Effect Of Shear Stress Research Articles

Shear stress effects on epididymal epithelial cell via primary cilia mechanosensory signaling.

Shear stress, resulting from fluid flow, is a fundamental mechanical stimulus affecting various cellular functions. The epididymis, essential for sperm maturation, offers a compelling model to study the effects of shear stress on cellular behavior. This organ undergoes extensive proliferation and differentiation until puberty, achieving full functionality as spermatozoa commence their post-testicular maturation. Although the mechanical tension exerted by testicular fluid is hypothesized to drive epithelial proliferation and differentiation, the precise mechanisms remain unclear. Here we assessed whether the responsiveness of the epididymal cells to shear stress depends on functional primary cilia by combining microfluidic strategies on immortalized epididymal cells, calcium signaling assays, and high-throughput gene expression analysis. We identified 97 genes overexpressed in response to shear stress, including early growth response (Egr) 2/3, cellular communication network factor (Ccn) 1/2, and Fos proto-oncogene (Fos). While shear stress triggered a rapid increase of intracellular Ca2+, this response was abrogated following the impairment of primary ciliogenesis through pharmacological and siRNA approaches. Overall, our findings provide valuable insights into how mechanical forces influence the development of the male reproductive system, a requisite to sperm maturation.

Development of a Custom Fluid Flow Chamber for Investigating the Effects of Shear Stress on Periodontal Ligament Cells.

The periodontal ligament (PDL) is crucial for maintaining the integrity and functionality of tooth-supporting structures. Mechanical forces applied to the tooth during orthodontic tooth movement generate pore pressure gradients, leading to interstitial fluid movement within the PDL. The generated fluid shear stress (FSS) stimulates the remodeling of PDL and alveolar bone. Herein, we present the construction of a parallel fluid-flow apparatus to determine the effect of FSS on PDL cells. The chamber was designed and optimized using computer-aided and computational fluid dynamics software. The chamber was formed by PDMS using a negative molding technique. hPDLCs from two donors were seeded on microscopic slides and exposed to FSS of 6 dyn/cm2 for 1 h. The effect of FSS on gene and protein expression was determined using RT-qPCR and Western blot. FSS upregulated genes responsible for mechanosensing (FOS), tissue formation (RUNX2, VEGFA), and inflammation (PTGS2/COX2, CXCL8/IL8, IL6) in both donors, with donor 2 showing higher gene upregulation. Protein expression of PTGS2/COX2 was higher in donor 2 but not in donor 1. RUNX2 protein was not expressed in either donor after FSS. In summary, FSS is crucial in regulating gene expression linked to PDL remodeling and inflammation, with donor variability potentially affecting outcomes.

Effects of Glass Bead Size on Dissolution Profiles in Flow-through Dissolution Systems (USP 4).

The effects of glass bead size in the conical space of flow-through cells on the dissolution profiles were investigated in a USP apparatus 4. Dissolution tests of disintegrating and non-disintegrating tablets in flow-through dissolution systems were performed using semi-high precision glass beads with diameters ranging from 0.5mm to 1.5mm. Computational fluid dynamics (CFD) was used to evaluate the effect of shear stress from the dissolution media flow. The use of smaller glass beads in a larger cell resulted in a faster dissolution of the model formulations under certain test conditions. The effect on the dissolution was highly dependent on the size of the beads in the top layer, including those in contact with the tablets. The absence of a bead-size effect on the dissolution of an orodispersible tablet in a small cell can be explained by the floating fragments during the test. CFD analysis showed that smaller bead diameters led to greater shear stress on the tablet, which was correlated with the dissolution rate. Hence, fluid flow through the narrow gaps between the small beads generated strong local flows, causing shear stress. The size of the glass beads used in flow-through cells affects the dissolution rate of tablets by altering the shear stress on the tablets in certain cases (e.g., direct deposition of the formulation on glass beads, large cells, and very low flow rates). Thus, glass bead size must be considered for a robust dissolution test in a flow-through cell system.

Is fluid retention a cardiovascular risk factor?

Endothelial dysfunction, the earliest manifestation of atherosclerosis, can be initiated by both biochemicals and biomechanical forces. Atherosclerosis occurs predominantly at arterial branch points, arterial bifurcations and the curved segments of great arteries. These are the regions that blood flows turbulently. Turbulence promotes endothelial dysfunction by reducing shear stress upon endothelial cells. The endothelial glycocalyx mediates the effect of shear stress upon the endothelium. A mathematical analysis of cardiovascular hemodynamics demonstrates that fluid retention increases turbulence of blood flow. While there is no empirical data confirming this relationship, fluid retention is associated with adverse cardiovascular events. Every medical condition that causes fluid retention is associated with increased risk of both atherosclerotic cardiovascular disease and venous thromboembolic disease. In addition, most medications that cause fluid retention are associated with increased adverse cardiovascular effects. Calcium channel blockers (CCBs) and pioglitazone are exceptions to this generalization. Even though data regarding CCBs and pioglitazone contradict the hypothesis that fluid retention is a cardiovascular risk factor, these medications have favorable cardiovascular properties which may outweigh the negative effect of fluid retention. Determining whether or not fluid retention is a cardiovascular risk factor would require empirical data demonstrating a relationship between fluid retention and turbulence of blood flow. While this issue should be relevant to cardiovascular researchers, clinicians and patients, it is especially pertinent to the pharmaceutical industry. Four-dimensional magnetic resonance imaging and vector flow Doppler ultrasound have the capability to quantify turbulence of blood flow. These technologies could be utilized to settle the matter.

Low shear stress protects chondrocytes from IL-1β-induced apoptosis by activating ERK5/KLF4 signaling and negatively regulating miR-143-3p

ObjectiveThis study investigated the protective effects of low fluid shear stress (FSS ≤ 2 dyn/cm²) against interleukin-1β (IL-1β)-induced chondrocyte apoptosis and explored the underlying molecular mechanisms.MethodsChondrocytes were cultured under four conditions: control, IL-1β stimulation, low FSS, and combined low FSS + IL-1β stimulation. Apoptosis was assessed using Hoechst staining and flow cytometry. Western blotting determined the expression of caspase-3 (CASP3), caspase-8 (CASP8), and NF-κB p65. Quantitative real-time PCR measured miR-143-3p expression. The roles of miR-143-3p and the extracellular signal-regulated kinase 5 (ERK5)/Krüppel-like factor 4 (KLF4) signaling pathway were further investigated using miR-143-3p mimics and inhibitors, an ERK5 inhibitor, and a KLF4 overexpression vector.ResultsIL-1β induced significant chondrocyte apoptosis, which was markedly inhibited by low FSS. Mechanistically, low FSS suppressed miR-143-3p expression, thereby enhancing ERK5 signaling. This activated ERK5 subsequently upregulated KLF4 expression, further mitigating IL-1β-induced damage. Importantly, miR-143-3p overexpression under low FSS conditions exacerbated IL-1β-induced apoptosis, while miR-143-3p inhibition attenuated it. Consistent with this, ERK5 inhibition augmented IL-1β-induced apoptosis, whereas KLF4 overexpression suppressed it.ConclusionLow FSS protects chondrocytes from IL-1β-induced apoptosis by suppressing miR-143-3p and activating the ERK5/KLF4 signaling pathway. This study reveals a novel mechanism by which mechanical stimulation protects cartilage.

Effect of Hydrodynamic Shear Stress on Algal Cell Fate in 3D Extrusion Bioprinting

The 3D bioprinting of aquatic photosynthetic organisms holds potential for applications in biosensing, wastewater treatment, and biofuel production. While algae cells can be immobilized in bioprinted cell‐friendly matrices, there is a knowledge gap regarding the thresholds of hydrodynamic shear stress that affect the cells’ functionality and viability during bioprinting. This study examines the effect of hydrodynamic shear stress on the fate of Chlamydomonas reinhardtii cells. Computational fluid dynamics models based on the Navier–Stokes equations are developed to numerically predict the shear stresses experienced by the cells during extrusion. Parallelly, cell culture experiments are conducted to evaluate the functionality, growth rates, and viability of algae cells within bioprinted constructs. By correlating cell culture and simulation results, the causal link between shear stress in the nozzle and cell viability and function has been characterized. The findings highlight that cell viability and function are significantly impacted by process factors. Notably, algae cell function is more sensitive to shear stress than cell viability. Functional impairments occur at maximum shear stresses around 5 kPa, while viability remains unaffected. Beyond 14 kPa, both functionality and viability decline significantly and irreversibly. The results emphasize the importance of assessing viability and function after bioprinting, rather than just viability.

Investigation of the Effect of High Shear Stress on Mesenchymal Stem Cells Using a Rotational Rheometer in a Small-Angle Cone-Plate Configuration.

Within the healthy human body, cells reside within the physiological environment of a tissue compound. Here, they are subject to constant low levels of mechanical stress that can influence the growth and differentiation of the cells. The liposuction of adipose tissue and the subsequent isolation of mesenchymal stem/stromal cells (MSCs), for example, are procedures that induce a high level of mechanical shear stress. As MSCs play a central role in tissue regeneration by migrating into regenerating areas and driving regeneration through proliferation and tissue-specific differentiation, they are increasingly used in therapeutic applications. Consequently, there is a strong interest in investigating the effects of shear stress on MSCs. In this study, we present a set-up for applying high shear rates to cells based on a rotational rheometer with a small-angle cone-plate configuration. This set-up was used to investigate the effect of various shear stresses on human adipose-derived MSCs in suspension. The results of the study show that the viability of the cells remained unaffected up to 18.38 Pa for an exposure time of 5 min. However, it was observed that intense shear stress damaged the cells, with longer treatment durations increasing the percentage of cell debris.

Hydrogen and vacancy concentrations in [formula omitted]-iron under high hydrogen gas pressure and external stress: A first-principles neural network simulation study

The metal-hydrogen-vacancy interaction in α-iron is crucial for understanding hydrogen embrittlement behavior and developing reliable materials for green gaseous hydrogen applications; however, it remains underexplored, particularly in contexts involving external stress and high hydrogen gas pressure. In this study, we performed quantitative analyses of metal-vacancy–hydrogen interactions in α-iron, measured by hydrogen solubility and the thermodynamics of vacancy–hydrogen complexes, under such challenging conditions using a reliable first-principles neural network potential. High hydrogen gas pressures reaching up to 2 GPa were investigated. As the atomic concentration surpasses approximately 0.01, hydrogen solubility is dominated by hydrogen-induced lattice distortion (primarily volumetric expansion) and the interactions between hydrogen atoms within the metal matrix, resulting in significant deviations from Sieverts’ law. Our results reveal a significant effect of shear stress on hydrogen solubility, deviating from previously used equations. Moreover, the influence of external stress on the thermodynamics of the vacancy–hydrogen complex, particularly vacancy formation free energy, is uniquely characterized by hydrogen solubility, regardless of the external stress magnitude. It thereby offers a rapid method to estimate the vacancy properties under external stress based on readily accessible external-stress-free data.

Effect of torsional shear stress on the deformation characteristics of clay under traffic load

The soft clay under the road ground will suffer cyclic torsional shear stress encountered traffic load in addition to axial stress, which will cause further deformation of clay. To investigate the effect of torsional shear stress on the cumulative axial strain of clay, a series of undrained tests under cardioid stress path were performed on K0 consolidated undisturbed samples by using a hollow cylinder apparatus (HCA). The effect of vertical cyclic stress ratio (VCSR) and shear stress ratio (η) on the deformation and degradation characteristics of clay was investigated. The results indicate that there is inconsistency between the strain path and stress path. The increase in η further accelerates the accumulation of axial strain, which resulted from the degradation of clay induced by torsional shear stress. Considering the VCSR and η, a calculation method of degradation index was developed. Furthermore, a cumulative axial strain prediction model of clay under the cardioid stress path was established considering the degradation. This model addresses the limitation of traditional prediction models by considering the impact of torsional shear stress on cumulative axial strain.

Low fluid shear stress stimulates the uptake of noxious endothelial extracellular vesicles via MCAM and PECAM-1 cell adhesion molecules.

Atherosclerotic lesions mainly form in arterial areas exposed to low shear stress (LSS), where endothelial cells express a senescent and inflammatory phenotype. Conversely, areas exposed to high shear stress (HSS) are protected from plaque development. Endothelial extracellular vesicles (EVs) have been shown to regulate inflammation and senescence, and therefore play a crucial role in vascular homeostasis. Whilst previous studies have shown links between hemodynamic forces and EV release, the effects of shear stress on the release and uptake of endothelial EVs remains elusive. We aim to decipher the interplay between these processes in endothelial cells exposed to atheroprone or atheroprotective shear stress. Confluent HUVECs were exposed to LSS or HSS for 24h. Large and small EVs were isolated from conditioned medium by centrifugation and size exclusion chromatography. They were characterised by TEM, Western blot, tunable resistive pulse sensing, flow cytometry and proteomics. Uptake experiments were performed using fluorescently-labelled EVs and differences between groups were assessed by flow cytometry and confocal microscopy. We found that levels of large and small EVs in conditioned media were fifty and five times higher in HSS than in LSS conditions, respectively. In vivo and in vitro uptake experiments revealed greater EV incorporation by cells exposed to LSS conditions. Additionally, endothelial LSS-EVs have a greater affinity for HUVECs than HSS-EVs or EVs derived from platelets, erythrocytes and leukocytes. Proteomic analysis revealed that LSS-EVs were enriched in adhesion proteins (PECAM1, MCAM), participating in EV uptake by endothelial cells. LSS-EVs also carried mitochondrial material, which may be implicated in elevating ROS levels in recipient cells. These findings suggest that shear stress influences EV biogenesis and uptake. Given the major role of EVs and shear stress in vascular health, deciphering the relation between these processes may yield innovative strategies for the early detection and treatment of endothelial dysfunction.

Advancing thermohydraulic performance of micro-grooved flat heat pipes through a combined numerical-experimental approach

A combined numerical-experimental model has been developed to predict the thermohydraulic characteristics of micro-grooved flat heat pipes (FHPs). This model uses a limited number of experimental data for calibration with two parameters, βexp,1 and βexp,2, which account for uncertainties in the accommodation coefficients used to determine evaporation and condensation mass fluxes. This calibration, which is a key feature of the developed model, addresses the uncertainties and challenges in determining these coefficients. Moreover, the model incorporates the effects of interfacial shear stress, axial wall conduction, heat transfer in the liquid block region, and the contact angle of the liquid–vapor interface. Furthermore, the evaporation mass flux from the curved liquid–vapor interface is calculated using a separate multiscale approach developed in two recent works for analyzing evaporation from the extended meniscus in microchannels, considering thin-film evaporation. The model demonstrates high accuracy in predicting the maximum heat transport capacity (Qmax) and wall temperature distribution across various input heat powers, with a maximum error of less than 0.5 % in wall temperature predictions, as validated against experimental data. The validated model is then used to explore a new micro-grooved wick structure featuring converging/diverging microchannels. In this structure, the channel width is constant and equal to Wf2 in the first half of the heat pipe, from the condenser end to the midpoint, and then it decreases or increases to Wf1 by the end of the evaporator section. Results indicate that a flat heat pipe with a converging micro-grooved wick structure (Wf1 = 200 µm and Wf2 = 160 µm) can enhance Qmax from 53 to 70 W, 70.8 to 91.8 W, and 91.2 to 116.5 W at working temperatures of 60 °C, 70 °C, and 80 °C, respectively. This means the new converging micro-grooved wick structure can boost flat heat pipe performance by more than 25 % compared to a flat heat pipe with a straight micro-grooved wick (Wf1 = Wf2 = 200 µm) without increasing the occupied space.

The Effect of Initial Static Shear Stress on Liquefaction Triggering of Coarse-Grained Materials

The Effect of Initial Static Shear Stress on Liquefaction Triggering of Coarse-Grained Materials

Reactive molecular dynamics of the fracture behavior in geopolymer: Crack angle effect

Reactive molecular dynamics was applied in this study to construct the sodium aluminosilicate hydrate (N-A-S-H) and tensile fracture models with various crack angles. The impact of crack angle on the behavior of N-A-S-H fractures was explored while considering structural mechanical properties and energy evolution. Furthermore, the fracture toughness and brittleness index for various crack angle models were calculated. The findings indicated that the ultimate strength and elastic modulus of the fracture models grew linearly with the increase in crack angle. The fracture toughness value progressively grew while the model’s elastic energy efficiency and new surface energy efficiency decreased simultaneously. The 45° crack model possessed the largest oblique crack development surface in the fracture process due to the coupling effect of tensile and shear stress. Its elastic energy efficiency decreased as well the most, while the new surface energy efficiency increased and the fracture toughness value dropped sharply. It is crucial to place a stronger emphasis on spotting cracks both in the in-service structures or structures being demolished. This ensures optimal performance and safety by enabling more effective adjustments to the direction of external forces and energy input.

Prediction of micro/meso scale forming limit for metal foils using a simple criterion

Accurately forecasting the forming limit of metal foils is essential in their micro-forming due to the appearance of necking failure easily. In order to accurately and easily forecast the forming limit of metal foils influenced by size effect, an idea for failure modeling of metal foils using the mechanism that different fracture modes of metal foils are related to shear bands is presented in this work. Based on the idea, a simple ductile failure criterion that considers the maximum shear stress and grain size effect but excludes the stress triaxiality is proposed, motivated by the demand to decrease the complexity of parameter calculation tests in micro-forming failure prediction. The proposed criterion and another criterion called as the μ-DF2022 model are applied to capture the forming limit curves of various thick copper and 304 stainless steel foils with different grain sizes to verify its advantage and performance, and the corresponding mechanisms of their prediction capabilities are also elucidated. Furthermore, the proposed and μ-DF2022 models are applied to forecast the limit drawing ratio of a 304 stainless steel foil to further show its performance and advantage in real micro-forming. The applications show that the proposed failure criterion effectively forecasts the forming limit of metal foils between equi-biaxial tension and uniaxial tension influenced by size effect. Moreover, the prediction accuracies using the proposed model and the μ-DF2022 model are comparable, whereas the proposed model does not require complex micro equi-biaxial tension tests, which are typically unavailable to many engineers and researchers, to calibrate its material parameters. Therefore, it is recommended to utilize the proposed criterion to capture the forming limit of metal foils in micro-forming. This work advances the forming limit modeling method of metal foils and provides insight into the application of uncoupled ductile failure criteria in the micro-forming of metal foils, which contributes to the development of their optimal micro-forming processes.

Instabilities of Marangoni and elasticity in a molten polymer film

This study conducts a comprehensive exploration of the elasticity and Marangoni instability exhibited by a non-Newtonian polymer film flow down an inclined plane within the context of an upper-convected Maxwell (UCM) model. The asymptotic solutions are derived utilizing the stream function and perturbation method based on the long-wave assumption. The numerical solutions are effectively solved at arbitrary wavelengths through the implementation of the Chebyshev spectral collocation technique. The results show that the presence of elastic stress renders the film more susceptible to destabilization. The underlying mechanisms that instigate the instability are examined from an energy balance perspective. It is determined that the instability of the film is predominantly governed by shear stress (SHE) and elastic stress (DIP) effects. Shear stress increases the perturbation kinetic energy to promote instability, while elastic stress decreases the perturbation kinetic energy to enhance stability. However, for the Weissenberg number Wi=1, the shear stress changes from an unstable to a stabilizing factor, and the elastic stress changes from stable to unstable when the wave number k>1. This intriguing inversion is attributed to the dual nature of elasticity, possessing both stabilizing and destabilizing tendencies. Despite the work of Marangoni stress (MAT) magnitude remaining within the order of 10−3, the Marangoni effect indirectly contributes to instability enhancement.

Endothelial cell elongation and alignment in response to shear stress requires acetylation of microtubules.

The innermost layer of the vessel wall is constantly subjected to recurring and relenting mechanical forces by virtue of their direct contact with blood flow. Endothelial cells of the vessel are exposed to distension, pressure, and shear stress; adaptation to these hemodynamic forces requires significant remodeling of the cytoskeleton which includes changes in actin, intermediate filaments, and microtubules. While much is known about the effect of shear stress on the endothelial actin cytoskeleton; the impact of hemodynamic forces on the microtubule network has not been investigated in depth. Here we used imaging techniques and protein expression analysis to characterize how pharmacological and genetic perturbations of microtubule properties alter endothelial responses to laminar shear stress. Our findings revealed that pharmacological suppression of microtubule dynamics blocked two typical responses to laminar shear stress: endothelial elongation and alignment. The findings demonstrate the essential contribution of the microtubule network to changes in cell shape driven by mechanical forces. Furthermore, we observed a flow-dependent increase in microtubule acetylation that occurred early in the process of cell elongation. Pharmacological manipulation of microtubule acetylation showed a direct and causal relationship between acetylation and endothelial elongation. Finally, genetic inactivation of aTAT1, a microtubule acetylase, led to significant loss of acetylation as well as inhibition of cell elongation in response to flow. In contrast, loss of HDAC6, a microtubule deacetylase, resulted in robust microtubule acetylation with cells displaying faster kinetics of elongation and alignment. Taken together, our findings uncovered the critical contributions of HDAC6 and aTAT1, that through their roles in the regulation of microtubule acetylation, are key mediators of endothelial mechanotransduction.

Effect of microstructure rafting on deformation behaviour and crack mechanism during high-temperature low-cycle fatigue of a Ni-based single crystal superalloy

The low cycle fatigue behaviours of a microstructure rafting Ni-based single crystal superalloy have been experimentally investigated at 980 ℃. Deformation of γ/γ’ phases and the corresponding dislocation configurations were investigated, highlighting rafting γ/γ’ morphology that contributes to crack initiation and propagation, as well as macro-scale accumulated plastic strain. Unlike the discrete slip lines of a virgin superalloy, intense slips developed along the parallel {111} slip plane result in crossed slip bands in the rafting superalloy. The decreased resistance of widened γ channels to dislocation movement, along with the prevention of dislocation cutting through γ’ precipitates in pre-existing dense dislocation networks, facilitates crack propagation in the γ channel in the slightly rafting superalloy. As the rafting state increases, the dislocation network loses its protective effect by reducing coherency stress and acting as a superdislocation source, which facilitates crack propagation along the γ/γ’ interface. Finally, a microstructure-based fatigue model is developed considering the reduction of deformation resistance induced by rafting. The fatigue loading control mode effect is introduced by a combination of resolved shear stress and tensile stress effects on crack initiation. The LCF life of rafting Ni-based superalloys significantly decreases under stress-controlled conditions compared to strain-controlled conditions due to the increase in cumulative plastic strain. However, the insignificant impact of the initial surface oxide layer on LCF life is revealed.

Engineered Biomaterials and Model Systems to Study YAP/TAZ in Cancer.

The transcriptional coactivators yes-associated protein (YAP) and transcriptional coactivator with PDZ-binding motif (TAZ) are master regulators involved in a multitude of cancer types and a wide range of tumorigenic events, including cancer stem cell renewal, invasion, metastasis, tumor precursor emergence, and drug resistance. YAP/TAZ are known to be regulated by several external cues and stimuli, such as extracellular matrix stiffness, cell spreading, cell geometry, and shear stress. Therefore, there is a need in the field of cancer research to develop and design relevant in vitro models that can accurately reflect the complex biochemical and biophysical cues of the tumor microenvironment central to the YAP/TAZ signaling nexus. While much progress has been made, this remains a major roadblock to advancing research in this field. In this review, we highlight the current engineered biomaterials and in vitro model systems that can be used to advance our understanding of how YAP/TAZ shapes several aspects of cancer. We begin by discussing current 2D and 3D hydrogel systems that model the YAP/TAZ response to ECM stiffness. We then examine the current trends in organoid culture systems and the use of microfluidics to model the effects of cellular density and shear stress on YAP/TAZ. Finally, we analyze the ongoing pitfalls of the present models used and important future directions in engineering systems that will advance our current knowledge of YAP/TAZ in cancer.

Ice slurry pigging technology in drinking water distribution system: From flow mechanisms to pipelines cleaning application

Drinking water distribution systems are prone to (bio)fouling over time, negatively impacting drinking water quality. Ice slurry pigging is a promising technology used to remove solids attached to the inner parts of the pipe walls with ice-water mixture. To understand the ice slurry pigging flow characteristics and optimize its operations, this study presents the development of a Computational Fluid Dynamics model (CFD) combined with the Kinetic Theory of Granular Flow model (KTGF) and a thermal model. Firstly, the model is validated with experimental data from the literature on solid-liquid Two-Phase Flow (TPF), including flow characteristics and thermal effects. Secondly, simulations for a typical ice slurry pigging process show uneven ice phase fraction and shear stress distributions in the main pipe flow and vertical direction. Results indicate that the main limitations of effective pipe cleaning are due to buoyancy and thermal effects. Moreover, ice slurry with 1.0 mm ice particles performs better in providing effective shear stress compared to 0.1 mm, 0.5 mm, and 1.5 mm ice particles. Additionally, the optimal injection ratios of ice slurry with 1.0 mm are determined to be over 0.3 and 0.26 when cleaning pipeline lengths within 500 m and 1000 m, respectively.

An analytical solution of direction evolution of crack growth during progressive failure in brittle rocks

AbstractMicrocrack growth during progressive compressive failure in brittle rocks strongly influences the safety of deep underground engineering. The external shear stress τxy on brittle rocks greatly affects microcrack growth and progressive failure. However, the theoretical mechanism of the growth direction evolution of the newly generated wing crack during progressive failure has rarely been studied. A novel analytical method is proposed to evaluate the shear stress effect on the progressive compressive failure and microcrack growth direction in brittle rocks. This model consists of the wing crack growth model under the principal compressive stresses, the direction correlation of the general stress, the principal stress and the initial microcrack inclination, and the relationship between the wing crack length and strain. The shear stress effect on the relationship between y‐direction stress and wing crack growth and the relationship between y‐direction stress and y‐direction strain are analyzed. The shear stress effect on the wing crack growth direction during the progressive compressive failure is determined. The initial crack angle effect on the y‐direction peak stress and the wing crack growth direction during the progressive compressive failure considering shear stress is also discussed. A crucial conclusion is that the direction of wing crack growth has a U‐shaped variation with the growth of the wing crack. The rationality of the analytical results is verified by an experiment and from numerical results. The study results provide theoretical support for the evaluation of the safety and stability of surrounding rocks in deep underground engineering.