Nonlinear Failure Research Articles

Obtaining the longitudinal compressive response of unidirectional laminate composites from fiber misalignment micrographs through machine learning

The longitudinal compressive behavior of unidirectional composite laminates with fiber waviness is highly complex and plays a crucial role in determining final failure of composites. Evaluating this behavior, especially considering nonlinear failure mechanisms like kink-band formation, typically requires computationally expensive finite element analysis, which is impractical for large-scale quality inspection. To address computational challenges, this paper developed a new computational framework using Convolutional Neural Network (CNN) models, providing an ultra-efficient prediction of the entire stress–strain curve of composites with fiber waviness. The CNN models were trained on simulation data generated from an experimentally validated mesoscale finite element model. The microstructures of the composites with fiber waviness were taken from realistic micrographs, resulting in diverse stress–strain curves. The proposed CNN models showed high accuracy and efficiency for predicting the highly nonlinear stress–strain curves of the composites, which can be employed as a real-time evaluation method of the criticality of fiber waviness.

Research on damage characteristics and contact interface evolution behavior of double-block ballastless track considering tunnel floor heave

Excessive railway tunnel floor heave (TFH) will reduce the durability of the track structure and jeopardize train operation safety. The TFH characteristics were fitted into cosine and bilinear curves according to the monitoring data. A nonlinear failure analysis model of double-block ballastless track under TFH was established. The deformation transfer law, structural damage mechanism and the interlayer bonding interface failure evolution of the track structure under different TFH characteristics were explored. The results show that the deformation of TFH can be well mapped to the track. The amplitude transfer ratio is less than 100 %. The maximum wavelength transfer ratio under the cosine and bilinear TFH is 129.3 % and 127.5 %, respectively. To avoid the damage of track structure, when the wavelength is 10 m, the amplitude of cosine and bilinear TFH should be controlled at 2.5 mm and 0.5 mm respectively. When the wavelength is greater than 10 m, the amplitude can be appropriately increased. To avoid interlayer bonding cracking, the cosine and bilinear amplitudes with a wavelength of 10 m should be controlled at 5 mm and 1.5 mm, respectively. The track-tunnel interlayer debonding failure under the cosine curve occurs at the edge of the TFH, while the bilinear curve occurs at the center and edge of the TFH. The gaps under the cosine and bilinear TFH exhibit double-peak and multi-peak shapes, respectively. This study can provide theoretical guidance for controlling the performance degradation of track structure caused by TFH.

Assessing swelling-induced damage in shale samples during triaxial testing

In shale testing, understanding the impact of effective stress and saturation conditions is crucial for accurate material behaviour assessment and parameter determination. In some cases, saturation in triaxial testing starts at low effective stress before ramping up for shearing. However, when in contact with water (or saline water), shales are prone to swelling, particularly at low effective stress levels, which can induce fissures and alter material properties. This study investigates the influence of fluid saturation strategies and stress/pressure variations on the mechanical behaviour of shales, particularly under low effective confinement. Building upon the comprehensive testing campaign (>140 tests) in Crisci et al. (2024), additional tests were conducted on Opalinus Clay shale, focusing on sample saturation methods and loading histories before shearing. The conditions under which tested specimens experience damage were detected through diagnostic indicators such as differences in stress path and lower strength and stiffness compared to intact specimens with identical basic properties. Micro CT scanning confirms that damage is related to the development of fissures. The volumetric changes in specimens were quantified throughout the testing phases and thresholds for tolerable strains and effective stresses, specific to this material, were established. Comparative analysis with Opalinus Clay from shallower depths and other shales globally revealed consistent findings. Notably, it is shown that, for all shale types analyzed, a linear failure envelope emerges in the low to intermediate effective stress regime when filtering out "damaged" specimens. This suggests that non-linear failure envelopes observed in some cases may stem from exposing specimens to low effective stress before shearing.

Statistical prediction for nonlinear failure function of linear loads: application to plate buckling in ship structure

AbstractThis study presents a practical method for calculating the probability of exceedance (PoE) of the nonlinear failure function of the linear loads randomly fluctuating in irregular waves. In general, obtaining the exact PoE of such nonlinear quantities requires sophisticated computational method that are not well-suited for practical design. In contrast, the author in a previous study proposed a practical formula of the PoE distribution for von Mises stresses by asymptotic approximation, which can be applied when the criterion surface is ellipsoid in the stochastic variable space. Following this, the present study shows a method for calculating the PoE for a more general function of which the isosurface is expressed as a combination of ellipsoids. As a specific example of its application, this paper takes the limit state of the plates in ship structures specified in the common structural rules (CSR) and presents the calculation procedure of direct numerical integration as well as asymptotic approximation approaches. Calculation of the 1/1000 maximum expected value of the evaluation function of plates in short-term sea states using 700 actual plates in a ship structure confirms that the proposed method, which does not require integration, is in good agreement with rigorous methods using numerical integration.

Upper Bound Limit Analysis of Deep Tunnel Face Support Pressure with Nonlinear Failure Criterion under Pore Water Conditions

Based on the nonlinear failure criterion and modified tangential technique, the upper bound solutions of the critical supporting pressure on the deep tunnel face were obtained under pore water pressure conditions. The influence of parameters on the critical supporting pressure and collapse range was investigated according to the unlimited block failure mechanism. It was found that the upper bound solutions of the critical supporting pressure increase with the growth of the nonlinear coefficient and pore water pressure coefficient. The collapse range of the tunnel face scales out with the increase in the nonlinear coefficient and shrinks with an increasing pore water pressure coefficient. Moreover, with the increase in the nonlinear coefficient, the impact strength on critical supporting pressure and collapse range declines gradually. According to the calculated results, both the pore water pressure and nonlinear criterion factors have negative impacts on the stability of the tunnel face. Thus, more attention should be paid to these parameters to ensure face stability in deep tunnel construction.

Damage evolution in asphalt mixtures based on in-situ CT scanning

A novel approach utilizing in-situ Computed Tomography (CT) scanning and digital image processing techniques was developed to overcome the limitations of traditional CT image analysis in studying microcrack evolution in asphalt mixtures. Two types of graded asphalt mixtures (continuous gradation/AC and intermittent gradation/SMA) were scanned in-situ to capture internal structural changes. Digital image processing distinguished primary voids from cracks and extracted crack evolution. Multivariate regression analysis linked crack parameters to compressive strain. The study found that crack evolution during uniaxial compression in asphalt mixtures can be divided into densification, linear elastic deformation, and nonlinear failure stages. As load increases, the number, volume, and void percentage occupied by cracks rise, peak, and then decrease due to merging and engulfing after the ultimate load. The skeletal structure of cracks was obtained, and a damage evolution equation was established, linking crack parameters to damage evolution. Crack tortuosity was used to characterize the resistance effect of different gradations on crack propagation. This methodology provides new insights and technical support for studying damage evolution and understanding the failure mechanisms of asphalt mixtures.

The three-dimensional stability analysis of piled slopes in unsaturated and inhomogeneous soils with nonlinear failure criterion

Under the nonlinear Mohr-Coulomb (MC) failure criterion, based on the upper-bound limit analysis theorem, the three-dimensional(3D) stability of piled unsaturated inhomogeneous slopes is analyzed. By incorporating the nonlinear strength parameters c t and φ t, the energy balance equation is established, and the explicit expression of slope safety factor (F S) is derived by the gravity increase method (GIM). In addition, a genetic algorithm (GA) is used to calculate the minimum F S. The results obtained were compared with those of existing literature to verify the effectiveness of the method used in this paper. The influence of nonlinear parameters on slope stability was studied through parameter analysis. The results show that the nonlinear parameters of soil have a significant influence on the stability of piled slopes. The F S increases with the increase of nonlinear coefficient and uniaxial tensile strength and decreases with the increase of initial cohesion of soil. In addition, the critical slip surface of the slope becomes shallower with the weakening of soil nonlinearity. Furthermore, ignoring the suction effect will overestimate the slope stability, and the slope stability intensified with decreased soil inhomogeneity.

Predictive analysis of power degradation rate in solar PV systems emphasizing hot spots and visual effects-based failure modes

A definite and exclusive long-term PV degradation projection is required to reduce financial vulnerability in the solar photovoltaic plant-based energy transition markets. So, in this paper beside a traditional linear rate approach, a non-linear design tool for quantifying long-term failure mode-based power degradation rate (Rd), is proposed. An on-field experimental investigation incorporating visual effects-based Solar I–V characterization and thermal imaging for a duration of 1 year (February 2022 to January 2023) is carried out on a realistic solar PV system exposed to field conditions for 5–6 years. The experimentally evaluated Rd is 7.7 %/year. Two non-linear failure mode-based Rd models employing machine learning approaches, with differences in inputs are developed and are proven economically useable against the reported assessment techniques. The root mean square error (RMSE) for model 1 and model 2 during testing is 0.0019 and 0.0020 respectively (LSTM based approach) whereas testing error for model 1 and model 2 using back propagation based approach is 0.00182 and 0.00132 respectively. The proposed tool is also validated for a realistic PV plant in Telangana. A closeness of prediction against the actual of 9.0 % is observed for model 1 during validation, whereas the same for model 2 is 9.6 %.

Deterioration evolution mechanism and damage constitutive model improvement of sandstone–coal composite samples under the effect of repeated immersion

Underground reservoirs in coal mines, consisting of goafs (By goaf, we mean the space that remains underground after the extraction of valuable minerals), are commonly utilized for mine water storage and drainage, with their primary load-bearing structures being the “roof–coal pillar” systems. Consequently, this structure must endure the repeated immersion behavior resulting from fluctuations in the mine water level, resulting in the risk of geological disasters. This paper analyzes the variation in mechanical properties of sandstone–coal composite samples after repeated immersion cycles through axial loading tests. The results indicate that the water content of the sample exhibits a notable and rapid increase with each successive immersion cycle. This corresponds to a decrease in the stress threshold and modulus parameters of the samples. Moreover, the acoustic emission signals serve as indicators of the softening characteristics of the samples. With the increase in immersion cycles, there is an augmentation in both the frequency and extent of shear cracks. The non-linear failure characteristics of the samples become more pronounced. Consequently, water significantly weakens the cementing material between rock grains. Both sandstone and coal display a decrease in deformation resistance capabilities at a macroscopic level. The constitutive model of the composite sample was improved based on the degradation characteristics of mechanical strength and strain energy parameters, which offers enhanced accuracy in analyzing the degradation process caused by water immersion. This paper offers a crucial theoretical foundation for comprehending the deterioration evolution characteristics of the “roof–coal pillar” bearing structure affected by repeated immersion.

Direction-dependent failure envelopes of sand-structure interfaces with snakeskin-inspired surfaces

Snakeskin-inspired surfaces generate direction-dependent interface strengths, with shearing in the cranial direction (i.e.; against the scales) generating greater strength than in the caudal one (i.e.; along the scales). This directionality is enabled by the transfer of load in friction and passive resistances. It is unclear if failure of these interfaces can be captured by models used for purely frictional interfaces. Interface shear tests complemented with particle image velocimetry (PIV) analyses were performed on snakeskin-inspired surfaces with different asperity geometries and on reference rough and smooth surfaces. The results of experiments performed at different initial effective stresses under constant normal stiffness boundary conditions show significant dilation-induced increases in effective stress. These increases were greater during cranial than caudal shearing, producing greater cranial strengths. These surfaces yielded nonlinear failure envelopes, with greater shear to effective stress ratios at smaller effective stresses, while the rough and smooth surfaces mobilized linear failure envelopes. The PIV analyses indicate that the snakeskin-inspired surfaces induce localized strains in the vicinity of the asperities, leading to wavy failure planes. The average shear strains are correlated with the mobilized shear strengths, with increases in effective stress leading to decreases in both strains and stress ratio.

PERIDYNAMIC SIMULATION OF FRACTURING IN HETEROGENEOUS ROCK BASED ON X-RAY DIFFRACTION AND SCANNING ELECTRON MICROSCOPE TESTS

The mechanical properties and fracture behavior of rocks are significantly influenced by their microscopic characteristics. At present, there is a prevalent treatment of rocks as homogeneous materials or an oversimplified assumption of mesoscopic material properties following the Weibull distribution, often overlooking the impact of mineral composition and porosity. This study addresses these limitations by utilizing X-ray diffraction (XRD) and scanning electron microscope (SEM) tests to capture and characterize the microscopic features of rocks, including mineral composition and porosity. Subsequently, a mesoscopic peridynamic (PD) model is developed employing the Knuth-Durstenfeld shuffling algorithm to accurately reflect the real rock microstructure. The efficacy of this method is validated through experiments conducted on sandy mudstone and fine-grained sandstone. Moreover, a parametric analysis is performed, considering variations in porosities and mineral compositions. As porosity increases, numerous small cracks emerge laterally in the model, causing a notable decline in the rock's strength. Rock comprising a single mineral composition typically displays linear failure behavior. Conversely, a rock with a diverse array of minerals tends to exhibit non-linear failure behavior, indicating an increased level of heterogeneity within the material.

Probabilistic assessment of seismic earth pressure against backfills with a nonlinear failure criterion

A novel approach for the probabilistic assessment of seismic earth pressure against nonlinear backfills is introduced in this study. To implement reliability-based design for the retaining structures under seismic loading condition, nonlinear upper bound analysis is adopted to obtain the seismic earth pressure through optimization procedure. Firstly, rigorous analytical function is formulated to reveal the normal-shear stress information along the failure surface in soil with nonlinear failure criterion. Subsequently, a kinematic equation is put forward to estimate the seismic earth pressures by balancing the external work rate and the internal energy dissipation rate. The solutions are verified by the Discontinuity Layout Optimization numerical modellings based on the derived stress data from the proposed method. To consider the probability analysis of nonlinear backfill properties, the moment method is presented by combining the adaptive dimension decomposition with the direct integral method. According to the estimated first four statistical moments, the approximated probability density function of the performance function is determined contently. Finally, the failure probability of seismic earth pressure is calculated based on the proposed moment method. Two numerical examples demonstrate that the moment method can be adapted to the characteristics of nonlinear backfills and further improve the accuracy of reliability estimation by introducing higher-order moments analytically.

Discrete element analysis and analytical method on failure mechanism of retaining structures with narrow granular backfill

AbstractAscertaining failure mechanism is a prerequisite of the derivation for earth pressure against retaining structures. Retaining structures constructed adjacent to existing structures and excavation with narrow backfill have become common in practical engineering. The backfill width has a significant effect on the failure mechanism, requiring further study. In this study, a series of discrete element analyses are conducted to investigate the shear localization in soil mass behind retaining structures with narrow backfill in the active and passive limit states at the grain scale. Furthermore, the distribution characteristic of failure surfaces in soil mass is discussed from three aspects: the development of the failure surface, the state of soil mass behind retaining structures, and the shape of the failure surface. Based on the typical nonlinear failure mechanisms observed in particle rotation contours with various backfill widths and interface friction angles, the failure mechanisms behind retaining structures with narrow spacing are categorized into three types according to the backfill widths. According to the stress characteristics of interfaces under different failure mechanisms, the variational method and Mohr stress circle analysis are adapted to analytically obtain the failure surfaces behind the retaining structure with narrow backfill. Comparisons with results obtained by the discrete element simulation show a reasonable agreement. In addition, a series of parameter studies are conducted to investigate the effect of backfill widths and interface friction angles on the failure mechanism.

Multivariable Regression 3D Failure Criteria for In-Situ Rock

Wellbore stability problems increase with the exploration and development of oil and gas reservoirs. A new 3D non-linear failure criterion is proposed as a trigonometric function considering the intermediate principal stress (2) on the triaxial compression test data. Mohr-Coulomb and Hoek-Brown are well-known failure criteria, but they do not consider the influence of (2) on rock strength. This new criterion produces a concave surface on the principal stress space (1,2, 3) with the influence of intermediate principal stress. In this study, sensitivity analysis for the variable is also done to understand the significant influence of parameters on the accuracy of the proposed criterion. Further validation of this non-linear criterion on three principal stresses (1,2, 3) was done compared with linear regression and second-degree polynomial regression results. It has been observed that the new non-linear 3D criterion with five material parameters reveals a good fit compared to linear regression and second-degree polynomial regression, which have four and six material parameters, respectively. The new non-linear criterion was further validated by comparison with existing criteria like the Priest, Drucker-Prager, and Mogi-Coulomb. It has been observed that the new 3D non-linear criterion shows a more accurate result than these existing criteria as certain rock types exhibit coefficient of determination (DC) values near one, precisely 0.95 for inada granite, 0.94 for orikabe monzonite, and 0.91 for KTB amphibolite. In contrast, other rock types have DC values ranging from 0.7 to 0.9. The new 3D non-linear criterion also yields lower root means square error (RMSE) values than the Mogi-Coulomb criterion for seven rock types. Specifically, the RMSE values by the new criterion are as follows: KTB amphibolite - 40.03 MPa, Dunham dolomite - 15.16 MPa, Shirahama sandstone - 9.08 MPa, Manazuru andesite - 22.14 MPa, Inada granite - 35.47 MPa, and Coconino sandstone - 19.047 MPa. This new 3D criterion gave precise predictions of the failure of the formation under in-situ stresses and was further helpful for the simulation of the wellbore in the petroleum industry. The variable in the new 3D criterion should be calculated from triaxial compression test data for each formation rock before applying this criterion to the wellbore stability problem and the sand production problem.

Seismic active earth pressure for 3D earth retaining structure following a nonlinear failure criterion

Stability analysis for three-dimensional (3D) earth retaining structures (ERSs) is a pivotal problem in geotechnical engineering, particularly for seismically active areas. In this work, the 3D ERSs in soil are assessed for seismic stability following a nonlinear strength criterion. The power-law strength criterion and seismic forces are introduced into the 3D ERS stability analysis via a multi-cone failure mechanism. The coefficient of active soil pressure Ka is derived by exploiting the energy balance equation. The upper bound solutions, that is the maximum results of the Ka are captured with the help of a genetic algorithm. The validity of the current study is verified by a comparative analysis, and the effects of soil strength nonlinearity, the seismic forces, the soil-wall friction angle, the height, the inclined angle and the 3D geometric traits of ERSs on the Ka solutions and the stability of ERSs are investigated. It is indicated that the height and the 3D geometric characteristics of the ERSs will not only determine the Ka solutions directly, but also influence the impact of soil strength nonlinearity on the stability of ERSs. Strength criteria should be chosen combining the geometric characteristics of ERSs to derive more critical estimates on the stability of 3D ERSs. Additionally, a range of seismic and static stability charts used for preliminary design are put forward as well.

Materials, Weaving Parameters, and Tensile Responses of Woven Textiles

Fabrics have been recognized as a necessary component of daily life due to their involvement in garments, home textiles, and industrial textiles. The mechanical performance of textiles was considered essential to meet the end-user requirements for strength and durability. The purpose of this work was to provide an overview of the textile structures and tensile strengths of woven textiles. Different types of textile structures, depending on the weaving methods (woven, braided, knitted, non-woven) and the most common architectures of woven fabrics (plain weave, twill and sateen), were presented. Common materials constituting the textiles’ structures and a comparison in terms of the density, Young’s modulus and tensile strength between natural (plant-based, animal-based, and mineral-based) and synthetic fibers were reported. The mechanical properties of woven textiles were presented for neat and coated textiles, primarily in terms of the tensile strength. Depending on the cases, typical regions in the load–displacement curve (i.e., crimp, elastic, non-linear failure, thread fracture) were highlighted. The impact of the architecture, yarn distance and size, and yarn twisting on the tensile strength of woven fabrics was then illustrated.

Planar Slope Failure in Heavily Jointed Rock: Tension Cracks and Nonlinear Strength

This work proposes the calculation of the factor of safety for a strongly jointed rock mass in the case of plane failure with a tensile crack whose exact position or depth is not known but is expected to exist. This calculation is performed by applying the non-linear failure criteria of the Focus Procedure of Úcar and Hoek–Brown’s and implementing the necessary formulae in a spreadsheet. The aim is to provide a simple, cost-effective, and easy-to-use procedure that is useful in the early stages of a project or as a starting point for more detailed investigations. Besides slope geometry and strength parameters, the required parameters are the RMR of the rock mass or its mi, depending on the criterion used. The proposed procedure allows for the estimation of the factor of safety, the position and depth of the tensile crack, and the inclination of the failure plane in the most unfavorable case, with reasonable accuracy, using an iterative process with the conventional tools available in common spreadsheet programs. An example is provided in which an accuracy of 86–96% for the factor of safety is obtained.

Study on creep behaviors and nonlinear creep constitutive model for sandy marine hydrate-bearing sediments

Marine natural gas hydrate (NGH) production is critically affected by reservoir damage, which is usually presented as creep deformation. Clarifying the creep behaviors of hydrate-bearing sediments (HBS) is essential for predicting potential geoengineering risks during long-term NGH mining. In this study, a series of multi-step loading creep tests on HBS samples are conducted and a modified creep model specialized for sandy HBS is proposed. The creep strain, creep rate, and long-term strength are experimentally evaluated under various hydrate saturation (Sh) and/or effective confining pressure (Pc). Three typical creep stages of deceleration creep, stable creep, and accelerated creep are observed in all experiments. The results show that the creep deformation of HBS is enhanced with the decrease in Sh under the same axial load. The long-term strength decays linearly with decreasing Sh and Pc. The creep model is established by modification of both the Kelvin element and the ideal viscoplastic element in the conventional Nishihara model. A nonlinear viscous coefficient and a time-damaged elastomer considering are introduced to describe the nonlinear creep and damage characteristics of HBS. The model is able to describe the whole failure process, especially the accelerated creep stage. The results might have some significance on the prediction of nonlinear failure behaviors of the reservoir during long-term NGH mining.

An Improved Incremental Procedure for the Ground Reaction Based on Hoek-Brown Failure Criterion in the Tunnel Convergence-Confinement Method

The purpose of this study is to introduce the Hoek–Brown nonlinear failure criterion into the convergence–confinement method (CCM), which is based on the linear failure criterion, and implant it into the ground reaction curve (GRC) in this theory. Based on consistent and rigorous theoretical analysis and according to the mechanical relationships, the principle of equilibrium, the material constitutive law, and the strain/displacement compatibility equation are used to deduce the closed-form analytical solution of the stress/displacement of the rock mass in the plastic region and to complete the simulation and interpretation of the nonlinear behavior of surrounding rock due to the advancing excavation of a circular tunnel. In this paper, confinement loss is regarded as the concept of increment in numerical analysis, and the calculation process and analysis steps of the explicit analysis method (EAM) are proposed. This method can not only realize the calculation of analytical solutions but can also be performed using simple spreadsheets. In addition, to verify the feasibility of this calculation method, this study uses published data to verify the validity of the analytical solution implemented by the incremental procedure and to study the influence of nonlinear failure criteria on the GRC, especially the mechanical behavior at the intrados of the tunnel and the distributions of tress/displacement on the cross-section of the tunnel. A comparison between the published results and the proposed solution in this study reveals consistent and favorable trends.

An Anisotropic Failure Criterion for Cross-anisotropic Soils

Strength anisotropy is an important feature closely related to soil microstructure characteristics. A new anisotropic failure criterion, extended from the Ogawa failure criterion, was developed to describe the strength anisotropy of cross-anisotropic soils. Nonlinearization of the failure curves of the Ogawa failure criterion was introduced to account for the nonlinear failure of cross-anisotropic soils in the meridian plane. Meanwhile, an anisotropic strength function based on fabric tensor was theoretically proposed to modify the failure strength under different loading directions and depositional angles. The evolution of the new anisotropic failure criterion in the deviatoric plane was investigated through a series of parametric studies. All of the undetermined parameters in the new criterion can be readily determined in laboratory tests. Compared with experimental results on several types of soils, the new anisotropic failure criterion showed good performance in strength prediction in the deviatoric plane, as well as predicting the peak friction angle. Finally, a linear theoretical relationship on construction of the anisotropic strength function was also elucidated and discussed. The new anisotropic failure criterion proposed in this paper can effectively predict the strength anisotropy of cross-anisotropic soils under different loading directions and depositional angles.