Publications

Journal of Engineering Mechanics - Journal paper #24

This paper investigates the effect of the horizon size on failure due to strain and damage localization in the case where peridynamics is a nonlocal theory by its own, which corresponds to most bond-based peridynamics models. Two constitutive relationships are discussed: the microelastic brittle model and a progressive damage model. The usual practice with the microelastic brittle model is to fit the microelastic constant for a given horizon size so that elasticity is recovered. At the same time, the fracture energy provides the critical bond stretch. This methodology yields an indirect determination of the tensile strength of the material, that goes to infinity as the horizon size trends to zero. With the damage model, the stretch at the inception of damage can be obtained from the tensile strength. Then, a simple one-dimensional case of wave propagation and interactions in a bar is considered. For fixed values of the horizon, convergence with a refinement of the discretization is checked. The energy dissipated upon fracture is found to be a linear function of the horizon. It is also a function of the softening response. The horizon cannot be chosen arbitrarily, unless the softening parameter is adjusted to fit the fracture energy, like in the crack band model. Surprisingly, such a methodology is very seldom mentioned in the current literature dealing with fracture modeled by peridynamics.

Journal of the Mechanics and Physics of Solids - Journal paper #23

The effect of crack-parallel stresses on the fracture properties of quasi-brittle materials has recently received significant attention in the fracture mechanics community. A new experiment, the so-called gap test, was developed to reveal this effect. While the finite element crack band model (CBM) with the physically realistic Microplane damage model M7 was quite successful in capturing the damage and fracture during the gap test, some questions remain, particularly the near doubling of the fracture energy at moderate crack parallel compression, which was underestimated by about 30%. Presented here is an in-depth meso-mechanical investigation of energy dissipation mechanisms in the Fracture Process Zone (FPZ) during the gap test of concrete, an archetypal quasi-brittle material. The Lattice Discrete Particle Model (LDPM) is here used to simulate the quasi-brittle material at the mesoscale, which is the length scale of major heterogeneities. The LDPM can capture accurately the frictional sliding, mixed-mode fracture, and FPZ development. The model parameters characterizing the given mix design are first calibrated by standard laboratory tests, namely the hydrostatic, unconfined compression, and four-point bending (4PB) tests. The experimental data used characteristic of the given mix design are calibrated by the Brazilian split-cylinder tests and by gap tests of different sizes with and without crack-parallel stresses. The results show that crack-parallel stresses affect not only the length but also the width of the FPZ. It is found that the energy dissipation portion under crack-parallel compression is significantly larger than it is under tension, which is caused by micro-scale frictional shear slips, as intuitively suggested in previous work. For large compressive stresses, the failure mode changes to inclined compression-shear bands consisting of axial splitting microcracks. Several complications experienced in the numerical modeling of gap tests are also discussed, and the solutions provided.

International Journal of Fracture - Journal paper #22

Up to the beginning of the twenty-first century, most of quasi-brittle structures, in particular the ones composed by concrete or masonry frames and walls, were designed and built according to codes that totally ignored fracture mechanics theory. The structural load capacity predicted by strength-based theories, such as plastic analysis and limit analysis, do not exhibit size-effect. Within the framework of fracture mechanics theory, this paper deals with the analysis of the effect of non proportional loadings on the strength reduction with the structural scaling. In particular, this study investigates the size-effect of quasi-brittle materials subjected to self-weight. Although omnipresent, gravity-load is often considered negligible in most studies in the field of fracture mechanics. This assumption is obviously not valid for large structures and in particular for geometries in which the dead load is a major driving force leading to fracture and structural failure. In this study, an analytical formulation expressing the relation between the strength-reduction and the structural scaling and accounting for self-weight, was derived for both notched and unnotched bodies. More specifically, a closed form expression for size and self-weight effects was first derived for notched specimens from equivalent linear elastic fracture mechanics. Next, equivalent linear elastic fracture mechanics theory being not applicable to unnotched bodies, a cohesive model formulation was considered. Particularly, the cohesive size effect curve and the generalized cohesive size effect curves, originally obtained via cohesive crack analysis for weightless bodies with sharp and blunt/unnotched notches, respectively, were equipped of an additional term to account for the effect of gravity. All the resulting formulas were compared with the predictions of numerical simulation resulting from the adoption of the Lattice Discrete Particle Model. The results point out that the analytical formulas match very well the results of the numerical model for both notched and unnotched samples. Furthermore, the analytical formulas predict a vertical asymptote for increasing size, in the typical double-logarithm strength versus structural size representation. The asymptote corresponds to a characteristic size at which the structure fails under its own weight. For large structural sizes approaching this characteristic size, the newly developed formulas deviate significantly from previously proposed size-effect formulas. The practical relevance of this finding was demonstrated by analyzing size and self-weight effect for several quasi-brittle materials such as concrete, wood, limestone and carbon composites. Most importantly, the proposed formulas were applied to the failure of semi-circular masonry arches under spreading supports with different slenderness ratios. Results show that analytical formulas well predict numerical simulations and, above all, that for vaulted structures it is mandatory accounting for the effect of self-weight.

International Journal of Solids and Structures - Journal paper #21

The effect of confinement and Alkali-Silica Reaction (ASR) in concrete is of paramount importance when assessing damage in existing structures. It appears that this effect has been only seldom investigated with respect to the vast literature on free-expanding ASR, especially in its modeling aspect. This paper proposes to address this topical issue. For this purpose, an exhaustive review on the effect of confinement and ASR was first provided. Key features that must be taken into account were discussed and a discrete model equipped with the relevant multi-physics models was proposed. The computational framework which includes models for moisture diffusion, heat transfer, cement hydration and aging, thermal expansion, creep, and shrinkage was validated through a detailed comparison with a recent large experimental campaign for which all model parameters have already been calibrated. After accounting for possible alkali-leaching in the experiments and adjusting three model parameters, the numerical framework was used to simulate expansion curves, crack distribution, and damage evolution in unconfined samples, and drilled cores. Results show that overall, the model is able to well reproduce the transfer of expansion in the transversal unrestrained direction, cracks having a preferential direction in the restrained direction, expansion behaviors in the three spatial directions, and the evolution of mechanical properties in time for different confinement configurations. The important effect of creep and shrinkage was also emphasized. Crack distributions numerically generated were found consistent with Damage Rating Index analysis. One major finding of this study is that the true strength inside concrete subjected to multi-axial confining loads was found unaltered due to ASR in the direction of confinement. This striking result confirms many practitioners’ field experience with core testing and raises the fact that as sophisticated modeling tools become more and more reliable, existing methods of assessment must be improved by incorporating results from numerical modeling.

Computational Mechanics - Journal paper #20

When simulating the mechanical behavior of complex materials, the failure behavior is strongly influenced by the internal structure. To account for such dependence, models at the length scale of material heterogeneity are required. These models involve multiple material parameters and are computationally intensive. Experimental data are needed to identify model parameters, and the highly nonlinear nature of the constitutive equations results in a challenging inverse problem. Direct inverse analysis (DIA) seeks the best parameter estimates by minimizing a well-defined objective function through an iterative optimization scheme. However, it is time-consuming, as just a single simulation is computationally costly. Another approach uses a machine learning (ML) model built from the complete mechanistic model, combined with an appropriate optimization algorithm. ML reduces the computational cost and enables parameter selection and feature importance as a by-product. This manuscript presents a comparative study between DIA and ML-based inverse analysis using the lattice discrete particle model, a state-of-the-art model simulating concrete at the coarse aggregate level. The study focuses on three mechanical tests: unconfined compression, hydrostatic, and tensile fracture. Experimental data was taken from the literature and augmented to form a consistent data set for a given mix design. Five different ML methods were explored, and results were compared with those from DIA. The two inverse analysis methods were compared in terms of goodness of fit and computational cost. Results confirm the validity of the identification procedure and show that inverse analysis based on ML reduces the computational cost by various orders of magnitude.

Theoretical and Applied Fracture Mechanics - Journal paper #19

Size-effect in concrete and other quasi-brittle materials defines the relation between the nominal strength and structural size when material fractures. The main cause of size-effect is the so-called energetic size-effect which results from the release of the stored energy in the structure into the fracture front. In quasi-brittle materials and in contrast to brittle materials, the size of the fracture process zone is non-negligible compared to the structural size. As a consequence, the resulting size-effect law is non-linear and deviates from the response predicted by linear elastic fracture mechanics. In order to simulate the size-effect, one needs to rely on numerical modeling to describe the formation, development and propagation of the fracture process zone. Although a number of models have been proposed over the years, it transpires that a correct description of the fracture and size-effect which accounts for boundary effects and varying structural geometry remains challenging. In this study, the Lattice Discrete Particle Model (LDPM) is proposed to investigate the effects of structural dimension and geometry on the nominal strength and fracturing process in concrete. LDPM simulates concrete at the aggregate level and has shown superior capabilities in simulating complex cracking mechanisms thanks to the inherent discrete nature of the model. In order to evaluate concrete size-effect and provide a solid validation of LDPM, one of the most complete experimental data set available in the literature was considered and includes three-point bending tests on notched and unnotched beams. The model parameters were first calibrated on a single size notched beam under three-point bending and on the mechanical response under unconfined compression. LDPM was then used to perform blind predictions on the load-crack mouth opening displacement curves of different beam sizes and notch lengths. Splitting test results on cylinders were also predicted. The results show a very good agreement with the experimental data. The quality of the predictions was quantitatively assessed. In addition, a discussion on the fracturing process and dissipated energy is provided. Last but not least, the Universal Size-Effect Law proposed by Bažant and coworkers was used to estimate concrete fracture parameters based on experimental and numerical data.

Construction and Building Materials - Journal paper #18

Accurate modeling of concrete mechanical behavior under cyclic loading with different levels of confinement is crucial in design and analysis of structures subjected to seismic events. One robust model for simulating concrete behavior is the Lattice Discrete Particle Model (LDPM), a discrete model formulated at the scale of aggregate and composed of polyhedral cells connected through a lattice of nonlinear fracturing struts. To improve the performance of LDPM for the prediction of mechanical behavior under different cyclic loading schemes and multi-axial confinement, a comprehensive cycling constitutive model, a modified volumetric–deviatoric compression law, and a modified frictional behavior under compression are established in this study. An effective strain and a corresponding effective stress at the mesoscale are formulated and used to determine the stress–strain relationship under monotonic loading. In addition, the constitutive relationships related to the tension and shear stresses are established separately to ensure a smooth stress transition from tension to compression state. Two material parameters are used to control the stiffness attenuation: the residual plastic strain, and the energy dissipation of concrete during loading and unloading, under both tension and compression. Further, a new constitutive equation for the frictional behavior under compression is proposed to simulate the post-peak behavior under confinement. The proposed constitutive model is used to simulate the mechanical behavior and failure mode of concrete under tension–compression cycling and hydrostatic pressure. Triaxial tests under different levels of confinement and unconfined compression tests are also simulated. Model validation is performed using multiple data sets available in the literature on concretes of various strengths. Simulation results show that the established cyclic constitutive model can effectively characterize the mechanical response of concrete under different cycling loadings and confining pressures.

Engineering Structures - Journal paper #17

Although widespread in civil engineering construction, brick masonry walls usually designed to resist only gravity loads are known to be vulnerable structural elements with respect to seismic loads. They are generally made of units (bricks, stones or concrete blocks) and mortar joints and are by definition non-homogeneous and composite structures. The mechanical behavior of brick masonry has been studied extensively in the past decades both experimentally and by means of numerical simulations, considering the complex interaction between units and the surrounding mortar. One major aspect of the structural vulnerability of masonry panels, not well explored in the current literature, is the presence of geometrical and material defects accidentally introduced within the masonry panel during the construction process. Accounting for these defects by performing experimental campaigns is very difficult under the point of view of the replicability and, also, it is a costly and time-consuming activity. This manuscript deals with the modeling of the compressive behavior of brick masonry panels accounting for the presence of geometrical and material defects. For this purpose, a micro-modeling approach is proposed where brick units, mortar joints, and unit-mortar interfaces are simulated explicitly and the nonlinear behavior of the constituent materials is taken into account. The model was first validated on a large set of experimental data by predicting the overall panels’ elastic behavior and bearing capacity of four different types of brick wall geometries. Next, geometrical and material defects were introduced in the model including: (i) the absence or the ineffectiveness or vertical mortar joints, (ii) the variability in the thickness of horizontal mortar joints and (iii) the inherent random distribution of bricks and mortar mechanical properties. Numerical results show that the quality of vertical joints defects does not significantly affect the mechanical response of masonry panels in compression, whereas the horizontal mortar joint defects can reduce the masonry compressive strength up to about 35%. In terms of material defects, the variability in compressive strength of brick units alone was found not to alter the mechanical behavior of the panels. On the other hand, both the overall strength and ductility of the masonry walls are appreciably affected when a not uniform distribution of the material properties are considered simultaneously in brick units and mortar joints.

Case Studies in Construction Materials - Journal paper #16

Characterized with remarkable tensile ductility, toughness and multi-cracking behavior under tension, Engineered Cementitious Composites (ECC) with Chinese local ingredients was developed in this paper, aiming to reduce the cost and to match a tensile strain capacity of 4%. Compression, tension and bending tests were carried out to determine the mechanical performance of this composite material. In addition, a numerical study to characterize the tensile and flexural behaviors of ECC specimens was conducted based on Lattice Discrete Particle Model (LDPM), which was recently developed to simulate quasi-brittle materials through a three dimensional assemblage of spherical particles. The effect of fiber reinforcement was investigated using the so-called LDPM-F which accounts for dispersed fibers at the meso-level. Plain mortar specimens without fibers were tested to calibrate the relevant LDPM parameters, while the LDPM-F parameters related to the fiber-matrix interaction were identified by matching three-point bending test of ECC specimens. Results show that the validated ECC numerical model realistically predicts the tension response of dogbone specimens. In addition, typical multi-cracking phenomenon and strain-hardening behavior of ECC are successfully captured. Finally, the effect of fiber length on ECC tensile response was further studied, and the results suggest that the best tensile performance of ECC is obtained for 18-mm-long polyvinyl alcohol (PVA) fiber reinforcement.

Buildings - Journal paper #15

Microbial-induced calcium carbonate precipitation (MICP) has been successfully applied to self-healing concrete with improved mechanical properties, while the performance of engineered cementitious composites (ECC) incorporated with bacteria is still lacking. In this study, Sporosarcina pasteurii, which has a strong ability to produce calcium carbonate, was introduced into engineered cementitious composites (ECC) with mechanical properties analyzed in detail. A multiscale study including compression, tension and fiber pullout tests was carried out to explore the Sporosarcina pasteurii incorporation effect on ECC mechanical properties. Compared with the control group, the compressive strength of S.p.-ECC specimens cured for 7 days was increased by almost 10% and the regained strength after self-healing was increased by 7.31%. Meanwhile, the initial crack strength and tensile strength of S.p.-ECC increased by 10.25% and 12.68%, respectively. Interestingly, the crack pattern of ECC was also improved to some extent, e.g., bacteria seemed to minimize crack width. The addition of bacteria failed to increase the ECC tensile strain, which remained at about 4%, in accordance with engineering practice. Finally, matrix/fiber interface properties were altered in S.p.-ECC with lower chemical bond and higher frictional bond strength. The results at the microscopic scale explain well the property improvements of ECC composites based on the fine-scale mechanical theory.

Engineering Fracture Mechanics - Journal paper #14

In the last decade the self-healing of cracks in cementitious materials has been gaining an increasing interest by both the concrete industry and the scientific community. Framed into the Horizon 2020 project ReSHEALience, the present research work aims to formulate a proposal for the numerical modelling of autogenous and stimulated autogenous healing in ordinary plain cement-based materials, whose composition is enriched, in the latter case, with crystalline admixtures. In this paper a meso-scale discrete model that also considers the healing process is presented, relying on the coupling and the enhancement of two models: the Hygro-Thermo-Chemical model, for the simulation of chemical, moisture and heat transport phenomena, and the Lattice Discrete Particle Model, for the mechanical part. The evolution of the healing phenomenon is implemented into the HTC discrete formulation, in order to simulate the degree of crack closure over time. The latter is then employed to capture how the self-repairing affects both moisture permeability and mechanical performances. Finally, the results of a laboratory campaign, carried out at the Politecnico di Milano, are used for calibrating and validating the model presented.

Journal of Building Engineering - Journal paper #13

This paper deals with the fracturing behavior of unreinforced masonry arches and vaults induced by spreading supports. The traditional method of limit analysis is limited in understanding the actual failure of arches, as it assumes the simultaneous formation of hinges once the thrust line reaches the edge of the masonry structure. The damage propagation phenomenon, starting from the trigger of the fracture up to the complete structural failure is thus ignored. Moreover, limit analysis does not capture the effect of structural size on the nominal strength due to strain-softening and damage localization. This manuscript proposes a thorough understanding of the fracturing behavior and size-effect of arches and vaults based on computational modeling and non-linear fracture mechanics concepts. For this purpose, the Lattice Discrete Particle Model (LDPM) is adopted to simulate a variety of stone masonry vaulted structures up to their collapse. The formation of hinges, the activation of the mechanism and the kinematic mechanism are analyzed for three different types of vaults, namely groin, barrel and depressed vaults, and for six different slendernesses. The effect of arch size on structural strength is then analyzed using LDPM, by simulating self-similar arches of five different sizes and of three different slenderness ratios. The numerical data of size-effect is also analyzed using a newly developed analytical formula based on non-linear fracture mechanics theory and taking into account self-weight, whose effect is of paramount importance in arches and vaults under spreading supports. Results show a strong reduction of structural strength as the size increases, as a matter of fact stronger than the typically observed reduction due to energetical size-effect. The difference is due to self-weight, one of the main driving forces in the collapse of thrusting arches. This might explain the reason why in some seismic locations, small sized vaulted structures remain almost undamaged whereas larger ones often collapse.

International Journal of Solids and Structures - Journal paper #12

This paper examines the effects of size range, distribution and content of reactive aggregate on concrete expansion and deterioration due to Alkali–Silica Reaction (ASR). The ASR model was formulated within the Multiphysics framework of the Lattice Discrete Particle Model to account for the heterogeneous character of ASR expansion, cracking and damage. The adopted model was extended in this study to include a general piecewise linear sieve curve that allows selecting the coarse aggregate pieces to be reactive or non-reactive according to content and size range of actual reactive aggregate. The overall framework was calibrated and validated by comparing simulation results with three sets of experimental data from the literature. The results demonstrate that the model can capture all the main features of the experimental evidence. In particular, the so-called “pessimum size” of ASR expansion is captured and explained as the competition results between porosity and diffusion effects in the ASR model. Based on simulation results, it is shown that ASR-induced cracks are mainly generated by the presence of reactive aggregates of different sizes producing heterogeneous expansion at the mesoscale. The loss in mechanical properties is found to be strongly related to these cracks and the heterogeneous expansion as opposed to the measured macroscopic strain.

Cement and Concrete Composites - Journal paper #11

This paper presents a constitutive model for the simulation of temperature and relative humidity effects on concrete expansion due to Alkali–Silica Reaction (ASR). The model was formulated within the multiphysics framework of the Lattice Discrete Particle Model (LDPM). LDPM simulates concrete internal structure at the mesoscale defined as the length scale of coarse aggregate pieces. As such it accounts for the heterogeneous character of ASR expansion, cracking and damage, creep, hygrothermal deformation as well as moisture transport and heat transfer. The overall framework was calibrated and validated by comparing several numerical simulations with a large database of experimental data gathered from the literature. The proposed model is able to capture accurately all available experimental evidence, including: (a) the increase of expansion rate for increasing temperature and its marked decrease for decreasing relative humidity; and (b) both increase or decrease of ASR ultimate expansion as function of temperature.

Engineering Structures - Journal paper #10

Masonry towers are characterized by a high susceptibility to seismic actions. For this task different approaches exist and they are selected depending on the desired level of accuracy of the analysis. The identification of the correct collapse configuration is however complex and necessitates thorough on-site surveys. Construction codes usually require the study of local and global collapse mechanisms based on simplified kinematic analysis. More elaborated approaches such as nonlinear finite element methods have been used to simulate the response of masonry towers. Although successful in many applications, these methods are limited in accurately capturing crack distributions and fracture mechanisms. In this work, an integrated discrete-analytical approach is proposed. First, the Lattice Discrete Particle Model (LDPM), which simulates masonry at the stone level and has a superior capability in capturing fracturing processes, is adopted to simulate masonry towers subjected to seismic excitation. The numerical model is used to predict the actual collapse mechanism. Next, the final fractured configuration is used in the kinematic analysis for the calculation of the ultimate condition. The proposed method is used to analyze the collapse of the Medici tower that collapsed during the 2009 L’Aquila earthquake. The simulations are able to predict the induced damage and the crack contours, which are used then to identify six different failure configurations. The subsequent kinematic analyses take into account the relative position of openings and fracture locations. The results show that the collapse of the Medici tower is well replicated by LDPM and the corresponding kinematic analyses demonstrate the efficiency of the proposed hybrid approach applied to this case study. The paper also points out that different load configurations, more specifically the direction of the seismic action, result in certain cases in more diffused damage and a clear failure pattern cannot be identified for kinematic analyses. In these cases, it appears fundamental to rely mainly on comprehensive numerical models, such as LDPM, to study the fracturing process from the cracks trigger to the ultimate complex collapse mechanism.

Journal of Structural Engineering - Journal paper #9

This paper focuses on the simulation of irregular stone masonry by the lattice discrete particle model (LDPM), which simulates the fracture and failure behavior of quasi-brittle heterogeneous materials by modeling the interaction among coarse material heterogeneities. LDPM is formulated at the length scale of the masonry stones whose interaction is described through constitutive equations featuring softening in tension and strain hardening in compression. The numerical results relevant to diagonal compression tests show that the intrinsic stochastic character of LDPM can quantify the variation of the mechanical properties of irregular masonry resulting from random stone size and stone-size distribution. Furthermore, the paper presents an analysis of the size effect on irregular stone masonry structures. This was obtained by simulating the shear behavior of geometrically similar samples of different sizes. The simulations demonstrate that increasing structural size leads to a significant reduction of both structural strength and structural ductility. The magnitude of the predicted size effect suggests that, contrary to typical experimental results on reduced size samples, real irregular masonry structures must be considered as perfectly brittle.

Construction and Building Materials - Journal paper #8

This investigation focused on identifying the impact of various types of steel fibers on the quasi-static mechanical behavior of ultra-high performance concrete (UHPC) through different laboratory experiments as well as their numerical modeling. UHPC specimens were fabricated with four steel fiber types: ZP305, Nycon type V, OL 10mm, and OL 6mm. Fiber shape and size had little impact on quasi-static properties of UHPC in compression, while they showed significant impact on flexural and tensile properties. The main benefits offered by the smaller fibers occurred prior to reaching the ultimate load carrying capacity. Once the ultimate strength was reached, larger fibers were more effective in bridging larger cracks. Numerical modeling of the presented experiments were performed using the Lattice Discrete Particle Model (LDPM) enriched with fibers effect. LDPM is a meso-scale model simulating concrete at the scale of coarse aggregate pieces, and it has been extensively used for the simulation of concrete mechanical behavior under various loading and environmental conditions. The extension of this model, the so-called LDPM-F, developed for the simulation of fiber-reinforced concrete, is employed in this research to verify and better understand the experimental observations.

Journal of Applied Mechanics - Journal paper #7

For a long time, geomechanicians have used scratch tests to characterize the compressive behavior and hardness of rocks. In recent years, this test has regained popularity in the field of mechanics, especially after a series of publications that highlighted the potential capability of the scratch test to determine the fracture properties of quasi-brittle materials. However, the complex failure mechanisms observed experimentally in scratch tests led to scientific debates and, in particular, raised the question of the size effect. This article intends to provide a better understanding of the problem by using numerical tools and fracture mechanics considerations. To narrow the investigation area, this study focuses on slab scratch tests of quasi-brittle materials and adopts two different numerical methods: (i) the lattice discrete particle model (LDPM) that includes constitutive laws for cohesive fracturing, frictional shearing, and nonlinear compressive behavior, and (ii) the meshless method based on Shepard function and partition of unity (MSPU) implementing linear elastic fracture mechanics (LEFM). The numerical results are further analyzed through Bažant’s size effect law (SEL) with an appropriate mixed-mode fracture criterion. Fracture properties are then calculated and compared to the results of typical notched three-point bending tests. The results show that mixed-mode fracture considerations are of paramount importance in analyzing the fracture process and size effect of scratch tests.

Engineering Structures - Journal paper #6

Seismic events highlight the inherent fragility and vulnerability of stone masonry buildings, which represent a large part of the existing historical and artistic heritage. In order to preserve these structures, numerous reinforcement techniques are typically used on masonry walls, including mortar injections, reinforced drilling, and reinforced concrete plaster. Nowadays new and less invasive strengthening techniques are preferred; among them Fiber Reinforced Cementitious Matrix (FRCM) system with lime-based mortar, which is considered to be more compatible with the intrinsic properties of these ancient structures as compared to cement-based mortar. This work aims to investigate experimentally and computationally FRCM applied as reinforcement to ancient stone masonry. In particular, the paper presents results from diagonal compression tests carried out at the University of L’Aquila (Italy) on stone masonry specimens strengthened with layers of Glass-FRCM (GFRCM). In comparison with unreinforced panels, those strengthened by the GFRCM exhibited a significant increase in shear modulus and shear strength. A computational framework based on the Lattice Discrete Particle Model (LDPM) was then used to reproduce the experimental results. The fracture behavior and the damage evolution in masonry panels were investigated under different assumptions on the GFRCM system features (bond behavior, mortar thickness, fiber anchors and fiber grid). The good agreement between experimental results and the LDPM simulations show that this approach predicts well the mechanical behavior and the damage evolution in stone masonry under quasi-static loading conditions. Moreover, it can be considered a viable tool for engineers in developing effective reinforcement techniques.

Engineering Structures - Journal paper #5

The vulnerability of stone masonry structures to seismic loading constitutes one of the main application areas of research in the field of structural engineering. This paper focuses on the analysis of the out-of-plane response of unreinforced masonry structures. Although successful in many applications, traditional continuum-based analysis, as well as simplified analytical models, fail to a large extent in correctly capturing complex failure mechanisms occurring for this type of structures. To overcome this issue, this study adopts a discrete model, the so-called Lattice Discrete Particle Model (LDPM), to describe the structural behavior of a variety of stone masonry structures up to their collapse. LDPM simulates the behavior of masonry at the stone level. The interaction between stones that are bounded by weak layers of mortar is governed by specific constitutive equations describing tensile fracturing with strain-softening, cohesive and frictional shearing, and compressive response with strain-hardening. This manuscript aims to validate the proposed model with experimental data available in the literature. Furthermore, overturning walls with and without openings are simulated, the associated local collapse mechanisms are analyzed and compared with the classical kinematic analysis. Finally, more complex mechanisms are numerically investigated to reproduce the behavior of systems of panels included within the continuity of a facade. The results show that LDPM is able to capture the damage evolution and the fracture propagation that lead to the overall collapse and it can be used confidently as an alternative method to perform the limit analysis of local collapse mechanisms. The proposed numerical approach provides engineers with a powerful modeling tool for the analysis of the behavior of stone masonry structures with a variety of geometrical configurations and under very general loading conditions.

Journal of Applied Mechanics - Journal paper #4

In the standard fracture test specimens, the crack-parallel normal stress is negligible. However, its effect can be strong, as revealed by a new type of experiment, briefly named the gap test. It consists of a simple modification of the standard three-point-bend test whose main idea is to use plastic pads with a near-perfect yield plateau to generate a constant crack-parallel compression and install the end supports with a gap that closes only when the pads yield. This way, the test beam transits from one statically determinate loading configuration to another, making evaluation unambiguous. For concrete, the gap test showed that moderate crack-parallel compressive stress can increase up to 1.8 times the Mode I (opening) fracture energy of concrete, and reduce it to almost zero on approach to the compressive stress limit. To model it, the fracture process zone must be characterized tensorially. We use computer simulations with crack-band microplane model, considering both in-plane and out-of-plane crack-parallel stresses for plain and fiber-reinforced concretes, and anisotropic shale. The results have broad implications for all quasibrittle materials, including shale, fiber composites, coarse ceramics, sea ice, foams, and fone. Except for negligible crack-parallel stress, the line crack models are shown to be inapplicable. Nevertheless, as an approximation ignoring stress tensor history, the crack-parallel stress effect may be introduced parametrically, by a formula. Finally we show that the standard tensorial strength models such as Drucker–Prager cannot reproduce these effects realistically.

Proceedings of the National Academy of Sciences - Journal paper #3

The line crack models, including linear elastic fracture mechanics (LEFM), cohesive crack model (CCM), and extended finite element method (XFEM), rest on the century-old hypothesis of constancy of materials’ fracture energy. However, the type of fracture test presented here, named the gap test, reveals that, in concrete and probably all quasibrittle materials, including coarse-grained ceramics, rocks, stiff foams, fiber composites, wood, and sea ice, the effective mode I fracture energy depends strongly on the crack-parallel normal stress, in-plane or out-of-plane. This stress can double the fracture energy or reduce it to zero. Why hasn’t this been detected earlier? Because the crack-parallel stress in all standard fracture specimens is negligible, and is, anyway, unaccountable by line crack models. To simulate this phenomenon by finite elements (FE), the fracture process zone must have a finite width, and must be characterized by a realistic tensorial softening damage model whose vectorial constitutive law captures oriented mesoscale frictional slip, microcrack opening, and splitting with microbuckling. This is best accomplished by the FE crack band model which, when coupled with microplane model M7, fits the test results satisfactorily. The lattice discrete particle model also works. However, the scalar stress–displacement softening law of CCM and tensorial models with a single-parameter damage law are inadequate. The experiment is proposed as a standard. It represents a simple modification of the three-point-bend test in which both the bending and crack-parallel compression are statically determinate. Finally, a perspective of various far-reaching consequences and limitations of CCM, LEFM, and XFEM is discussed.

Cement and Concrete Composites - Journal paper #2

The traditional approach for predicting self-desiccation is to simulate hygro-mechanics directly at the macroscale and to provide hydration-related inputs via phenomenological constitutive models. This manuscript presents instead a novel method that consists of obtaining inputs to such constitutive relations from direct simulations of cement hydration at the microscale, using a state-of-the-art simulator, namely the Cement Hydration in Three Dimensions (CEMHYD3D). This allows avoiding lengthy calibrations from experimental data. The prediction capabilities of the proposed model are demonstrated using experimental data of self-desiccation relevant to about 50 different mix designs of concrete, mortar and cement paste, with water to cement ratios ranging from 0.20 to 0.68 and silica fume to cement ratios from 0.0 to 0.39. The mixes are characterized by various cement chemical compositions, particle size distributions and Blaine finenesses, and the experiments span numerous time scales, from one week up to two years.

International Journal of Damage Mechanics - Journal paper #1

Alkali silica reaction and its effect on concrete and mortar have been studied for many years. Several tests and procedures have been formulated to evaluate this reaction, particularly in terms of aggregate reactivity. However, the data given in the literature concerning the mechanical properties of concrete and mortar are scattered and very little information is available for some properties such as fracture energy. In this study, the mechanical behavior of mortar was evaluated and monitored, under normal and accelerated environmental conditions. Fracture energy, compressive strength and tensile strength were measured for mortar specimens, casted with highly reactive Spratt crushed aggregate, at two different storage temperatures (23℃ and 80℃) and at two different alkali concentrations (immersed in water and in 1 N NaOH solution). Moreover, free expansion tests (according to ASTM C1260) and petrographic observations were performed, in order to relate them to the evolution of the mechanical properties of mortar. Results show a decrease of the mechanical properties associated with specimens at 80℃ in alkali solution and that the deterioration due to alkali silica reaction is counter-balanced by the strengthening of mortar resulting from the hydration process. A multi-physics computational framework, based on the Lattice Discrete Particle Model is then proposed. Numerical simulations based on a complete calibration and validation with the obtained experimental data capture the behavior of mortar subjected to the complex coupled effect of strength build-up and alkali silica reaction at different temperatures and alkali contents.

Procedia Structural Integrity - Conference proceeding #10

This study presents a novel integrated discrete-analytical approach for analyzing the collapse behavior of the masonry Medici tower (L'Aquila, Italy). Due to their slenderness, masonry towers are characterized by high susceptibility to seismic actions and several approaches can be adopted to analyze their seismic vulnerability. Generally, engineers-practitioners and researchers study the local and global collapse mechanisms based on simplified kinematic analysis, as prescribed by national and international construction codes or, alternatively, more sophisticated approaches such as nonlinear finite element methods have been adopted to simulate the response of masonry towers. Although successful in some applications, these methods are limited in accurately capturing crack distributions and fracture mechanisms. In fact, they completely ignore the damage propagation phenomenon, starting from the trigger of the fracture up to the complete structural failure condition, that is instead fundamental aiming to analyze intermediate damage states for the check of serviceability limit states or to individuate a more realistic structural crack distribution in ultimate conditions. This work proposes a hybrid discrete-kinematic approach: first, the Lattice Discrete Particle Model (LDPM), that simulates masonry at meso-scale, is used to individuate the actual collapse mechanism; next, the individuated cracked configuration is used in the kinematic analysis for the analysis in ultimate conditions. The results show that the collapse of the Medici tower due to the 2009 L'Aquila earthquake is well predicted by LDPM and the corresponding limit analyses demonstrate the efficiency of the proposed hybrid approach applied to this case study. Additional results point out that different load configurations, more specifically variations in the direction of the seismic action, provoke in certain cases a more diffused damage and a clear failure pattern can not be identified for kinematic analyses. In these cases, relying mainly on comprehensive numerical models, such as LDPM, is fundamental to study the fracturing process from the cracks trigger up to the ultimate complex collapse mechanism.

Procedia Structural Integrity - Conference proceeding #9

This study presents a novel meso-scale approach to investigate the fracturing and collapse behaviors of unreinforced masonry vaulted structures induced by spreading supports. Traditionally, the behavior of masonry vaulted structures is investigated by resorting on limit analysis method, that is a limited approach as: (i) it tackles just the failure condition of the arched structural configuration as it assumes the simultaneous formation of hinges once the thrust line reaches the edge of the masonry structure, (ii) it completely ignores the damage propagation phenomenon, starting from the trigger of the first fracture up to the complete structural failure condition. The comprehension of this fracturing process is fundamental aiming to analyze intermediate damage states for the check of serviceability limit states and to individuate a more realistic structural crack distribution in ultimate conditions. This paper proposes a thorough understanding of the fracturing behavior of masonry vaults based on non-linear fracture mechanics concepts. For this purpose, the Lattice Discrete Particle Model (LDPM) is adopted to simulate a variety of stone masonry vaulted structures up to their collapse. LDPM simulates the behavior of masonry at the stone level. The interaction between stones that are bounded by weak layers of mortar is governed by specific constitutive equations describing tensile fracturing with strain-softening, cohesive and frictional shearing, and compressive response with strain-hardening. The formation of hinges, the activation of the mechanism and the kinematic mechanism are analyzed for three different types of vaults, namely groin, barrel and depressed vaults, and for six different slenderness. The first conclusion of this study is that LDPM can be used as an alternative tool to perform typical limit analysis for the assessment of safety of arches and vaults in ultimate conditions. Most importantly, LDPM is able to show that the fracturing process is a progressive phenomenon, the cracked surfaces are never strictly symmetric respect to the vertical axis and do not appear simultaneously. In particular, the features of non simultaneity and asymmetry of the cracks increases as the distance between the crown of the vault and the imposts increases, i.e. going from depressed vaults to groin vaults. Finally, the evolution of the fracturing process occurs more progressively and exhibits less pronounced asymmetry in the case of depressed vaults as compared to groin vaults for which, in turn, the damage appears to be more brittle and characterized by asymmetry in the cracks distribution.

Euro-C - Conference proceeding #8

There are in general two classes of time integration algorithms for dynamics problems, namely implicit and explicit methods. While explicit methods are conditionally stable and often require a very small time step, implicit algorithms are unconditionally stable and larger time steps can be used. In terms of memory usage, implicit algorithms require more memory as a system of equations needs to be solved one or several times per step for the solution to advance. Implicit methods are usually used to solved problems in which low frequency modes dominate. Nevertheless, one often faces convergence issues when the material behavior is highly nonlinear and explicit methods seem more appropriate in that case. In this study, the performance of the Lattice Discrete Particle Model (LDPM), newly implemented in the implicit solver CAST3M was investigated. LDPM is a mesoscale model developed to simulate concrete and other granular quasi-brittle materials. It incorporates complex nonlinear constitutive equations and for this reason, it is currently used within the dynamic explicit framework ABAQUS Explicit. This manuscript presents preliminary results on the comparison between explicit central difference algorithm and implicit average acceleration scheme for LDPM. For this purpose, a classical three-point bending test under quasi-static conditions was considered. Three different integration methods were used: dynamic explicit, dynamic implicit and static implicit. Load-displacement responses were obtained and discussed, along with the force imbalance at loading points to assess static equilibrium. For each simulation, the computational cost was also obtained. Results show that quasi-static simulations can be performed using dynamic explicit integration method if the effect of inertia is small enough. In addition, the computational cost for static and dynamic implicit simulations is much lower than for dynamic explicit calculations. Last but not least, the time step size in the dynamic implicit method needs to be chosen carefully to avoid spurious energy growth or higher modes due to time discretization.

Euro-C - Conference proceeding #7

Size-effect of quasi-brittle materials such as concrete defines the relation between nominal strength and structural size when material fractures. One main type of size-effect, which is the focus of this manuscript, is the so-called energetic size-effect and is due to the release of stored energy of the structure into the fracture front. In contrast to brittle materials, the fracture process zone size has a non-negligible size in concrete, which makes the size-effect law non-linear. In order to simulate size-effect, a numerical model must be able to describe accurately the development and propagation of the fracture process zone. Over the years, a number of models have been proposed to describe the fracturing process in concrete. Nevertheless, it appears challenging to obtain a correct description of fracture and size-effect when the structural dimension and shape are varying. In this study, the Lattice Discrete Particle Model (LDPM) was proposed to overcome this lack of accurate models. The use of mesoscale discrete models such as LDPM, which describes concrete at the aggregate level, is especially adequate in simulating complex cracking mechanisms. In order to investigate the effect of structural dimension and geometry on the fracturing process and the nominal strength, one of the most comprehensive experimental data set available in the literature was considered, which includes three-point bending tests of notched and unnotched beams. First, the relevant material parameters in LDPM were calibrated on a single size notched beam on the corresponding entire load-Crack Mouth Opening Displacement (CMOD) curve. The model was then used to predict the load-CMOD curves of different beam sizes with the same notch length. Predictions on one unnotched beam were also made to test the model’s capability to simulate crack initiation from a smooth surface. Preliminary results show very a good agreement with the experimental data, which suggests that LDPM is an efficient model in predicting concrete size-effect.

Euro-C - Conference proceeding #6

In solid mechanics, size effect is very often observed. This lecture provides a brief overview of two sorts of size effect: size effect on the structural strength observed at the macro-scale and size effect on elasticity and fracture observed at the micro-scale on porous materials. Both size effects are investigated with the same methodology, that is the help of up-scaling techniques : lattice approaches at the meso-to-macro scale and molecular mechanics at the nano-to-micro scale. These two up-scaling techniques provide ways to account for material heterogeneities and for surface effects that are at the origin of these size effects. In the two examples discussed in this contribution, accurate constitutive relations and continuum models at the macro-scale remain a very open issue, without the help of up-scaling. The methodology and results discussed in this paper may enlighten future extended continuum theories.

COMPDYN ECCOMAS - Conference proceeding #5

Stone masonry buildings are known to be highly vulnerable to seismic actions. In this context, the analysis of the out-of-plane response of unreinforced masonry structures is crucial. For this purpose, the Lattice Discrete Particle Model (LDPM) was employed to simulate the mechanical behavior of stone masonries up to their failure. Unlike commonly used continuum-based methods or simplified analytical models, that are often limited in modeling correctly complex failure mechanisms, LDPM is able to capture accurately crack distributions and failure patterns. LDPM describes the masonry at the scale of stones and takes into account their interactions through tailored constitutive equations for tensile, compressive, shear, and frictional behaviors. First, LDPM was validated against experimental results on masonry panels subjected to out-of-plane loading. Next, the vertical bending mechanism was studied in the cases of one- and two-story walls with and without openings. Finally, more complex mechanisms were considered where the damage evolution and the fracture propagation were analyzed for a set of panels assumed to be placed within the continuity of a facade. The overall results presented in this paper show that LDPM can realistically predict the collapse mechanisms associated with out-of-plane loading for different structural configurations and geometries.

EUROSTRUCT - Conference proceeding #4

In this paper, the sorption behavior of Ultra High-Performance Fiber Reinforced Concrete (UHPFRC) is experimentally investigated. As UHPFRC has a very low permeability, the sorption measurement presents an interesting challenge and has required the modification and optimization of the Dynamic Vapor Sorption Method (DVS) already applied for ordinary concrete. Indeed, the experimental results indicate that isotherm measurement on UHPFRC highly depends on the time step setup and the mass stabilization criteria in the DVS computer-controlled system. The results also showed that UHPFRC also has a strong sorption hysteresis (like other cementitious materials), but with a surprising triangular shape.

FraMCoS-X - Conference proceeding #3

In this paper a numerical model for autogenous healing of normal strength concrete is presented in detail, along with preliminary results of its validation, which is planned to be achieved by comparing the results of numerical analyses with those of a dedicated experimental campaign. Recently the SMM (Solidification-Microprestress-Microplane model M4) model for concrete, which makes use of a modified microplane model M4 and the solidification-microprestress theory, has been extended to incorporate the autogenous healing effects. The moisture and heat fields, as well as the hydration degree, are obtained from the solution of a hygro-thermo-chemical problem, which is coupled with the SMM model. The updated model can also simulate the effects of cracking on the permeability and the restoring effect of the self-healing on the mechanical constitutive laws, i.e. the microplane model. In this work, the same approach is introduced into a discrete model, namely the Lattice Discrete Particle Model (LDPM). A numerical example is presented to validate the proposed computational model employing experimental data from a recent test series undertaken at Politecnico di Milano.

The New Boundaries of Structural Concrete - Conference proceeding #2

Traditionally self-desiccation is predicted by the simulations of hygro-mechanics directly at the macro-scale providing hydration-related inputs via phenomenological constitutive models. Instead a novel method is here proposed that consists of obtaining inputs to such constitutive relations from direct simulations of cement hydration at the micro-scale using Cement Hydration in Three Dimensions (CEMHYD3D) model. This allows avoiding lengthy calibrations from experimental data. The prediction capabilities of the proposed model are demonstrated using experimental data of self-desiccation relevant to many different mix designs of concrete, mortar and cement paste, with water to cement ratios ranging from 0.20 to 0.68 and silica fume to cement ratios from 0.0 to 0.39.

Euro-C - Conference proceeding #1

Cement hydration in concrete and mortar has been studied thoroughly over the past 50 years. To fully understand hydration in concrete and predict the evolution of the hygral, thermal, and mechanical properties at the structural level, one needs to study not only the reaction  kinetics but also the development of the microstructure. Many models have been developed for this purpose, some of them looking only at the micro-scale or at the macro-scale and others tackling the fundamental nature of the issue, which can be qualified as a multiscale problem. This paper proposes a novel approach that consists of combining a cement hydration model at the microstructural level, the CEMHYD3D model, with a macroscopic hygro-thermo-chemical model, the HTC model. The coupling is performed by post-processing the output of the  CEMHYD3D model, in particular with reference to cement hydration degree, silica fume reaction degree, and amounts of evaporable water and chemically bound water in order to identify through a curve fitting routine the parameters of the HTC formulation. This approach allows  the possibility of predicting concrete behavior at multiple scales based on the actual chemical and microstructural evolution, thus enhancing the capabilities of the so-called HTC-CEMHYD3D model. This paper focuses on 1) introducing the concepts behind the formulation of  self-desiccation and 2) demonstrating the predictive capabilities of the coupled model using some available experimental data.