Time-dependent Behavior Research Articles

Viscoelastic–plastic rheological model and its application to tunnels

Tunnels exhibit obvious continuous deformation during excavation and operation. This behaviour is closely associated with the time-dependent behaviour of rocks, which is induced by groundwater-level fluctuation and prolonged periodic rainfall infiltration. This paper proposes a rheological model consisting of a Hooke elastomer, Kelvin body and novel plastic element in series (called the HKP model) to describe the creep response of rocks considering the characteristics of dry–wet cycles. First, dry–wet cycle creep tests were carried out to investigate the time-dependent behaviour: that is, the creep behaviour of sandstone. Then the creep equation of the viscoelastic–plastic model was derived, and the damage coefficients under the effect of dry–wet cycles and time were obtained. Finally, the HKP model was established to investigate continuous deformation during tunnel excavation. The results reveal that dry–wet cycles have obvious effects on the physical properties and creep behaviour of sandstone. The creep behaviour of sandstone undergoes three stages – namely, the decaying, steady and accelerated stages – that can be reasonably described by the proposed HKP model. In practice, the proposed model can accurately predict the creep behaviour of rocks in tunnels owing to excavation. Thus, the HKP model can help in establishing tunnel maintenance strategies to ensure long-term safety.

Modeling concrete deposition via 3D printing using reproducing kernel particle method

The quality and geometry conformity of 3D concrete printing are the two major concerns facing autonomous construction. To investigate the geometry of printed concrete and optimize the printing strategy, the reproducing kernel particle method (RKPM) was developed and implemented for the first time to describe the flow of fresh concrete and simulate the process of 3D printing. The proposed novel numerical simulation method is associated with a Bingham constitutive model, which was determined by a rotational rheometer. Physical slump tests were performed at various resting times to investigate the time-dependent behavior of concrete. An experimental parametric study of the geometry of a single-layer printed concrete was also conducted at various printing speeds and nozzle heights. Multi-layer printing cases were performed to investigate the cross-sectional deformation over the printed layers. The simulated values of slump over time compared well with the experimental measurements. As such, the proposed RKPM ability to capture time-dependent concrete behavior has been validated. The simulations based on the initially verified RKPM method can yield precise geometry predictions of a single- and multi-layer printed concrete, proving a wide range of application scenarios of the novel RKPM modeling approach.

Regional noise source location based on the time delays between station pairs from ambient noise interferometry

Identifying the location of a potential noise source assists in understanding the characteristics of the seismic or volcanic activity and provides valuable information for hazard assessment. Unlike the conventional waveform-based techniques that rebuild the source energy into the possible source region, we apply a simplified method to determine the absolute location of the noise source based on the station-pair time-delays from ambient noise interferometry. Synthetic tests demonstrate the robustness of the method and the locating precision is mainly influenced by the signal-to-noise ratio of the synthetic waveforms, and the higher frequency bandwidth source signals are more likely to result in accurate detection of the source. An application at the Central Tien Shan indicates that our method is capable of locating the known virtual source from the empirical Green’s functions. Furthermore, assuming a surface wave velocity, the depth of the source can be generally recovered from ambient noise interferometry in a simplified 3-D homogeneous model. The new method sheds light on applications of ambient noise interferometry for locating potential sources, making it suitable for detecting time-dependent behavior.

A space-time formulation for time-dependent behaviors at small or finite strains

A space-time formulation for time-dependent behaviors at small or finite strains

A unique time-dependent deformation behavior of coral reef limestone

Catastrophic failure in engineering structures of island reefs would occur when the tertiary creep initiates in coral reef limestone with a transition from short-to long-term load. Due to the complexity of biological structures, the underlying micro-behaviors involving time-dependent deformation are poorly understood. For this, an abnormal phenomenon was observed where the axial and lateral creep deformations were mutually independent by a series of triaxial tests under constant stress and strain rate conditions. The significantly large lateral creep deformation implies that the creep process cannot be described in continuum mechanics regime. Herein, it is hypothesized that sliding mechanism of crystal cleavages dominates the lateral creep deformation in coral reef limestone. Then, approaches of polarizing microscope (PM) and scanning electronic microscope (SEM) are utilized to validate the hypothesis. It shows that the sliding behavior of crystal cleavages combats with conventional creep micro-mechanisms at certain condition. The former is sensitive to time and strain rate, and is merely activated in the creep regime.

Analysis for Time-Dependent Behavior of Soft Rock Through a Reinforced Learning Fusion Constitutive Model

The long-term stability of tunnel structures is significantly influenced by the time-dependent behavior of the surrounding rock. Existing constitutive models often deviated from surrounding deformation due to the anisotropic nature of rock mass. In response, this study introduces a novel reinforced learning fusion constitutive model to accurately capture the time-dependent behaviors of soft rock. The framework and methodologies are first outlined, followed by the instantiation of the constitutive model of Burgers and creep parameters using laboratory testing data. To enhance accuracy, an XGBoost model is trained to reinforce the results of the constitutive model. The reliability of the proposed model is then validated against the original constitutive model and other representative machine learning models. Experimental findings demonstrate the superior characterization ability and stability of the presented reinforced model, where the calculation error reduces by 7.2E−06 at least, and [Formula: see text] score is improved by at least 1% to others. Consequently, the proposed model is reliable, offering a promising approach to capturing the actual time-dependent behaviors of tunnel surroundings in practical field applications.

Processing-structure-microscale properties of silicon nitride

This paper presents an overview of recent works on microscale mechanical and other properties of silicon nitride (Si3N4) determined by microcantilever bending tests and their relationships with the processing and microstructures. We first focus on deformation behaviors and fracture strength of Si3N4 single crystals. β-Si3N4 single crystals are plastically deformed at room temperature under high bending stress, and the yield stress depends on the crystal orientation. The critical resolved share stress of the primary slip system is determined to be below 1.5 GPa from the yield stress. Next, we address microscale mechanical properties of Si3N4 polycrystalline ceramics. Emphasis is placed on their grain-boundary strength or toughness in conjunction with intergranular glassy film (IGF) which is determined by processing parameters such as sintering additives. Assessment is made on two cases of fractures at the IGF-grain interface and that within the IGF, and in each of the cases, effects of rare earth oxide additives are discussed. In Si3N4 ceramics doped with Al2O3, β-SiAlON layer forming on β-Si3N4 grains enhances the microscale grain-boundary strength. Finally, we shed light on microscale property-degradation behaviors of Si3N4 ceramics, including the deterioration due to the contact with molten Al and the corrosion in sulfuric acid solution. The variation of the microscale properties appears in very short periods compared to the macroscale approaches, demonstrating the advantage in terms of rapid assessment of time-dependent degradation behaviors.

Time-dependent soil–structure interaction analysis using a macro-element foundation model

The delayed settlement of foundations due to soil consolidation, creep or particle breakage can alter the internal load distribution and differential settlements in a superstructure through soil–structure interaction (SSI). The study introduces a novel methodology to simulate time-dependent SSI that overcomes the complexity of incorporating the time-dependent behaviour of foundations into routine SSI analysis. The proposed approach represents the superstructure as a condensed stiffness matrix, and replaces the foundations and underlying soils with macro-element foundation models that encapsulate the foundation–soil interaction into load–displacement relationships derived from constitutive models. To examine the performance of the proposed method, a macro-element model for time-dependent analysis of shallow foundations on sand was integrated with structural analysis to simulate two tests performed in a geotechnical centrifuge on a 3D-printed aluminium framed structure supported by footings on sand. The simulated responses of the superstructure and foundations were found to agree well with those observed in the centrifuge tests. Parametric analyses were conducted to investigate the effect of loading history, load level on the superstructure, and creep tendency of soil on post-construction load redistribution and differential settlements. The findings suggest that creep of foundations on sand facilitates load redistribution in the structure from heavily loaded sections to lightly loaded sections. Moreover, post-construction load redistribution depends on the differential creep between footings and should be considered for structures that are quickly constructed or at high levels of strength mobilisation (low factor of safety). Overall, the study highlights the potential of the proposed methodology in analysing the time-dependent SSI and its applicability in practical SSI analysis.

Thermo-mechanical aging of carbon-black reinforced styrene-butadiene rubber under cyclic-loading

PurposeThe research aims to investigate the impact of thermo-mechanical aging on SBR under cyclic-loading. By conducting experimental analyses and developing a 3D finite element analysis (FEA) model, it seeks to understand chemical and physical changes during aging processes. This research provides insights into nonlinear mechanical behavior, stress softening and microstructural alterations in SBR compounds, improving material performance and guiding future strategies.Design/methodology/approachThis study combines experimental analyses, including cyclic tensile loading, attenuated total reflection (ATR), spectroscopy and energy-dispersive X-ray spectroscopy (EDS) line scans, to investigate the effects of thermo-mechanical aging (TMA) on carbon-black (CB) reinforced styrene-butadiene rubber (SBR). It employs a 3D FEA model using the Abaqus/Implicit code to comprehend the nonlinear behavior and stress softening response, offering a holistic understanding of aging processes and mechanical behavior under cyclic-loading.FindingsThis study reveals significant insights into SBR behavior during thermo-mechanical aging. Findings include surface roughness variations, chemical alterations and microstructural changes. Notably, a partial recovery of stiffness was observed as a function of CB volume fraction. The developed 3D FEA model accurately depicts nonlinear behavior, stress softening and strain fields around CB particles in unstressed states, predicting hysteresis and energy dissipation in aged SBRs.Originality/valueThis research offers novel insights by comprehensively investigating the impact of thermo-mechanical aging on CB-reinforced-SBR. The fusion of experimental techniques with FEA simulations reveals time-dependent mechanical behavior and microstructural changes in SBR materials. The model serves as a valuable tool for predicting material responses under various conditions, advancing the design and engineering of SBR-based products across industries.

Investigation on failure mechanism and time-delay fracturing behavior of hard-rock tunnel under extremely high geostress state

To investigate the failure mechanism and time-delay fracturing behavior of hard-rock tunnel under extremely high geostress state, a series of conventional triaxial compression tests and time-delay loading–unloading mechanical tests on rocks were conducted. Combining testing results and on-site data of deep-buried tunnels, the generation mechanism and failure process of time-delay rockbursts were analyzed. The results indicate that with the increase of confining pressure, the failure mode of hard-rock exhibits a transition from axial splitting type and shear-slip type to special squeezing-expansion type. The progressive damage of rocks under extremely high stress state mainly manifests as aging lateral and volumetric expansion. Under time-delay compression tests, the long-term strength of hard-rock is lower than the threshold stress of σeb. In extremely high stress state, the fracture and dissipated energy evolution of rocks has significant time-dependent characteristics. Under extremely high stress conditions, rocks can store a large amount of releasable energy internally and gradually generate numerous cracks without the need for external work, ultimately leading to sudden unstable failure. Affected by the superposition of time-delay pressure and loading–unloading effects, the hard-rock also exhibits the same time-dependent fracturing behavior as soft-rock under high stress state, but its deformation mechanism is dominated by lateral expansion and crack volumetric dilatancy. When the stress level is far from reaching the ultimate strength required for rockmass failure, it is sufficient to cause the propagation of internal microcracks. Under the action of time-delay loads, the spalling and peeling failure of surrounding rock is significantly reduced, but the scale of unstable blocks is larger. Based on the failure process and microseismic monitoring date of rockburst in hard-rock tunnels, the entire evolution process of time-delay rockbursts can be divided into the following six stages: before excavation, rockmss excavation, aging cracking, squeezing-expansion, instability and spalling, time-delay rockburst. Time-delay rockburst has an obvious acoustic emission calm period before its occurrence, making its incubation process has strong suddenness and randomness.

Time-dependent performance of large piled raft in clayey soil

In this study, three-dimensional numerical analysis has been performed to comprehend the time-dependent behavior of large piled rafts founded in saturated clayey soil, explicitly for the time of superstructure construction and post-construction up to the end of soil consolidation. The performance under different construction times for the corresponding unpiled raft and the piled raft with uniform pile length configuration of varying pile number, spacing, and length have been examined and then compared with that of non-uniform length configuration for the same total pile length. The dissipation of excess pore water pressure, average settlement, and differential settlement are presented and discussed in detail. A quicker dissipation rate of excess pore pressure is noted with either fewer piles, wider pile spacing, or shorter-length piles. An increase in construction time results in a lesser total average settlement at the end of consolidation. The piled raft with uniform pile length configuration shows a higher differential settlement than the unpiled raft. However, by adopting a suitable non-uniform length configuration, negligible differential settlement, higher load-carrying capacity, and a significant reduction in pile material volume can be achieved. Predictive expressions have been proposed to estimate the average and differential settlements of piled raft with uniform length configuration.

Modeling of time-dependent mechanical behavior of oleic acid nanocomposites using nanoindentation

Supercrystalline nanocomposites are a burgeoning class of hybrid inorganic–organic materials. Studies showed that self-assembly of iron oxide particles surface-functionalized with organic (e.g. oleic acid) ligands produces a supercrystalline nanocomposite with exceptional mechanical properties. Consequently, significant research has been conducted on these materials to experimentally characterize the mechanical properties of such materials. However, so far all modeling studies used time and rate independent elastoplastic material models. In the light of new experimental results, we propose to extent this view and use time-dependent models to capture viscoelastic behavior. To this end, we quantified this behavior using nanoindentation creep experiments and modeled it using a rheological network model with several parallel Maxwell branches and an additional elasto-plastic branch. We demonstrate how the parameters of such a model can be found using inverse analysis. With the calibrated material model, a good agreement of the time dependent behavior between simulation and experimental results is achieved. Thus, a method is provided to model time dependent behavior using complex non-classical experiments like nanoindentation.

A thermo-hydromechanical damage model and its application to a deep geological radioactive repository

This study conducts a numerical analysis of long-term thermo-hydromechanical (THM) processes, with a particular focus on deep geological disposal of radioactive waste. It emphasizes the modeling of damage zones resulting from excavation activities, as well as changes in pore pressure and temperature. The numerical model presented in this paper delineates the fundamental relations of thermo-poro-elasticity. It also introduces a double phase field model specifically formulated for rock materials under compressive stress, taking into account THM coupling and time-dependent behavior. The proposed model has been implemented in a finite element code and applied to numerical analysis of short and long terms responses around a horizontal borehole in the context of the French High-Level Waste (HLW) disposal concept. In particular, displacements, temperature changes, pore fluid pressure variations as well as evolution of induced damage zones are presented and analyzed for different periods including excavation, operation and post-closure. It is found that the occurrence of damage zones is clearly related to the spacing distance between two neighboring disposal boreholes. The time-dependent deformation of host rock plays an significant role in the long-term responses.

Direct Evidence of Electric Double Layer (EDL) Repulsive Force Being Responsible for the Time-Dependent Behavior of Clay Gels in the Structural Rejuvenation Mode.

A strong EDL repulsive force is needed to accentuate the time-dependent behavior of charge and shape anisotropic clay gels at the stepdown shear rate. This force was strengthened by P2O74- adsorption, increasing the negative charge density of the clay particles. At the stepdown shear rate of 10 s-1, it is strong enough to disrupt the flow-aligned structure attained at 1000 s-1 and orient the particles to form more bonds. The resultant outcome is stepdown shear stress increasing with time until these structure disruption and bond formation processes reach an equilibrium state. The number of lower energy approach configurations (-ve face - +ve edge) for bonding is reduced by the strengthened EDL repulsive force, slowing the bonding process. The time to reach the equilibrium stepdown shear stress value increased initially and then decreased and became zero at a high negative charge density where the charge anisotropy of the particles no longer exists. The need of a sufficiently strong EDL repulsive force for the display of time-dependent behavior is true for all clay gels: Laponite, hectorite, NaMnt, sepiolite, and kaolin gels. The untreated NaMnt gel already displayed time-dependent behavior as its EDL repulsive force is sufficiently strong. The same EDL-control time-dependent behavior was obtained if pH was used to vary the negative charge density of the clay particles.

Fractional cyclic cohesive zone model for time-dependent fatigue behavior of soft adhesives under mode-II loading

Soft adhesives exhibit nonlinear viscoelastic behavior during cyclic loading, suggesting that their cycle-dependent fatigue behavior can be significantly affected by the time-dependent deformation behavior. Soft adhesives are frequently subject to various cyclic conditions in practical applications, presenting potential safety risks. This paper has proposed a fractional cyclic cohesive zone model (CZM) to characterize the time-dependent fatigue behavior of soft adhesives. To capture the nonlinear evolution of fatigue damage under asymmetric stress-controlled cyclic loading, a fatigue damage model that considers the contribution of in-situ stress/strain was incorporated into fractional-order viscoelastic model. The proposed CZM was validated through single-lap shear creep tests at various stress levels and fatigue tests at various stress amplitudes and loading periods. Furthermore, the impacts of stress ratio and peak stress level on fatigue failure under different loading periods were investigated using the proposed CZM. The results indicate that under a short loading period, the failure of the soft adhesives is primarily influenced by cycle-dependent fatigue damage, while under a long loading period, it is primarily affected by time-dependent creep deformation. Overall, this work offers a numerical strategy to describe the fatigue failure of nonlinear viscoelastic soft adhesives and to understand their time-dependent fatigue failure mechanism, with implications for product design and optimization.

An analytical–numerical method for the hydraulic–mechanical coupling analysis of time-dependent behavior of pressurized tunnels: Impact of an excavation damaged zone

The issue of pressurized tunnels has been sufficiently investigated in the literature; nevertheless, the long-term behavior of the problem, which is the case in very squeezing conditions, remains unexplored. From a practical standpoint, the development of a damaged zone around the tunnel, due to the poor quality of blasting for excavation, imposes an additional challenge in predicting tunnel responses. This paper introduces an analytical approach addressing both water seepage and the excavation damaged zone (EDZ) concerning the long-term behavior of lined circular pressurized tunnels. To achieve this goal, the rheological behaviors of the initial rock mass and damaged zone are modeled using the Burgers model, along with considering the time-dependent variation in the rock mass hydraulic conductivity. After the validation of the model, the conducted parametric studies reveal that rock mass and lining hydraulic conductivities, EDZ radius, and the Burger shear modulus are the most influential parameters.

Characterization of the layer, direction and time-dependent mechanical behaviour of the human oesophagus and the effects of formalin preservation.

The mechanical characterization of the oesophagus is essential for applications such as medical device design, surgical simulations and tissue engineering, as well as for investigating the organ's pathophysiology. However, the material response of the oesophagus has not been established ex vivo in regard to the more complex aspects of its mechanical behaviour using fresh, human tissue: as of yet, in the literature, only the hyperelastic response of the intact wall has been studied. Therefore, in this study, the layer-dependent, anisotropic, visco-hyperelastic behaviour of the human oesophagus was investigated through various mechanical tests. For this, cyclic tests, with increasing stretch levels, were conducted on the layers of the human oesophagus in the longitudinal and circumferential directions and at two different strain rates. Additionally, stress-relaxation tests on the oesophageal layers were carried out in both directions. Overall, the results show discrete properties in each layer and direction, highlighting the importance of treating the oesophagus as a multi-layered composite material with direction-dependent behaviour. Previously, the authors conducted layer-dependent cyclic experimentation on formalin-embalmed human oesophagi. A comparison between the fresh and embalmed tissue response was carried out and revealed surprising similarities in terms of anisotropy, strain-rate dependency, stress-softening and hysteresis, with the main difference between the two preservation states being the magnitude of these properties. As formalin fixation is known to notably affect the formation of cross-links between the collagen of biological materials, the differences may reveal the influence of cross-links on the mechanical behaviour of soft tissues.

Modelling time-dependent relaxation behaviour using physically based constitutive framework

The application of interrupted die motion during the deformation process in a servo press cycle is known to enhance the forming limit of metallic materials. This observation is generally attributed to the transient effects associated with stress relaxation phenomenon. However, attempts to model stress relaxation behaviour using physically based constitutive formulations in the finite element method are scarce. In this work, a modified version of the Kocks–Mecking–Estrin (KME) dislocation density model is used to evaluate the substructural changes during relaxation. An ‘uncoupled’ elasto-viscoplastic approach is employed to accommodate the plastic strain rate effect. This modelling approach is implemented in the commercial finite element software via a user material subroutine. The model is validated through simulations of interrupted uniaxial tensile tests for aluminium alloy AA7075 under two different aging conditions. The implemented model is shown to closely capture the experimental results and account for changes in dislocation density and the athermal component of flow stress during relaxation. Subsequently, the model is applied to simulate monotonic and interrupted hole expansion tests (HET), and the results are discussed qualitatively.

The formation mechanism of low-angle loess-mudstone seismic landslides

Seismic-induced landslides represent intricate geological phenomena requiring a multidisciplinary investigative approach. This study examines the formation mechanisms of low-angle loess-mudstone landslides triggered by the 1920 Haiyuan M8.5 earthquake. We employ a synthesis of field investigations, high-density electrical resistivity tests, drilling, laboratory experiments, and numerical simulations. High-density resistivity results support the identified zone at the loess-mudstone interface, indicating a saturated area prone to liquefaction. Dynamic triaxial tests further verify liquefaction occurrences during seismic events within this zone. Additionally, numerical simulations conducted with FLAC2D and the PM4Silt constitutive model provide valuable insights into the temporal and spatial progression of landslides. The liquefaction zone experiences severe shear strain, precisely aligning with the location of the sliding band. Shear strain time-history analyses elucidate early manifestations and time-dependent behaviors at interfaces, providing a nuanced understanding of deformation patterns. The study delineates a comprehensive failure mechanism, unraveling how liquefaction in the saturated loess layer initiates in the upper and toe regions, subsequently propagating throughout the slope. Tension in the upper part and compressive uplift at the toe manifest, resulting in overall landslide movement. These findings highlight the significance of differential shear strain, leading to a layered shear deformation zone. The results yield invaluable insights for seismic stability assessments in regions with similar geological characteristics. This research not only advances the understanding of earthquake-induced landslides but also demonstrates the synergy between field investigations, advanced geotechnical testing, and numerical modeling in unraveling complex geological processes.

Experimental Study on the Accelerating Creep of Rock Under Dry and Wet Conditions Based on a New Test Method

Creep tests under constant stress are among the most important tests for investigating the time-dependent behavior of rock. In previous studies, creep tests were conducted under various loading and environmental conditions; however, it was very difficult to demonstrate accelerating creep at failure at stresses less than 50% of strength in conventional creep tests. In this study, a new test method is proposed that combines an alternating loading-rate test and a creep test in the post-failure region. The accelerating creep as well as the loading-rate dependence of strength were successfully obtained simultaneously from a single specimen. This test method was applied to three rock types under dry and wet conditions. The results of Sanjome andesite under both dry and wet conditions, Kimachi sandstone under dry conditions, and Tage tuff under dry conditions showed a similar relationship between creep strain, creep strain rate, and residual time (i.e., creep lifetime minus elapsed time), from high to low creep stress levels, and a close relationship between accelerating creep and the loading-rate dependence of strength. Further, the mechanism responsible for the time dependence was found not to change significantly from high to low stress levels. In contrast, different results were obtained when high and low creep stress levels were compared in Kimachi sandstone and Tage tuff under wet conditions. The larger increase in creep strain with increasing creep strain rate at lower creep stress levels was related to the shape of the stress–strain curve in the post-failure region.