Critical Stress State Research Articles

Performance of Recycled Opaque PET Modified by Reactive Extrusion

A comparative study of the structural integrity of an opaque recycled poly(ethylene terephthalate) (rPET-O) has been carried out with two types of modified rPET-O by applying reactive extrusion techniques, namely (a) using a multi-epoxide reactive agent (REx-rPET-O) and (b) a 90/10 (wt/wt) rPET-O/polycarbonate (PC) blend. The chemical modifications introduced during reactive extrusion were confirmed using differential scanning calorimetry (DSC) and rheological dynamic analysis (RDA). For the quantification of the fracture parameters, an instrumented pendulum impact testing machine was used using specimens in SENB configuration. The structural modifications generated during reactive extrusion promote an increase of between 16 (REx-rPET-O) and 20% (rPET-O/PC) in the stress-intensity factor (KQ) compared to unmodified rPET-O. The most significant differences between both modifications are registered in the “specific work of fracture” (wf) (alternative parameter to the standardized impact strength), where an increase of 61% is reached for the case of rPET-O/PC and only 11% for REx-rPET-O. This trend can be attributed to the type of reactive modification that is generated, namely chain branching (REx-rPET-O) vs. the generation of a random copolymer “in situ” (rPET-O/PC). This copolymer decreases the crystallization capacity and degree of crystalline perfection of rPET-O, promoting an increase in the critical hydrostatic stress conditions for the generation of crazing and crack propagation.

Mechanism of rockburst induced by the microseismic event in the floor strata of high tectonic stress zones: A case study

With the increase of mining scope, rockburst occurs frequently, but its generation mechanism has not been understood comprehensively. Based on a rockburst in the coal pillar area of high tectonic stress zones (HTSZs), this study analyzed the distribution characteristics of large-energy microseismic (MS) events by using data statistics. The mechanical cause of the MS event that induced the rockburst was revealed by means of seismic moment tensor inversion. On this basis, by using numerical simulation, this study explored the distribution characteristics of static load in rockburst area and the effect of dynamic load in the floor, and then proposed the rockburst mechanism. The results show that under the squeezing action, the floor strata in HTSZs implode and transmit energy outward in the form of stress waves. This causes the cumulative damage and stress of the coal body in the fast track of coal pillar area increase in a short time. Since the coal in this area has already been in the critical stress state, small stress changes may lead to coal failure and rockburst. In this case of rockburst, the high static load of coal is the main force source, and the dynamic load plays a role in increasing coal body damage and inducing rockburst. Combined with seismic moment tensor inversion and numerical simulation, this paper proposes a rockburst research scheme, which makes the simulation of dynamic load more reasonable. The results provide the theoretical basis for rockburst control under similar conditions.

Effect of Stress and Thermal Deformation Modes on Correlation of Permeability of Naturally Fractured Sandstone and Shale Formations

Summary Proper correlations of the variations of petrophysical properties like the permeability of naturally fractured porous subsurface formations are developed under different effective stress and thermal deformation modes. The threshold or critical stress and temperature conditions splitting the different deformation modes are determined by analyzing the experimental data. The stress and thermal deformation mode changes occurring at the critical stress and temperature are referred to as the stress and thermal shock phenomena. The improved correlations are developed using the experimental permeability data of the naturally fractured porous sandstone and shale formations based on the theoretically sound modified power-law equation. The critical effective stress and temperature values are determined at the slope discontinuity observed in the variation of the parameters of the modified power-law equation. The parameters of the modified power-law correlations are also correlated as functions of the effective stress and temperature. It is demonstrated that correlating the data separately over the different portions of the full data set divided by the critical stress and temperature values yields more accurate and representative correlations of the naturally fractured porous formations than the correlations obtained using the full-range data. The improved analytical and theoretically sound methodology and approaches presented in this paper can be applied effectively for the development of the improved correlations of the permeability of subsurface porous rock formations deforming by variation of the effective stress and temperature conditions, such as in geothermal and thermally stimulated petroleum reservoirs, and the subsurface storage processes considered for energy transition.

Are the Carpathians tectonically active?: Geomechanical study in deep boreholes in the outer Carpathians (Poland)

Present-day tectonic stress state was investigated in three deep boreholes located in the eastern segment of the Polish Outer Carpathians (POC). Significant rotations of the maximum horizontal stress (SH) were observed in these boreholes, located at the hinge of the anticlines in the upper part of the nappes. For the deepest borehole, D-1 (5.5 km depth), 1D geomechanical modelling was performed to determine the stress gradient profiles. An optimal solution of the model, validated by numerous compressional and extensional failures (breakouts and drilling-induced fractures, respectively) of the borehole wall, was obtained for variable elastic horizontal strain. The strain varies stepwise across the Main Thrust Fault (MTF) and linearly within its walls. The dominance of a strike-slip faulting stress regime was determined for the Carpathian nappes, with contributions from thrust faulting above the MTF and normal faulting below the MTF. A critical stress state for reactivation of preferentially oriented pre-existing faults and fractures was inferred for the competent strata. A consistent interpretation of the variations in stress orientation and magnitude, suggests a contemporary refolding of the anticline at a shallower structural level, enhanced by the reactivation of the MTF and a lack of reactivation of the Carpathian Bottom Thrust. Integration of these results with measurements from previous studies in the eastern segment of the POC indicates a different regional orientation of SH in the autochthonous basement (N-S) and in the nappes (NE-SW). These results indicate a thin-skinned compressive reactivation of the upper part of the accretionary wedge, with the lower part of the nappes remaining passive, or locally prone to minor strike-slip or normal faulting. These results contradict the hypothesis of a contemporaneous extensional collapse of the POC.

Mechanism and Prevention of Rock Burst in a Wide Coal Pillar under the Superposition of Dynamic and Static Loads

To address the frequent occurrence of rock burst disasters in areas with wide coal pillars during mining in the western mining area of China, the wide coal pillar area of the Tingnan coal mine in Shanxi Province was used as the research background. Theoretical analysis, numerical simulation, and field tests were used to establish the mechanical criterion and the energy criterion for the dynamic instability of wide coal pillars. The process and mechanism of wide coal pillar dynamic instability under dynamic and static load disturbances were revealed, and a wide coal pillar rock burst prevention and control scheme was proposed. The results indicated that when the load above a coal pillar reached the stress failure index and the energy failure index was met, the coal pillar reached the critical conditions for rock burst. With increasing static load, the stress, energy, and range of the plastic zone all showed increasing trends on both sides of the coal pillar. Under a given dynamic load, the stress and plastic zone range of the coal pillar significantly increased compared to those without a dynamic load. Under a given static load, the greater the dynamic load, the more likely the coal pillar was to undergo dynamic instability. The evolution of coal pillar dynamic instability was divided into three stages: energy accumulation, local instability, and dynamic instability. When the critical stress and energy conditions for coal pillar dynamic instability are exceeded, rock burst will occur. To reduce the static and dynamic loads of coal pillars, a rock burst prevention and control scheme of energy release and load reduction was proposed and applied onsite. The monitoring results showed that this control plan effectively reduced the stress of the coal pillar and the dynamic load generated by the fracture of the overlying rock layer, indicating safe mining in this area of wide coal pillars.

Post-failure deformation mode switching in volcanic rock.

Beyond a threshold applied compressive stress, porous rocks typically undergo either dilatant or compactant inelastic deformation and the response of their physical properties to deformation mode is key to mass transport, heat transport and pressure evolution in crustal systems. Transitions in failure modes-involving switches between dilatancy and compaction-have also been observed, but to date have received little attention. Here, we perform a series of targeted mechanical deformation experiments on porous andesites, designed to elucidate complex post-failure deformation behaviour. By investigating a sample suite and effective pressure range that straddles the transition between positive and negative volumetric responses to compression, we show two post-failure critical stress states: a transition from compaction to dilation ( ), and a transition from dilation to compaction, which we term . We demonstrate that multiple switches in deformation mode can be driven by stress application under conditions relevant to the shallow crust. While the effect on fluid flow properties of compaction-to-dilation switching may be masked by a net reduction in sample porosity, samples that underwent dilatant-to-compactant failure mode switching exhibited an increase in permeability of approximately two orders of magnitude, despite only slight net volumetric change. Such a substantial permeability enhancement underscores the importance of post-failure deformation in influencing solute and heat transfer in the crust, and the generation of supra-hydrostatic fluid pressures in volcanic environments.

Strength behaviour of stacked phosphogypsum incorporating dissolution–recrystallisation equilibrium

Large phosphogypsum (PG) stacks risk dam failure, with an insufficient consensus on the shear strength parameters for stability analysis. To this end, a combination of scanning electron microscopy (SEM) and triaxial tests was undertaken to investigate the underlying mechanism between crystal structure and shear strength of in situ and remoulded PG samples. The shear strength and deformation of PG were significantly affected by dissolution and recrystallisation. Dissolution weakened the cementation between particles, leading to a stabilisation of approximate 11 kPa under different confining pressures in the initial shear stage. The hardening phenomenon was related to the formation of cluster crystals under saturated conditions. An increase from 1.57 to 1.73 in the critical state stress ratio on remoulded samples occurred as the K0 consolidation time increased from 4 to 28 days. The compressive deformation of PG is accompanied by chemical consolidation, which is mainly impacted by the consolidation conditions (saturation) rather than the consolidation time. In the engineering design of the PG stacks, φ’ could be taken to a higher value at saturation and c’ could be higher when the dry density is higher than 1.2.

Critical state behaviour of an unsaturated kaolin mixture

In this paper, a series of suction-controlled triaxial tests were conducted to investigate the hydromechanical behaviour of an unsaturated kaolin mixture. The studied variables included the mean net stress, suction, and initial dry density. The suction was controlled over a wide range – in the span of 0–390 MPa using the axis translation method and the vapour equilibrium technique, aiming to holistically study the mechanical response of unsaturated soils. The discussion focused on the critical state behaviour and dilatancy characteristics of the tested soil. The experimental results indicate that the ductility of the soil decreases and shifts towards brittleness with increasing suctions. The critical state stress ratio (Ma) of the soil exhibits a significant increase with suction, and this increase becomes more pronounced with higher initial dry density. Conversely, the impact of suction on the critical state line in the specific volume-mean net stress plane (v-lnpnet plane) diminishes with higher initial dry density. Furthermore, suction notably influences the stress-dilatancy relationship of kaolin mixtures, while the effect of confining pressure appears to be marginal. The influence of suction on the stress-dilatancy relationship primarily stems from its impact on the critical stress ratio (Ma), which can be normalized by dividing the stress ratio by the critical state stress ratio. Lastly, the stress-dilatancy equation of the modified Cam-clay model is extended to capture the effect of suction on the dilatancy characteristics of unsaturated soils.

Strength-induced Peridynamic model for the dynamic failure of porous materials

Predicting the dynamic failure process of porous materials is a challenging task due to their complex structure. To minimize the use of time-consuming peridynamic (PD) models and to avoid surface effect issues in the dynamic failure of complex porous materials, this paper proposes a strength-induced PD model. The paper first presents the dynamic formula and relevant finite element discrete equation of the coupled PD and classical continuum mechanics (PD-CCM) model based on the Morphing method. The Morphing function is implemented to control the material parameters and enable the free transformation of PD and CCM models. Based on the coupled PD-CCM model, the strength-induced PD model is established to adaptively expand the PD subdomain in porous materials by controlling the Morphing function value through the strength state of the structure. This model enables the PD subdomain to appear automatically when the porous materials reach the critical stress state. The proposed model accurately predicts the location of crack initiation and path while minimizing computational costs and improving efficiency. Three two-dimensional numerical examples are used to verify the effectiveness, efficiency, and accuracy of the model. The results of the simulation suggest that the location where the crack initiates in the porous materials is strongly influenced by the amplitude of the dynamic load. Cracking is dependent on the pores and typically occurs through them.

A shear‐transformation‐zone model for time‐dependent behaviours of clay

AbstractA shear‐transformation‐zone (STZ) model is proposed for time‐dependent behaviours of clay, in which the viscoplastic deformation is described by the evolution of a temperature‐like state variable. The model is featured by rate‐dependent dilatancy and a unique critical state stress ratio. In its present form, it has nine parameters, most of which can be handily calibrated, and can predict the rate‐dependent undrained shear strength, primary, and secondary creep, as well as stress relaxation for normally consolidated clay under complex stress paths using a single set of parameters. The capabilities of the model have been verified by available experimental results on five different clays.

Subgrade soil response to rail loading: Instability mechanisms, causative factors, and preventive measures

The demand for more efficient heavy-haul rail networks over soft subgrades poses significant geotechnical challenges and requires a comprehensive understanding of stress conditions as well as the failure potential of subgrade soil under moving wheel loads and increasing rail speeds. Unfavourable stress conditions in the subgrade can result in various types of failures, three of which are identified in this article: (i) excessive plastic settlement, (ii) progressive shear failure, and (iii) subgrade fluidisation (mud pumping). Through a series of advanced testing schemes using cyclic triaxial, hollow cylinder, and an in-house dynamic filtration apparatus, critical stress conditions and soil characteristics prone to subgrade instability are discussed. The results demonstrate that under adverse combinations of loading frequency (f) and cyclic stress ratio (CSR) the continuous application of cyclic loads can lead to an unstable state of soil where excess pore pressure and axial strain increase rapidly. This study also reveals that low to medium plasticity soils (PI < 22) are more vulnerable to subgrade fluidisation, where the rapid internal migration of pore water transforms the upper soil to a fluid-like state with substantial loss in soil stiffness. The layered response of soil through dynamic filtration tests showed larger hydrodynamic forces induced by differential hydraulic gradients in the top layer during cyclic loading causes moisture to move upwards. Various factors that can influence soil instability such as the degree of compaction degree, clay content, soil fabric and stress rotation are also addressed in this paper. Finally, novel solutions for stabilising subgrade such as a vertical drain-composite system and the use of eco-friendly biopolymers are presented.

Measurement of tensile and shear strength of interfacial bonding in fiber reinforced soft composites combining experiments and simulation

Interfacial bonding strength plays a key role in the mechanical performance of fiber reinforced polymers. However, measurement of interfacial bonding strength in fiber reinforced soft composites (FRSCs) becomes a challenging issue, because the large deformation capability of soft matrix invalidates most of current testing methods. This paper demonstrates an advanced method combining experiments and simulation, which provides a convenient and reliable means to measure both tensile strength and shear strength of interfacial bonding for FRSCs. The specimen is made by embedding a fiber bundle in a soft plate for transverse tensile test. Various stress states along the fiber–matrix interface can be realized by controlling the inclination angle of fiber bundle to the stretching direction. Tensile strength and shear strength of interfacial bonding in FRSCs can be estimated based on the analysis of critical stress states. The comparison with the widely adopted fiber pull-out test indicates that the nominal shear strength obtained in pull-out test is severely underestimated.

Seismological Evidence for the Existence of Long‐Distance Hydrological Channel and Its Implication for Fluid Overpressure in Southern Sichuan, China

AbstractUnprecedented levels of seismicity have been seen in southern Sichuan, China, since the large‐scale exploitation of shale gas. Fluid and pore pressure transported through hydrological channel are thought as pivotal elements in the induction of earthquakes. Our high‐resolution tomography results reveal two inclined seismic anomalies featured by low Vs and high Vp/Vs at different depth range. The deeper anomaly extends 15 km from NE to SE and connects the well g048 from 3 km depth to the vicinity of the Ms 4.7 Gongxian earthquake 5.4 km deep, which is hinted to be a hydrological channel inferred from the high fluid overpressure of 28 Mpa calculated from focal mechanism solution. The injection operation of multiple shale gas wells along the channel may potentially accumulate the pore pressure and cause the fault near the end of the channel to reach critical stress state through various mechanisms.

Deformation and Strength of Unsaturated Loess—Hydraulic Coupling Effects under Loads

The volumetric change in unsaturated loess during loading causes serious damage to the foundation and structure, accompanied by changes in hydraulic conditions. Therefore, quantifying the change in the load effect of loess under hydraulic coupling is of great significance for revealing the mechanism of hydraulic interaction. This study conducts isotropic compression and undrained shear tests on unsaturated compacted loess, simultaneously introducing the strength parameter η to enhance the Glasgow coupled model (GCM). The objective is to elucidate the hydraulic and mechanical coupling mechanism, where saturation increases under mechanical effects lead to strength degradation. The results show that saturation increases under mechanical effects improve the compressibility of the sample, and saturation has a direct impact on the stress–strain relationship. The increase in water content and confining pressure increases the trend of the critical state stress ratio M decreasing, and the strain softening trend increases. The compression of volume during shear tests increases the saturation, changes the hydraulic characteristics of loess, and affects the deformation and strength of loess. The modified GCM improves the applicability and prediction accuracy of unsaturated loess under the same initial state. The research results are of great significance for revealing the hydraulic and mechanical behavior of loess.

Glass Beads Test with True Triaxial Stress Path Achieved by Conventional Triaxial Apparatus

The impact of fabric anisotropy, fractal dimension, and breakage on the strength and deformation of granular materials were diminished by uniform-size spherical glass beads. Triaxial drained and undrained tests were performed on glass beads based on a novel method to substitute true triaxial stress paths with conventional triaxial apparatus equivalents with varying intermediate principal stress coefficients (b-values). The result indicates that all specimens manifested a noticeable strain-softening phenomenon. The peak strength decreased with increasing b-value, and the specimens showed more pronounced dilatancy. This pattern is similar to the results of the true triaxial test in current research. Compared to the undrained test, the peak friction angle in the drained test displayed a greater variation with varying b-values, which indicated that the mechanical response of glass beads is sensitive to water. This difference provides experimental evidence for comprehending effective stress in granular materials with constant friction coefficients. The experiments reflect the effect of b-value changes on the p-q stress path, as well as on the peak stress ratio, the state transition stress ratio, and the critical state stress ratio. The specimens exhibited a distinct shear band at different b-values ranging from 0.2 to 0.6, which is different from observations in conventional triaxial tests for granular materials.

Determination of the Activity of the fimF Gene and Its N-Terminal Domain Disrupted Mutant on Biofilm Formation and Its Contribution to the Oxidative Stress Response in S. Typhimurium

Fimbriae is an important virulence factor which plays a key role in cell attachment and colonization of the intestinal mucosa during an infection of Salmonella, a pathogen that causes gastroenteritis and systemic infection in humans. In S. Typhimurium, type 1 fimbriae production strengthens the oxidative stress response. This study aimed to determine the effectiveness of the fimF gene and its N-terminal domain on biofilm formation in S. Typhimurium and their contribution to the oxidative stress response. Before the experiments to prove whether the N-terminal domain of the FimF protein is the region that determines the mechanism and function of the fimF gene; only the N-terminal domain of the fimF gene was cloned behind the pBAD promoter. As a result of biofilm experiments on polystyrene surfaces, it was determined that the biofilm production capacity was reduced significantly in mutant strains in terms of fimF and dam genes (p &lt; 0.05). In the oxidative stress response experiment conducted in the presence of hydrogen peroxide (H2O2), it was determined that the mutant strains were more resistant to hydrogen peroxide than the wild-type strain, therefore Salmonella cells perceived the absence of Dam methylase enzyme and FimF protein as a critical internal stress condition and produced strong responses to these stress conditions. As a result of comparative analysis of the N-terminal domain cloned mutant strain with the wild-type, it was proven that the N-terminal domain of the protein in question acts as an adapter protein, due to its close similarities with the wild-type.

Dependence of Critical Stress Intensity Factor on Crack Depth From the Loading Boundary of Crystalline Silicon

Abstract In the present work, an atomistic scale investigation is done on crystalline silicon to understand the effect of crack depth from the loading (pulling) boundary on the critical near-tip state of stress. For various depths of embedded cracks, the near-tip stress field has been calculated at the critical state just before the crack propagation initiation. This atomistically calculated stress field is found to be quite close to those found using continuum linear elasticity. Thereafter, the critical stress intensity factor (SIF) is calculated for all cases by fitting the atomistically calculated normal stress over inverse square-rooted distance from the crack tip. It has been found that the closer the crack is located to the loading boundary (i.e., lesser depth), the lower is the (locally calculated) critical SIF. This implies that it is easier to initiate crack propagation when the crack is located closer to the loading boundary. The claim is also strengthened by a similar observation of (globally calculated) boundary stresses at the critical state just before crack propagation initiation.

On the friction dependency of the stress Lode angle

AbstractThe shape of the failure locus of a material is significant for its strength predictions. Even when constitutive models include the same critical stress surface, different critical stress ratios can be predicted for an identical applied isochoric strain path. In this article, we investigate critical stress predictions of different constitutive models, which include the surface according to Matsuoka–Nakai (MN). We perform analytical investigations, true triaxial test simulations with hypoplasticity and barodesy, and discrete element modelling (DEM) simulations to investigate the friction dependency of the stress Lode angle. Our results demonstrate that in hypoplasticity, the direction of the deviatoric stress state at critical state depends solely on the direction of the applied deviatoric strain path. In contrast, in barodesy, the predictions are also dependent on the friction angle of the material. In addition, we compare these results with those obtained with a standard elastoplastic MN model. To validate this friction dependency on the stress Lode angle, we conduct DEM simulations. The DEM results qualitatively support the predictions of barodesy and suggest that a higher friction results in a higher Lode angle at critical stress state.

Constraint strategies for estimating in-situ stress from borehole measurements

In this study, we describe strategies to reduce uncertainties in the estimation of in-situ stresses. The strategies are based on the commonly used poro-elastic model with strain corrections for in-situ stress estimation. In addition to the calibration of the minimum horizontal stress magnitudes from measurement data, we further constrain the magnitude of maximum horizontal stress quantitatively with (i) a critical stress state model, (ii) (non)-occurrences of breakout and/or drilling-induced fracture observed from image logs, and (iii) qualitatively with elliptical borehole shapes observed from multi-arm caliper logging data. The methodology is demonstrated using wells near Dawson Creek, Northeast British Columbia and Northwest Alberta, in Western Canada Sedimentary Basin (WCSB). The uncertainty of the estimated maximum horizontal stress magnitude was reduced and the range of the maximum horizontal stress was narrowed after the application of these constraint strategies. It is also observed that in the east of the study area, the in-situ stress regime is a normal fault stress regime. The presence of a normal fault stress regime is unexpected since a strike–slip fault stress regime is typically considered for the entire region. Yet, analysis of caliper data in two horizontal wells has confirmed its presence.

Experimental and numerical study on press-fitted railway axles: Competition between fretting and plain fatigue

To investigate the competitive relationship between plain and fretting fatigue in press-fitted railway axles, the plain fatigue limit and fretting fatigue strength were tested, respectively, by changing the depth of the stress relief groove. Next, detailed information on fretting and plain fatigue, as well as on fretting wear, was gathered. Finally, an evaluation methodology integrating the finite element (FE) simulation with the Modified Wöhler Curve Method (MWCM) was established to evaluate the damage in both fretting and plain fatigue scenarios. It was found that as the groove depth increased, the plain fatigue limit decreased while the fretting fatigue strength increased. The optimal groove depth, hopt, that equalized the anti-fatigue capabilities of the groove and wheel seat, was affected by the number of test cycles. For this press-fitted railway axle, hopt was 0.2 mm < hopt < 0.4 mm for 107 test cycles, and hopt > 0.6 mm for 108 cycles. The calculated critical local stress condition, σCri, required for initiating a crack, was 161.8 MPa, which almost agreed with the theoretical value. The calculated σMWCM values can be used to characterise the fretting and plain fatigue damage. The local stress condition for determining an optimal groove depth was: σMWCM in the wheel seat and groove root simultaneously reached σCri.