Program

Intrinsic drying creep assessment by Digital Image Correlation

Farid Benboudjema - LMPS, France

Drying creep in concrete is still a challenging problem to tackle. The induced strain by concomitant drying and mechanical loading contains at least 2 components. The 1^st one corresponds to a difference of cracking between loaded and non-loaded specimens (cracking is due to drying shrinkage gradient and incompatibilities between concrete phases at different scales). The 2^nd is considered to be intrinsic, and is difficult to separate from the 1^st component. By using thin cement paste specimens, slow and fast drying rates, numerical simulations and digital image correlation technique, intrinsic drying creep strain has been “isolated”. Experimental results obtained in an environmental SEM (1D test) and in a climate chamber (2D tests) are presented and discussed.

Molecular Insights of Creep and Upscaling Methods

Tulio Honorio - LMPS, France

Molecular simulations are deployed to gain insights into how the rheology (in terms of shear modulus, yield stress, shear stress, and shear viscosity) of C-S-H stack of layers depends on (slit) pore size (from interlayer up to large gel pores) and force perpendicular to the layers. It is shown how the rheological behavior is related to self-diffusion (highlighting the critical role of subdiffusion in micropores) and Stern layer in C-S-H. Complex shear modulus are also computed using molecular simulations. The idea of fractal element is deployed to understand the rheological behaviour of C-S-H. Finally, upscaling strategies linking atomistic and continuum mechanics are discussed.

Multiscale insight into creep of cementitious materials gained from macroscopic three-minutes uniaxial compression experiments

Bernhard Pichler - TU Wien, Austria

The elastic stiffness and the creep activity of cement pastes at early ages and the impact of temperature on the stiffness of mature cement pastes is studied. Early-age characterization of ordinary Portland cement pastes with different compositions was carried out at 20 °C. Every specimen was subjected to a series of in total 168 hourly-performed three-minute creep tests. Macroscopic test evaluation in the framework of the linear theory of viscoelasticity, using a power-law creep function, reveals increasing elastic and creep moduli over time, with slightly decreasing or quasi-constant creep exponents. The determined elastic moduli agree well with ultrasonic measurements. A multiscale model is developed. The creep shear modulus and the corresponding power-law exponent of micron-sized hydrate gel needles are identified from several hundred macroscopic three-minute creep tests. The model is capable of predicting the 30 days creep of a 30 years old cement paste. The elastic stiffness and the creep activity of mature cement paste is explored at 20 °C, 30 °C, and 45 °C, again using three-minutes creep tests. The multiscale model is extended towards temperature-dependent stiffness properties. The Arrhenius-type activation energy of the creep modulus is found to be equal to that of water; independent of scale, composition, and maturity due to ineffective stress redistribution from creeping to purely elastic material constituents.

Monitoring and modelling early age basic creep of alkali-activated slag mortar by means of repeated minute-long loadings in compression

Stéphanie Staquet - ULB, Belgium

Basic creep plays an important role for assessing the risk of early age cracking in massive structures. In recent decades, several models have been developed to characterize how the reactions process impacts the development of basic creep. In this research, the development of elastic and non-aging creep properties of sodium hydroxide-activated blast furnace slag mortar, with two distinct molarities of the activator solution and a reference OPC-based mixture is studied since the earliest age. The experimental phase involves a series of hourly-repeated five-minute long creep tests on the aging material. This approach enables continuous monitoring making easier the determination of the early-age elastic stiffness and creep properties. In order to model short-term creep, a power-law creep function is utilized. The use of the calorimetry-derived cumulative heat release allows to establish linear correlation between (compressive) strength and heat release, along with a power function relationship between unloading (elastic) modulus and heat release. An optimal alkali dosage (Na₂O content) appears to be key parameter for long-term strength development. Moreover, the creep parameters, namely amplitude (A) and kinetic (K), demonstrate a gradual decrease, although the values are higher than those of the corresponding OPC mixture, as the heat release progresses.

A potential reason why nano- and micro-indentation make it possible to characterize the long-term creep kinetics of cement-based materials in minutes

Matthieu Vandamme - Navier, France

Cement-based materials (i.e., concrete, mortar, or cement paste) creep over decades at a rate that can be detrimental to civil engineering infrastructures. After several days, cement-based materials submitted to a constant load start deforming logarithmically with respect to time. Although this logarithmic kinetics of creep is observed after days macroscopically, it is observed after seconds at the micrometer or sub-micrometer scale when creep is characterized by micro- or nano-indentation. We show that the logarithmic creep kinetics measured in minutes by micro- or nano-indentation of cement pastes is quantitatively representative of concrete's long-term logarithmic creep kinetics.

We wonder why indentation makes it possible to reach the logarithmic creep kinetics of cement-based materials orders of magnitude faster than macroscopic testing. To shed some light on this question, we study two creep models inspired by the literature on the creep of metals, called the exhaustion model and the work-hardening model. Those two models consider that creep originates from local microscopic relaxations. They differ by how the energy barriers of those local microscopic relaxations are distributed and evolve during the creep process. Both models can explain a logarithmic evolution of creep in the long term. Also, both models predict that sufficiently large stresses can tremendously lower the characteristic time to reach logarithmic creep, which can explain why indentation makes it possible to reach logarithmic creep so fast.

Matthieu VANDAMME is an engineer from École des Ponts ParisTech and from Ecole Polytechnique (Paris, France). He obtained his Ph.D. in civil engineering from MIT (Cambridge, MA) in 2008. Since then, he has been working as a researcher at École des Ponts ParisTech in Laboratoire Navier (École des Ponts ParisTech, Université Gustave Eiffel, CNRS), where he focuses on building materials. He is interested in their poromechanical behavior (i.e., in how in-pore physical processes impact their mechanical behavior) and in their time-dependent behavior. Since 2022, he is vice-head of the Civil engineering and construction department at École des Ponts ParisTech

Time-stress-moisture-dependent (creep) behavior of plant fibres and their composites

Vincent Placet - Univ. Bourgogne Franche-Comté, France

Materials derived from wood and plants are currently undergoing exponential growth across various sectors, including construction and transportation. Undoubtedly, they present themselves as formidable candidates for enhancing the overall sustainability and circularity of associated structures and products, all while substituting for highly emissive and environmentally impactful materials. However, despite their numerous advantages, these materials are characterized by complex mechanical behaviour, scattered mechanical properties and moisture sensitivity, which may discourage engineers from their use or necessitate the application of high safety factors. So, when it comes to high-end structural applications, it becomes imperative to employ sophisticated models and establish comprehensive design and dimensioning guidelines, as well as in-depth understanding of the nano- and micro-structural underpinnings influencing the macroscopic material behaviour.
These materials are particularly characterised by their time-dependent behaviour. While it has been extensively studied for several decades for wood, wood tissue, and paper [1-4], there is limited research on the creep behaviour of plant fibre composites [5], and even fewer studies focus on the fibre scale [6-13]. In this presentation, after briefly reviewing the knowledge at the macroscopic level, we will shift our focus to the fibre scale. This knowledge is particularly crucial for the development of multiscale approaches and models capable of accurately predicting and reproducing macroscopic behaviours.
At the fibre’s scale, it has been demonstrated that elementary fibres exhibit both instantaneous elastic deformation and delayed, time-dependent deformation when subjected to an externally applied load, resulting in permanent strain when the load is removed [6-8, 13]. Wood and plant fibres also display an increase in creep compliance with rising moisture content. Several authors have observed significantly greater creep in cyclic humidity conditions compared to a constant environment, particularly at high humidity levels [9-11, 13, 14]. This accelerated creep phenomenon, induced by the sorption and desorption of water in the fibre wall, is known as the mechanosorptive (MCS) effect. Therefore, the time-dependent behaviour of wood fibres not only depends on temperature, loading history, and moisture content but also on moisture content history and variations. These parameters can interact and produce coupling effects [1].

Delayed behavior of timber members in service and ultimate limit states

Frédéric Dubois - GC2D, Univ. Limoges

This work deals with the long-term behaviour of timber members in a regulatory approach covering both service and ultimate limit states. Timber structures in service are subject to creep effects mainly due to long-term loads such as dead loads. These delayed effects result in creep behaviour which is expressed in a Eurocode approach by a long-term displacement amplification coefficient (kdef coefficient) and reduction coefficients that take into account the loading duration class. Recent research has shown that the effects of long-term creep depend on the type of load (e.g. flexural vs. compressive). It is therefore important to understand these coefficients when designing innovative timber structures such as engineering structures or high-rise buildings. In addition, creep effects affect the strength parameters through the kmod coefficient. It is therefore necessary to use creep tests or regulatory data to determine weighting values that take into account not only the service class or load duration class, but also the nature of the load.

Characterization of rolling and longitudinal shear creep for CLT panels

Arthur Lebée - Navier, France

This talk presents the characterization of the short and long term rolling and longitudinal shear modulus of CLT panels. A four-point bending test is achieved on sandwich beams with steel skins and wooden core. This allows to isolate the CLT cross-layer and to characterize the shear behavior. The experiment is performed in a controlled environment during 6 months. A power law fits very well time series and reveals that shear creep is significantly faster than longitudinal creep in timber.

Arthur Lebée is a researcher at Laboratoire Navier. He is working on advanced multiscale methods applied to the design and modelling of structures and architected materials. He also contributes to the mechanical modelling and experimental characterization of timber structures.

Elastoplastic models for the deformation of disordered materials

Jean-Louis Barrat - LIPhy, Univ. Grenoble Alpes, France

Disordered or amorphous solids cover a large class of systems, “soft” (colloidal pastes, foams, grains) or “hard” (metallic glasses, oxide glasses), which are not ordered at the microscopic level. They therefore do not exhibit dislocations like crystalline solids. Their flow, which occurs beyond a threshold stress, is the result of the local instability of localized zones, the "shear transformations", which interact elastically with each other, giving rise to collective avalanche phenomena. This physics is well described by elastoplastic models  of the “cellular automaton” type. After having motivated these elastoplastic models,  I will discuss their mean field analysis and the type of constitutive equation that results, and how they can be used to describe various flow phenomena such as strain localisation or creep flow and fluidisation.

Delayed yielding of amorphous materials

Suzanne Fielding - Durham University, UK

Amorphous solids include soft materials such as emulsions, foams, colloids, granular matter, and gels, as well as harder metallic and molecular glasses. In contrast to conventional crystalline solids, the internal arrangement of their constituent microstructures (emulsion droplets, foam bubbles, etc.) lacks any intrinsic order. Understanding the rheological (deformation and flow) properties of these materials thus poses a considerable challenge. Typically, they behave elastically at low loads then yield plastically at larger loads. In this talk I shall summarise recent progress in understanding the yielding transition between an initially solid-like state and a finally fluidised one, as a function of time since the application of an imposed strain or load, with a particular focus on the concept that yielding can be very heavily delayed after the inception of shear.

Local mechanisms of plasticity in amorphous solids

Anaël Lemaitre - Navier, France

The last two decades have seen significant advances in our understanding of the mechanisms of plasticity in amorphous solids. Irreversible deformations result from the accumulation of local rearrangements that create elastic strains in their surroundings, thus triggering secondary events and plastic avalanches. These rearrangements are controlled by the crossing of global elastic instabilities, which are largely determined by local yield stress heterogeneities. Algorithms designed to access local yield stress values provide meaningful predictors of the plastic activity, and shed light on major phenomena such as strain localization or the Bauchinger effect.

Effects of temperature and humidity on the time dependent behaviour of geomaterials

Jean-Michel Pereira - Navier, France

All geomaterials are characterised by a mechanical behaviour with a more or less pronounced time dependency, which translates into creep and loading rate sensitivity. Time effects generally arise from various physico-chemical origins, such as water diffusion between different porosity scales, pressure-solution, sub-critical crack propagation... The macroscopic viscous behaviour of geomaterials have been characterised experimentally in many studies. However, the influence of humidity and temperature on the time-dependent behavior of these materials has been less investigated. In this presentation, time effects are first reviewed for some geomaterials, with an emphasis on a series of experiments on chalk saturated by several fluids or pair of fluids (air, water, oil, water-oil at different saturation levels). A constitutive framework to model these observations at the continuum scale is then presented, and the simulation results are compared to experimental data.

Micromechanics of sub-critical failure in a porous rock: insights from integrating sound and x-ray vision during sandstone deformation

Alexis Cartwright-Taylor - Heriot-Watt University, UK

Failure in brittle, porous materials initiates when structural damage localises along an emergent failure plane in a transition from stable crack growth to dynamic rupture. Due to the rapid nature of this critical transition, the precise micro-mechanisms involved are not fully understood and difficult to capture. However, these mechanisms are crucial drivers for earthquakes, including induced seismicity. Here we observe these micro-mechanisms directly by controlling the rate of micro-seismic events to slow down the transition in a unique triaxial deformation apparatus that combines acoustic monitoring with contemporaneous in-situ x-ray imaging of the microstructure. The results [Cartwright-Taylor et al., 2022] provide the first integrated picture of how damage and associated micro-seismic events evolve together during sample weakening, allowing us to directly constrain the partition between seismic and aseismic deformation at the micro- scale. The evolving damage in the 3D x-ray volumes and local strain fields undergoes a breakdown sequence involving self-organised exploration of candidate shear zones, spontaneous tensile failure and rotation of individual grains within a localised shear zone, and formation of a proto-cataclasite, highlighting the importance of aseismic mechanisms such as grain rotation in accommodating bulk shear failure. Dilation and shear strain remain strongly correlated throughout failure confirming the existence of a cohesive zone but with crack damage distributed rather than concentrated solely at the propagating front of a discontinuity. Seismic amplitude is not correlated with local imaged strain intensity, and the seismic strain partition coefficient is very low overall. We explain the stress evolution in terms of a new, sub-critical fracture mechanics model, and compare the seismic signatures between this experiment and a sister experiment carried out under constant strain rate loading [Mangriotis et al., in review]. Compared with loading under a constant strain rate, reactive loading to maintain a constant micro-seismic event rate increases the seismic b-value, decreases the maximum event magnitude, suppresses the number of events of all sizes, and reduces the seismic strain partition coefficient. Adding event rate control to that of maximum recorded magnitude may therefore be more effective than the current 'traffic light' system for managing induced seismicity. Effective management of induced seismicity is essential for safe operation of subsurface activities that disturb tectonic stresses in the Earth's crust, such as geothermal energy production and geological storage of carbon dioxide and hydrogen, to minimise risk from damage and potential loss of public confidence as we progress towards a net zero carbon economy.

Alexis Cartwright-Taylor is a geophysicist and experimentalist at Heriot-Watt University. Her research interests include the micro-mechanics of damage localisation and faulting, fluid-rock interactions, the statistical physics of fracture phenomena, and the controls on and predictability of material failure. Specifically, she combines high-resolution, time-resolved (4D) x-ray micro-tomographic imaging of in-situ rock deformation with seismology and statistical physics approaches to better understand the processes behind catastrophic material failure. She finished her Ph.D. in 2015 at University College London and worked as a postdoctoral researcher at the University of Edinburgh. In her new role as Assistant Professor in the Geoenergy Group at Heriot-Watt, she will focus on understanding and quantifying the micro-physical subsurface processes relevant to achieving Net Zero (i.e. the use of geothermal energy, seasonal storage of H2, long-term storage of CO2), and the associated risks of damage and induced seismicity.

Will the energy transition creep up on us?: The role of time-dependent deformation in human-induced subsurface activities

Suzanne Hangx - Utrecht University, Netherlands

With global temperatures rising, we are in the process of transitioning away from high-carbon energy sources, such as coal and oil, towards zero-carbon energy sources, such as geothermal energy and renewably generated electricity. This transition will inevitably lead to an increased use of our subsurface space. On the one hand, natural gas may play an immediate role as a (temporary) low-carbon alternative, while temporary hydrogen fuel and long-term CO₂ storage will become more important in the next decade. However, subsurface exploitation removes the natural system from its chemical and physical equilibrium. Indeed, the impact of our geo-resources needs on the environment has already become noticeable. Prolonged hydrocarbon production has led to subsidence and seismicity in offshore and onshore hydrocarbon fields. In the Netherlands, tens of centimetres of subsidence occurring above the gasfields of Groningen and Friesland, and associated induced seismicity, are key issues in the news. This may impact the potential for natural gas in aiding in the energy transition, as well as the potential for other human-induced activities to mitigate climate change.

In this contribution, I will consider what processes may control deformation in sandstone reservoirs, under realistic reservoir conditions. I will start with an overview of what research on the Groningen gasfield has taught us about time-independent and time-dependent deformation. Eventually descriptions of these grain-scale mechanisms should be included in mechanism-based models for assessing compaction creep and its role in controlling subsidence and associated seismicity. Since many of the grain-scale mechanisms are impacted by the presence of fluids and the chemical environment, I will conclude by shedding some light on what this could mean for alternative uses of subsurface storage space.

Creep of rock salt from the engineering perspective

Laura Blanco Martin - Centre de Géosciences, France

Rock salt (natural form of NaCl) is a polycrystalline material and exhibits creep, or time-dependent deformation. The mechanical behaviour of rock salt is not only important for the understanding of man-made underground facilities (such as nuclear waste repositories, leached caverns or mines), but also to understand Earth dynamics (e.g., creation of salt structures, such as pillows and domes).

Investigations at the microscopic scale reveal that there are several creep mechanisms in rock salt, each dominating under particular conditions (stress state, temperature, brine availability). However, their interactions are complex and not well understood. From the engineering perspective, a macroscopic, phenomenological approach is sought, at the expense of losing information on the dominant deformation mechanisms. The time-dependent behaviour of rock salt is inferred from laboratory tests on centimetric-scale samples, and the trends observed are extrapolated to the long-term. The duration of such test is much shorter than the lifespan of the underground facilities, and research is still needed to improve the predictive capabilities of constitutive models.

This talk will overview the main creep mechanisms in rock salt, the standard workflow for the design of underground structures in such rock and some recent tests to limit stress extrapolation. A quick overview of time-dependent models will be also presented.

Micromechanics of brittle creep in rocks

Nicolas Brantut - Department of Earth Sciences, University College London (UCL), UK

This presentation will review the phenomenology of brittle creep and the underlying physical processes responsible for time-dependent brittle deformation in rocks under elevated confining pressure. Under constant applied stress conditions, brittle rocks may undergo time-dependent creep and eventual failure (often called static fatigue). Creep occurs in two distinct phases: an initial decelerating phase (primary creep), followed by an accelerating phase towards failure (tertiary creep). In between these phases, an extended period exists where strain rate is (transiently) stable (secondary creep). Both the creep strain rate and the time-to-failure depend very sensitively on the applied maximum compressive stress, and on environmental conditions (humidity, water saturation, temperature, fluid chemistry). Typically, a few MPa change in stress can lead to an order of magnitude change in strain rate and time-to-failure.

The phenomenon of brittle creep and static fatigue can be qualitatively explained by subcritical crack growth of stress-induced microcracks. The transition from primary creep to tertiary creep corresponds to the microstructural state where interactions between microcracks start to dominate the local stress field around the cracks. A simple wing-crack model is capable of capturing all the phenomenology of brittle creep. However, macroscale predictions remain inherently challenging due to the extreme sensitivity of the results to initial microstructural parameters and the over-simplification of the crack network geometry. The phenomenon of progressive strain localisation can be captured by damage mechanics model, with the caveat that such theories often remain phenomenological.

In addition to subcritical crack growth, rock deformation experiments have shown that time-dependent friction at the microscale could play an important role in the long-term brittle deformation of rocks. Time-dependent friction could be a key additional mechanism that favours brittle creep, and should be included in future models aimed at capturing the mechanical behaviour of rocks undergoing complex loading paths.

Nicolas Brantut is currently a Professor of Geophysics at University College London, where he specialises in experimental rock deformation and rock physics. He obtained my PhD in 2011 from Université Paris 7, under the supervision (at ÉNS) of Dr. Alexandre Schubnel and Pr. Yves Guéguen. After a brief postdoctoral experience at Harvard, he joined UCL as a postdoc in 2011, where he became a NERC Fellow and an academic member of staff since 2013. His research is motivated by the need to understand large-scale geological phenomena, notably the physics of earthquakes. The focus of his work is to provide experimental observations and models of coupled deformation and fluid-flow processes in rocks, both in the brittle regime (shallow crust) and across the brittle-plastic transition in the lithosphere.