capabilities of the models are assessed by means of two numerical benchmark examples, namely the L-shaped panel test and three-point bending tests on notched specimens. In conclusion, both approaches are promising in terms of their ability to deliver mesh-insensitive solutions, localized crack patterns, and overall structural response. Hence, in the future, a more detailed investigation, including more complex failure mechanisms, is required for an in-depth assessment of the models.

Advances in 3D-printed concrete (3DPC) require numerical models capable of capturing its lay-ered structure and interfacial behavior. This work introduces a novel LDPM-based modelling approach in which the full specimen is discretized with tetrahedra, and interlayer behavior is described by locally modifying the meso-scale properties of elements positioned within the printed interfaces. As a first proof of concept, interlayer facets are assigned reduced mechanical properties, assuming a 30%, 35% and 40% decrease in tensile, shear strengths and fracture energy relative to the bulk material. A parameter-sensitivity study is performed across multiple LDPM realizations to assess how random meso-structural arrangements influence the global response. The simulations exhibit characteristic variability in failure patterns, with crack initiation occurring either along mid-span or along the weakened interlayer depending on the seed. The results demonstrate the capability of this location-based LDPM strategy to capture interlayer-driven variability and lay the groundwork for future cali-bration against experimental data.

This contribution presents a three-dimensional force-based Timoshenko beam formulation for the nonlinear analysis of prestressed concrete members with evolving bond-slip interaction. A set of slip degrees of freedom is introduced at the element level to represent the relative displacement between tendons and concrete, governed by a nonlinear bond law and compatible with arbitrary tendon layouts. Prestressing can be applied through initial strains, imposed slip, or force-controlled loading, and the element naturally accommodates staged activation, grouting, and time-dependent losses due to shrinkage, creep, and relaxation. Tendon strains are obtained by projecting the beam deformation field onto the tendon axis through an isoparametric mapping, enabling the simulation of curved bonded or unbonded tendons. Concrete behavior is modeled through a three-dimensional damage-plasticity law, while tendons and reinforcing steel follow uniaxial nonlinear constitutive models. The resulting element combines force interpolation, explicit slip kinematics, and consistent sectional integration within a computationally efficient force-based framework. A validation study on prestressed CFRP-strengthened beams demonstrates the ability of the model to capture bond degradation, anchorage softening, prestress losses, and rupture-induced force redistribution. The formulation provides an efficient and general tool for simulating prestressed concrete structures with complex tendon configurations, partial bonding, and staged construction effects.

The J-integral is a well-known path integral used to calculate the energy release rate in an elastic, homogeneous medium with a localized crack. In this study, it is extended to a heterogeneous medium, where Young’s modulus varies spatially according to a lognormal random field. It is shown that the mean of the J-integral remains path-independent and accurately represents the mean energy release rate. However, in a random medium, the mean energy release rate differs slightly from the deterministic case based on the average modulus. The coefficient of variation (CoV) of the J-integral, on the other hand, is generally pathdependent. This means that the variability in the energy release rate is influenced by the specific path chosen for the calculation of the J-integral. The CoV of the J-integral matches the CoV of the energy release rate only when the domain enclosed by the contour is smaller than the correlation length of the elastic modulus field. When the contour encloses a larger domain, the J-integral significantly underestimates the variability in energy release rate. This indicates that, for larger domains, a simple path-based approach is inadequate to fully capture the statistical variations introduced by material heterogeneity. To accurately capture the energy release rate statistics for arbitrary contours, an additional term is derived for the J-integral. This new term is a domain integral that accounts for material heterogeneity.
Furthermore, the analysis reveals that the correlation length of the elastic modulus field has minimal impact on the mean energy release rate but strongly influences its variability. Specifically, for a given specimen, the CoV of the energy release rate decreases significantly as the correlation length decreases.

This study investigates the algorithms for mapping the random fields of material properties onto finite element (FE) meshes and examines their consequences for stochastic FE analysis of damage and fracture in quasibrittle materials. A continuum damage constitutive modeling framework is adopted, in which the constitutive law of each finite element is regularized to ensure correct energy dissipation for different mesh sizes. Three mapping methods for random fields are considered: (1) local mapping, where the constitutive property of an element is directly sampled from the random field at a specific point (e.g., element centroid or integration point); (2) local averaging, where the property is obtained by averaging the random field over the element domain; and (3) mechanism-based mapping, where the projection of the random field onto the FE mesh is governed by the prevailing damage mechanism within the element. These methods are implemented in stochastic FE simulations of recent bending beam tests on Dunnville sandstone. Comparison between experimental and simulated results demonstrates the critical role of linking the mapping algorithm to the evolving damage behavior of individual finite elements. The analysis further elucidates the influence of multiple characteristic length scales—including FE mesh size, correlation length, and fracture process zone width—on the choice of mapping method.

In multiscale modeling of heterogeneous softening materials, the choice of boundary conditions (BCs) applied to the fine-scale (micro/meso scale) model significantly influences both the strain localization patterns and the macroscopic response. Commonly used Periodic BCs tend to produce artificially ductile behavior, characterized by excessive energy dissipation, when the localization band inclination does not match the periodicity directions. To address this limitation, recently proposed Tessellation and Percolation-path-aligned BCs adapt the periodicity frame to align with the evolving localization zones and enable the formation of arbitrary localization bands. In this work, we perform a numerical study to assess the applicability of these BCs to a discrete lattice particle model of concrete at the mesoscale. A two-dimensional square fine-scale model is subjected to uniaxial tension under varying loading directions. The resulting macroscopic responses and localization patterns are compared against those obtained using conventional periodic BCs. The results indicate that Percolation-path-aligned BCs exhibit major shortcomings: they can lead to multiple localization bands due to uneven straining of their two boundary sections, with the weakly constrained section prone to spurious localization. In contrast, Tessellation BCs consistently produce a single, well-defined localization band. The band length is determined solely by the square geometry of the model, making it straightforward to account for during post-processing. Consequently, the observed dependency of the dissipated energy on the loading direction can be clearly attributed to the geometry of the model rather than artifacts of the boundary conditions.

The transition towards a greener and more resilient construction sector often deals with mix design optimization to fulfil target performance. Customised mixes generally differ in terms of aggregate and binder types, aggregate size distribution, and additives. Optimizing concrete mixes requires understanding how different components interact and affect the concrete’s overall performance. This contribution presents a 2-phase discrete meso-scale model able to simulate how chemical reactions and transport phenomena of heat and moisture are affected by aggregate and binder properties. Benchmark numerical simulations of 1D moisture and heat diffusion in concrete are performed to showcase the enhanced capability of the proposed model to capture the spatial variability in moisture and temperature gradients.

A new DEM-based 3D model for fracture propagation was developed to simulate pore-scale ther-mal-hydro-mechanical processes, including heat transfer and phase changes (evaporation and condensation) in low-porosity, non-saturated frictional-cohesive materials (like concrete). Numerical simulations used a bonded granular specimen, combining DEM with CFD (based on a fluid flow network) and heat transfer to integrate discrete mechanics with fluid and heat transfer at the meso-scale. Both the fluid (through diffusion and advection) and bonded particles (via conduction) participated in heat transfer. The coupled thermal-hydraulic-mechanical (THM) model’s results were validated through a thermal contraction test with a bonded particle assembly during cooling, which led to the formation of a macro-crack. The study examined the im-pact of the macro-crack on the distribution of fluid pressure, density, velocity, and temperature.

Carbonation in concrete has been of wide interest lately due to its potential applications in selfhealing, carbon capture/storage and carbon curing. Mineralization of CO2 in concrete is a chemo mechanical process, initiated by the dissolution of Ca2+ into the solution from portlandite (CH). It is further controlled by factors such as saturation index, mechanical stress and crystallization pressure. In a recent study by the authors (Alex et. al., 2023), the nanoscale modeling of concrete carbonation was carried out, focusing on nano-crystalline structure formation, dissolution/precipitation rates, and the development of mechanical properties, thereby establishing a benchmark for future research. In this work we make a further improvement to the simulator: coarse grain the nano-scale particles to microscale (1 particle=1 micron). The extended simulator is also designed to accommodate biologically mediated pathways such as microbially induced carbonate precipitation (MICP). Because MICP relies on the same coupled dissolution–precipitation chemistry as abiotic carbonation, the present coarse-grained formulation offers a natural bridge between these processes. In this paper we present the coarse graining part of the work. The coarse-grained system samples larger time and length scales and is validated against transition state theory (TST) rates of CH dissolution and precipitation.

This study focuses on soil-structure interaction (SSI) under seismic excitation, using a direct hybrid method. During an earthquake, repeated impacts between the soil and the foundation lead to nonlinear dynamic behavior. In this context, a new subdomain coupling method is proposed to treat the contact between the soil integrated in time using a central difference scheme, and the concrete foundation integrated using the Newmark implicit scheme. The approach is implemented and validated in MATLAB through two illustrative applications. First, a one-dimensional benchmark problem involving two bars in contact demonstrates that the formulation accurately reproduces displacements, velocities, and contact forces in excellent agreement with a full explicit algorithm. Then, a two-dimensional case study of soil-concrete foundation interaction subjected to gravity loading highlights reduced computational time compared with the full explicit method. This work pro-vides a robust and efficient framework for simulating nonlinear SSI problems in the time domain.

The LT-Bridge construction method has been developed in recent years at TU Wien. In this method, thin-walled longitudinal (L) girders made of high-strength concrete are combined with transverse (T) deck slab elements and subsequently connected by a layer of in-situ concrete. Compared to the conventional construction of multi-span post-tensioned concrete bridges with full in-situ concrete and temporary supporting structures, the LT-Bridge method enables faster construction and reduced material consumption. The Pinkabach Bridge, completed in 2022, was the first bridge built using this method. Currently, four additional LT-Bridges with lengths of up to 260 m are in the design phase in Austria. The structural design of LT-Bridges follows Eurocode 2. The webs of the thin-walled longitudinal girders typically have a thickness of only 120 mm, yet they must resist considerable shear forces and transverse bending moments that are mainly induced by traffic loads. The interaction formula for shear and transverse bending given in the new Eurocode 2 is conservative and leads to high quantities of stirrup reinforcement in the webs. To address this issue, the application of a layered shell element has been proposed for the design of the longitudinal girder webs. In this element, nonlinear material models are implemented according to Eurocode 2 for both the high-strength concrete C80/95 and the reinforcement (stirrups and longitudinal bars). This allows a realistic assessment of the load-bearing capacity under the combined action of shear and transverse bending moments. While the reinforcement of the webs in the Pinkabach Bridge was designed using the interaction formula of the new Eurocode 2, the LT-Bridges that are currently being designed can achieve further reductions in material consumption by applying nonlinear analysis with the layered shell element.

Delayed Ettringite Formation (DEF) can induce expansive products in the porosity of concrete which leads to internal swelling pressure and damage that can jeopardize the performance of the affected struc-tures. Numerical modelling can provide an appropriate solution to predict such evolution over time especially in the case of massive and critical structures. Such predictive modelling can only be reliable if the modelling hypotheses have been validated and their limitations fully assessed. This work contributes to such purpose using the poromechanical model by Sellier (2021). To evaluate the predictive capacities of the model, we select here a bridge’s pier affected by DEF and show some induced cracking that is monitored and characterized. Blind calculations are done using two distinctive softwares: finite element code Cast3M (open) and the finite volume code FLAC3D (restricted). Eventually, this benchmark aims at exploring the sensitivity to the inputs, modelling hypotheses and tools used.

Ensuring the long-term performance and safety of reinforced concrete (RC) structures depends on the ability to understand their evolving condition and the ability to assess their situation. Within Structural Health Monitoring (SHM), this requires physically meaningful indicators that capture a structure’s inherent ductile or brittle tendencies. This study revisits a validated Integrated Fracture-Based Model (IFBM) and establishes it as a foundation for damage quantification and performance assessment. The IFBM analytically describes lightly reinforced concrete beam behaviour across two key stages; crack propagation with tensile softening and crack rotation with compression softening, through a closed-form solution satisfying equilibrium, compatibility, and constitutive relationships, including bond-slip and post-cracking stress distribution. A dimensionless Ductility Number (DN) is formulated from dimensional analysis of the IFBM, integrating material, geometric, and interface parameters such as reinforcement ratio, concrete strength, elastic moduli, bond stress, and critical crack opening. The DN characterises the stability of cracking, where higher values indicate ductile, bond-controlled failures and lower values correspond to brittle, reinforcement-fracture modes. Validation against Digital Image Correlation experiments confirmed strong correlation between DN and observed failure mechanisms. The DN thus quantifies a structure’s intrinsic ductility potential, enabling SHM systems to interpret sensor data within a mechanical context. As a mechanics-based indicator, it provides a baseline for condition tracking, risk assessment, and early detection of performance deviations in reinforced concrete structures.

The existing models of concrete degradation are being challenged by the sustainability-driven emergence of new chemical compositions and exposure conditions, such as from high fractions of cement replacements in new concretes or from service life extension of existing structures. This article identifies three challenges to address for concrete degradation models to become relevant also for unconventional compositions and exposure conditions: (i) being able to draw physical predictions of macroscale behaviours starting from chemo-mechanical processes at the microscale; (ii) conceiving experiments that are model-oriented, away from the current paradigm where full degradation experiments are run first, and then models are calibrated and validated on them without feeding back to the experiments; (iii) distilling the complexity of the microscale simulations into simpler, engineering-oriented tools describing the constitutive behaviour of the concrete. The first challenge, on modelling micro-chemo-mechanical processes, is discussed in detail, presenting the structure and capabilities of a recently developed simulator, MASKE, based on off-lattice, coarse-grained, kinetic Monte Carlo. Sample results are presented, from simulations of stress-induced dissolution, dissolution-induced strain-rate dependence of stress, crystallisation pressure, and cement paste carbonation. Potential solutions to the other two challenges are then discussed, envisaging a possible interplay between reverse-engineered experiments and short-term model predictions, and the use of machine learning to surrogate the results of the microscale simulations.

This paper presents a three-dimensional analytical framework for evaluating the structural behavior of box girder bridges, with particular emphasis on long-term effects such as creep, shrinkage, and shear lagfactors often neglected in traditional one-dimensional analyses. The proposed methodology integrates advanced material models and numerical strategies to simulate sustained loading and environmental influences, thereby improving the accuracy of stress and deformation predictions crucial for reliable bridge assessment. A rate-type creep formulation is developed based on the continuous retardation spectrum, removing the need to recompute Kelvin-chain stiffness parameters at each time step. Both EuroCode 2 and Model Code 2020 creep laws are incorporated, with approximate creep functions obtained through the PostWidder inversion technique. Cracking is represented using a continuous damage mechanics framework, enabling the gradual simulation of concrete degradation and crack evolution. The implementation is carried out in Abaqus/Standard through user subroutines and implicit time integration. The framework accurately models both reinforced and prestressed concrete structures, accounting for nonlinear creep, cyclic loading, shrinkage, cracking, and steel relaxation. A detailed case study of a three-span rigid-frame bridge further demonstrates the enhanced predictive performance of the model and confirms its consistency with experimental observations.

This paper presents preliminary numerical simulations of the gap test for plain concrete using
an advanced damage-plastic constitutive model. A few fundamental model parameters are calibrated against standard bending tests of geometrically similar specimen sizes of three different sizes. The primary objective is to trace the evolution of the stress and damage distributions during the two loading stages of the full gap test, and to reveal the mechanisms underlying the observed increase and decrease in peak bending load. The results show that the non-uniform, multiaxial stress state and the resulting damage pattern induced during the initial compressive stage critically affect the specimen’s performance in the subsequent bending stage. Such structural effects are suggested to play a more important role than the specific material behavior under tension combined with transversal compression.

The progress in computational modeling of the load-bearing behavior of concrete structures from the 1980s until today is reviewed by focussing on selected topics, in which the first author and former and present co-workers were involved. The topics include ultimate load FE-analyses of a prestressed shell structure, regularization techniques for the softening behavior of concrete and modeling of the time-dependent material behavior of shotcrete. Special attention is paid to the validation and application of the numerical models to projects in engineering practice.