Strength criterion for crystalline rocks considering grain size effect and tensile-compressive strength ratio

The macroscopic mechanical properties of rocks are significantly influenced by their microstructure.As a material bonded by mineral grains,the grain morphology of crystalline rock is the primary factor influencing the strength.However,most strength criteria neglect the strength variations caused by different grain characteristics in rocks.Furthermore,the traditional linear criteria tend to overestimate tensile strength and exhibit apex singularity.To address these shortcomings,a piecewise strength criterion that considers the grain size effect has been proposed.A part of an ellipse was employed to construct the envelope of the tensive-shear region on the meridian plane,to accurately reproduce the low tensile-compressive strength ratio.Based on the analysis of experimental data,both linear and exponential modification functions that account for grain size effects were integrated into the proposed criterion.The corresponding finite element algorithm has been implemented.The accuracy and applicability of the proposed criterion were validated by comparing with the experimental data.

Rock strength weakening subject to principal stress rotation:Experimental and numerical investigations

During the construction and operation of gas storage reservoirs,changes in the principal stress direction can induce fracture propagation under conditions of lower differential stress,potentially leading to failure in the surrounding rock.However,the weakening of strength due to pure stress rotation has not yet been investigated.Based on fracture mechanics,an enhanced Mohr-Coulomb strength criterion considering stress rotation is proposed and verified with experimental and numerical simulations.The micro-damage state and the evolution of the rock under the pure stress-rotation condition are analyzed.The findings indicate that differential stress exceeding the crack initiation stress is a prerequisite for stress rotation to promote the development of rock damage.As the differential stress increases,stress rotation is more likely to induce rock damage,leading to a transition from brittle to plastic failure,characterized by wider fractures and a more complex fracture network.Overall,a negative exponential relationship exists between the stress rotation angle required for rock failure and the differential stress.The feasibility of applying the enhanced criterion to practical engineering is discussed using monitoring data obtained from a mine-by tunnel.This study introduces new concepts for understanding the damage evolution of the surrounding rock under complex stress paths and offers a new theoretical basis for predicting the damage of gas storage reservoirs.

Experimental investigation on shear strength deterioration at the interface between different rock types under cyclic loading

The shear strength deterioration of bedding planes between different rock types induced by cyclic loading is vital to reasonably evaluate the stability of soft and hard interbedded bedding rock slopes under earthquake;however,rare work has been devoted to this subject due to lack of attention.In this study,experimental investigations on shear strength weakening of discontinuities with different joint wall material(DDJM)under cyclic loading were conducted by taking the interface between siltstone and mudstone in the Shaba slope of Yunnan Province,China as research objects.A total of 99 pairs of similar material samples of DDJM(81 pairs)and discontinuities with identical joint wall material(DIJM)(18 pairs)were fabricated by inserting plates,engraved with typical surface morphology obtained by performing three-dimensional laser scanning on natural DDJMs sampled from field,into mold boxes.Cyclic shear tests were conducted on these samples to study their shear strength changes with the cyclic number considering the effects of normal stress,joint surface morphology,shear displacement amplitude and shear rate.The results indicate that the shear stress vs.shear displacement curves under each shear cycle and the peak shear strength vs.cyclic number curves of the studied DDJMs are between those of DIJMs with siltstone and mudstone,while closer to those of DIJMs with mudstone.The peak shear strengths of DDJMs exhibit an initial rapid decline followed by a gradual decrease with the cyclic number and the decrease rate varies from 6%to 55.9%for samples with varied surface morphology under different testing conditions.The normal stress,joint surface morphology,shear displacement amplitude and shear rate collectively influence the shear strength deterioration of DDJM under cyclic shear loading,with the degree of influence being greater for larger normal stress,rougher surface morphology,larger shear displacement amplitude and faster shear rate.

Relationships between Quadriceps:Hamstring Strength Ratio and Lower Extremity Injuries in Netball Players

Background: Netball is a popular sport. Due to high impact and quick movement, there is an enormous load on the lower extremities which increases the risk for injury. Aim: The aim of this study was to investigate the relationship between the quadricep and hamstring strength and the prevalence of lower extremity injuries in netball players. Setting: Twenty-five female netball players (age: 20.8 ± 1.4 years) voluntarily participated. Methods: The Cybex Isokinetic dynamometer was used to determine concentric knee torques. Quadriceps:hamstring strength ratio was determined. Occurrence of lower extremity injuries was documented bi-weekly. Results: Medium effect sizes were noted for flexion torque:work for the left leg and for the quadriceps:hamstring ratio (≥60%) for the right leg. All the other measured variables have a small effect size. 18.75% of lower extremity injuries and ConQ:ConH of Conclusion: Injuries to the ankle and knee are especially common among netball players. Hamstring and quadriceps muscle asymmetry (>10%) were found to be a potential indicator of lower extremity injury. Contribution: This study highlights awareness on lower extremity injuries and the strength ratio between the quadriceps and hamstrings. This can aid coaches and netball players to lower the risk for injuries and thus improve individual- and team performance.

Adaptive strategy of Nitraria sibirica to transient salt,alkali and osmotic stresses via the alteration of Na+/K+fluxes around root tips

Nitraria sibirica Pall.is an important shrub with a strong salt-alkali tolerance,but the mechanism underlying this tolerance remains obscure.In this study,N.sibirica,with salt-sensitive Vigna radiata(Linn.)Wilczek as the control,was subjected to transient salt stress(100 mM NaCl),alkali stress(50 mM Na_(2)CO_(3)),and osmotic stress(175 mM mannitol).The ionic fluxes of Na^(+)and K^(+)in the root apical region were measured.Results show that,under salt and alkali stress,N.sibirica roots exhibited higher capacities to limit Na+influx and reduce K+efflux,thereby resulting in lower Na^(+)/K^(+)ratios compared with V.radiata roots.Alkali stress induced stronger Na^(+)influx and K+efflux in the root salt stress treatment;Na^(+)influx was mainly observed in the root cap,while K^(+)efflux was mainly observed in the elongation zone.While under osmotic stress,N.sibirica roots showed stronger Na+efflux and weaker K+efflux than V.radiata roots.Na+efflux was mainly observed in the root elongation zone,while K+efflux was in the root cap.These results reveal the ionic strategy of N.sibirica in response to transient salt,alkali,and osmotic stresses through the regulation of Na+/K+flux homeostasis.

STRENGTH CRITERION FOR PLAIN CONCRETE UNDER MULTIAXIAL STRESS BASED ON DAMAGE POISSON’S RATIO

A new unified strength criterion in the principal stress space has been proposed for use with normal strength concrete （NC） and high strength concrete （HSC） in compressioncompression-tension, compression-tension-tension, triaxial tension, and biaxial stress states. The study covers concrete with strengths ranging from 20 to 130 MPa. The conception of damage Poisson＇s ratio is defined and the expression for damage Poisson＇s ratio is determined basically. The failure mechanism of concrete is illustrated, which points out that damage Poisson＇s ratio is the key to determining the failure of concrete. Furthermore, for the concrete under biaxial stress conditions, the unified strength criterion is simplified and a simplified strength criterion in the form of curves is also proposed. The strength criterion is physically meaningful and easy to calculate, which can be applied to analytic solution and numerical solution of concrete structures.

Evolution of microstructure and properties of a novel Ni-based superalloy during stress relief annealing

We discussed the decrease in residual stress,precipitation evolution,and mechanical properties of GH4151 alloy in different annealing temperatures,which were studied by the scanning electron microscope(SEM),high-resolution transmission electron microscopy(HRTEM),and electron backscatter diffraction(EBSD).The findings reveal that annealing processing has a significant impact on diminishing residual stresses.As the annealing temperature rose from 950 to 1150℃,the majority of the residual stresses were relieved from 60.1 MPa down to 10.9 MPa.Moreover,the stress relaxation mechanism transitioned from being mainly controlled by dislocation slip to a combination of dislocation slip and grain boundary migration.Meanwhile,the annealing treatment promotes the decomposition of the Laves,accompanied by the precipitation ofμ-(Mo_(6)Co_(7))starting at 950℃ and reaching a maximum value at 1050℃.The tensile strength and plasticity of the annealing alloy at 1150℃ reached the maximum(1394 MPa,56.1%)which was 131%,200%fold than those of the as-cast alloy(1060 MPa,26.6%),but the oxidation process in the alloy was accelerated at 1150℃.The enhancement in durability and flexibility is primarily due to the dissolution of the brittle phase,along with the shape and dispersal of theγ′phase.

Wellbore stability model in shale formation under the synergistic effect of stress unloading-hydration

According to the transversely isotropic theory and weak plane criterion, and considering the mechanical damages due to stress unloading and hydration during drilling, a shale wellbore stability model with the influence of stress unloading and hydration was established using triaxial test and shear test. Then, factors influencing the wellbore stability in shale were analyzed. The results indicate that stress unloading occurs during drilling in shale. The larger the confining pressure and axial stress, the more remarkable weakening of shale strength caused by stress unloading. The stress unloading range is positively correlated with the weakening degree of shale strength. Shale with a higher development degree of bedding is more prone to damage along bedding. In this case, during stress unloading, the synergistic effect of weak structural plane and stress unloading happens, leading to a higher weakening degree of shale strength and poorer mechanical stability, which brings a higher risk of wellbore instability. Fluid tends to invade shale through bedding, promoting the shale hydration. Hydration also can weaken shale mechanical stability, causing the decline of wellbore stability. Influence of stress unloading on collapse pressure of shale mainly occurs at the early stage of drilling, while the influence of hydration on wellbore stability mainly happens at the late stage of drilling. Bedding, stress unloading and hydration jointly affect the wellbore stability in shale. The presented shale wellbore stability model with the influence of stress unloading and hydration considers the influences of the three factors. Field application demonstrates that the prediction results of the model agree with the actual drilling results, verifying the reliability of the model.

Strength Model of Soda Residue Soil Considering Consolidation Stress and Structural Influence

Soda residue(SR)is a type of industrial waste produced in the soda process with the ammonia-soda method.Applying SR to backfilling solves the land occupation and environmental pollution problems in coastal areas and saves material costs for foundation engineering.The strength characteristics of soda residue soil(SRS)under different consolidation conditions are the key points to be solved in the engineering application of SRS.Triaxial compression tests were performed on the undisturbed SRS of Tianjin Port.The shear properties of SRS under different consolidation conditions were then discussed.Meanwhile,a structural strength model(SSM)based on Mohr-Coulomb theory was proposed.SSM reflects the influence of soil structure on undrained strength(Cu)and divides the Cu into the following two parts:friction strength(C_(uf))and original structural strength(C_(u0)).C_(uf)characterizes the magnitude of friction between soil particles,which is related to the consolidation stress.Meanwhile,C_(u0)represents the structural effect on soil strength,which is related to the soil deposition and consolidation processes.SSM was validated by the test data of undisturbed soils.Results reveal that the undisturbed soil generally had a certain C_(u0).Therefore,the SRS strength model was established by combining the experimental law of SRS with SSM.Error analysis shows that the SRS strength model can effectively predict the Cu of undisturbed SRS in Tianjin Port under different consolidation conditions.

Correlation between the rock mass properties and maximum horizontal stress:A case study of overcoring stress measurements

Understanding the mechanical properties of the lithologies is crucial to accurately determine the horizontal stress magnitude.To investigate the correlation between the rock mass properties and maximum horizontal stress,the three-dimensional(3D)stress tensors at 89 measuring points determined using an improved overcoring technique in nine mines in China were adopted,a newly defined characteristic parameter C_(ERP)was proposed as an indicator for evaluating the structural properties of rock masses,and a fuzzy relation matrix was established using the information distribution method.The results indicate that both the vertical stress and horizontal stress exhibit a good linear growth relationship with depth.There is no remarkable correlation between the elastic modulus,Poisson's ratio and depth,and the distribution of data points is scattered and messy.Moreover,there is no obvious relationship between the rock quality designation(RQD)and depth.The maximum horizontal stress σ_(H) is a function of rock properties,showing a certain linear relationship with the C_(ERP)at the same depth.In addition,the overall change trend of σ_(H) determined by the established fuzzy identification method is to increase with the increase of C_(ERP).The fuzzy identification method also demonstrates a relatively detailed local relationship betweenσ_H and C_(ERP),and the predicted curve rises in a fluctuating way,which is in accord well with the measured stress data.

Influence of axial stress on rockburst in deep tunnels: insight from model experiment

Frequent rockburst disasters in deep-buried engineering projects severely impact construction. To explore the influence of axial stress on rockburst in deep-buried tunnels, large-scale true triaxial rockburst experiments were conducted under four different axial stress ratio conditions (ηt, axial loading stress/vertical loading stress) using a self-developed true triaxial loading device under the condition of "pre-loading before excavation". The influence of axial stress on the rockburst process and failure characteristics in deep tunnels was studied using a combination of real-time video monitoring, rockburst debris sieving, and acoustic emission monitoring. The results indicate: (1) all four specimens subjected to different axial stress ratio loading conditions exhibited three stages of macroscopic failure: small particle ejection, flake spalling, and large fragment ejection. Ultimately, "V"-shaped notches appeared on both sides of the tunnel. (2) The failure stress, fragment volume, and fragment size distribution of the rockburst specimens exhibited a clear two-stage failure characteristic with increasing axial stress ratio. In the lower axial stress ratio stage (ηt ≤ 0.7), the increase in the axial stress ratio enhances lateral confinement, thereby increasing the crack initiation strength of the surrounding rock, inhibiting crack formation and propagation, and thus suppressing damage to the surrounding rock of the tunnel. In the higher axial stress ratio stage (ηt > 0.7), the increase in axial stress ratio makes the Poisson effect of the surrounding rock more pronounced, promoting the generation and propagation of cracks along the tunnel axis direction, thereby promoting damage to the surrounding rock. (3) Based on the analysis of acoustic emission parameters (fracture properties), it can be concluded that in the lower axial stress ratio stage (ηt ≤ 0.7), an increase in the axial stress ratio leads to a higher proportion of shear fracture in rockburst damage. Conversely, in the higher axial stress ratio stage (ηt > 0.7), the increase in axial stress ratio gradually reduces the proportion of shear fracture in rockburst damage.

Retrospective and prospective review of the generalized nonlinear strength theory for geomaterials

Strength theory is the basic theory for calculating and designing the strength of engineering materials in civil,hydraulic,mechanical,aerospace,military,and other engineering disciplines.Therefore,the comprehensive study of the generalized nonlinear strength theory(GNST)of geomaterials has significance for the construction of engineering rock strength.This paper reviews the GNST of geomaterials to demonstrate the research status of nonlinear strength characteristics of geomaterials under complex stress paths.First,it systematically summarizes the research progress of GNST(classical and empirical criteria).Then,the latest research the authors conducted over the past five years on the GNST is introduced,and a generalized three-dimensional(3D)nonlinear Hoek‒Brown(HB)criterion(NGHB criterion)is proposed for practical applications.This criterion can be degenerated into the existing three modified HB criteria and has a better prediction performance.The strength prediction errors for six rocks and two in-situ rock masses are 2.0724%-3.5091%and 1.0144%-3.2321%,respectively.Finally,the development and outlook of the GNST are expounded,and a new topic about the building strength index of rock mass and determining the strength of in-situ engineering rock mass is proposed.The summarization of the GNST provides theoretical traceability and optimization for constructing in-situ engineering rock mass strength.

Prediction Model-based Multi-objective Optimization for Mix-ratio Design of Recycled Aggregate Concrete

The prediction model for mechanical properties of RAC was established through the Bayesian optimization-based Gaussian process regression(BO-GPR)method,where the input variables in BO-GPR model depend on the mix ratio of concrete.Then the compressive strength prediction model,the material cost,and environmental factors were simultaneously considered as objectives,while a multi-objective gray wolf optimization algorithm was developed for finding the optimal mix ratio.A total of 730 RAC datasets were used for training and testing the predication model,while the optimal design method for mix ratio was verified through RAC experiments.The experimental results show that the predicted,testing,and expected compressive strengths are nearly consistent,illustrating the effectiveness of the proposed method.

Analytical investigations of in situ stress inversion from borehole breakout geometries

This study aims to investigate the feasibility of deriving in situ horizontal stresses from the breakout width and depth using the analytical method.Twenty-three breakout data with different borehole sizes were collected and three failure criteria were studied.Based on the Kirsch equations,relatively accurate major horizontal stress(sH)estimations from known minor horizontal stress(sh)were achieved with percentage errors ranging from 0.33%to 44.08%using the breakout width.The Mogi-Coulomb failure criterion(average error:13.1%)outperformed modified Wiebols-Cook(average error:19.09%)and modified Lade(average error:18.09%)failure criteria.However,none of the tested constitutive models could yield reasonable sh predictions from known sH using the same approach due to the analytical expression of the redistributed stress and the nature of the constitutive models.In consideration of this issue,the horizontal stress ratio(sH/sh)is suggested as an alternative input,which could estimate both sH and sh with the same level of accuracy.Moreover,the estimation accuracies for both large-scale and laboratory-scale breakouts are comparable,suggesting the applicability of this approach across different breakout sizes.For breakout depth,conformal mapping and complex variable method were used to calculate the stress concentration around the breakout tip,allowing the expression of redistributed stresses using binomials composed of sH and sh.Nevertheless,analysis of the breakout depth stabilisation mechanism indicates that additional parameters are required to utilise normalised breakout depth for stress estimation compared to breakout width.These parameters are challenging to obtain,especially under field conditions,meaning utilising normalised breakout depth analytically in practical applications faces significant challenges and remains infeasible at this stage.Nonetheless,the normalised breakout depth should still be considered a critical input for any empirical and statistical stress estimation method given its significant correlation with horizontal stresses.The outcome of this paper is expected to contribute valuable insights into the breakout stabilisation mechanisms and estimation of in situ stress magnitudes based on borehole breakout geometries.

Assessing the range of blasting-induced cracks in the surrounding rock of deeply buried tunnels based on the unified strength theory

Blasting-induced cracks in the rock surrounding deeply buried tunnels can result in water gushing and rock mass collapse,posing significant safety risks.However,previous theoretical studies on the range of blasting-induced cracks often ignore the impact of the in-situ stress,especially that of the intermediate principal stress.The particle displacement−crack radius relationship was established in this paper by utilizing the blasthole cavity expansion equation,and theoretical analytical formulas of the stress−displacement relationship and the crack radius were derived with unified strength theory to accurately assess the range of cracks in deep surrounding rock under a blasting load.Parameter analysis showed that the crushing zone size was positively correlated with in-situ stress,intermediate principal stress,and detonation pressure,whereas negatively correlated with Poisson ratio and decoupling coefficient.The dilatancy angle-crushing zone size relationship exhibited nonmonotonic behavior.The relationships in the crushing zone and the fracture zone exhibited opposite trends under the influence of only in-situ stress or intermediate principal stress.As the in-situ stress increased from 0 to 70 MPa,the rate of change in the crack range and the attenuation rate of the peak vibration velocity gradually slowed.

Prediction of the undrained shear strength of remolded soil with non-linear regression,fuzzy logic,and artificial neural network

This study aims to predict the undrained shear strength of remolded soil samples using non-linear regression analyses,fuzzy logic,and artificial neural network modeling.A total of 1306 undrained shear strength results from 230 different remolded soil test settings reported in 21 publications were collected,utilizing six different measurement devices.Although water content,plastic limit,and liquid limit were used as input parameters for fuzzy logic and artificial neural network modeling,liquidity index or water content ratio was considered as an input parameter for non-linear regression analyses.In non-linear regression analyses,12 different regression equations were derived for the prediction of undrained shear strength of remolded soil.Feed-Forward backpropagation and the TANSIG transfer function were used for artificial neural network modeling,while the Mamdani inference system was preferred with trapezoidal and triangular membership functions for fuzzy logic modeling.The experimental results of 914 tests were used for training of the artificial neural network models,196 for validation and 196 for testing.It was observed that the accuracy of the artificial neural network and fuzzy logic modeling was higher than that of the non-linear regression analyses.Furthermore,a simple and reliable regression equation was proposed for assessments of undrained shear strength values with higher coefficients of determination.

Stress-Strength Structural Reliability Model with a Stochastic Strength Aging Deterioration Process

A stress-strength structural reliability model was proposed with a stochastic strength aging deterioration process. In structural engineering,the deterioration of structure's strength should be the total of the deterioration owing to continual wear, fatigue,corrosion,etc.,and the abrupt deterioration as a result of randomly variable loads. The deterioration of structure's strength should be influenced by both the internal deterioration owing to direct wear and the external deterioration due to randomly variable loads.Meanwhile,the load process was given as Poisson square wave process. The reliability was derived using stress-strength interference theory. In particular,the reliability was also given when random variables followed the normal distribution.

Evolution of mechanical parameters of Shuangjiangkou granite under different loading cycles and stress paths

Surrounding rocks at different locations are generally subjected to different stress paths during the process of deep hard rock excavation.In this study,to reveal the mechanical parameters of deep surrounding rock under different stress paths,a new cyclic loading and unloading test method for controlled true triaxial loading and unloading and principal stress direction interchange was proposed,and the evolution of mechanical parameters of Shuangjiangkou granite under different stress paths was studied,including the deformation modulus,elastic deformation increment ratios,fracture degree,cohesion and internal friction angle.Additionally,stress path coefficient was defined to characterize different stress paths,and the functional relationships among the stress path coefficient,rock fracture degree difference coefficient,cohesion and internal friction angle were obtained.The results show that during the true triaxial cyclic loading and unloading process,the deformation modulus and cohesion gradually decrease,while the internal friction angle gradually increases with increasing equivalent crack strain.The stress path coefficient is exponentially related to the rock fracture degree difference coefficient.As the stress path coefficient increases,the degrees of cohesion weakening and internal friction angle strengthening decrease linearly.During cyclic loading and unloading under true triaxial principal stress direction interchange,the direction of crack development changes,and the deformation modulus increases,while the cohesion and internal friction angle decrease slightly,indicating that the principal stress direction interchange has a strengthening effect on the surrounding rocks.Finally,the influences of the principal stress interchange direction on the stabilities of deep engineering excavation projects are discussed.

Fatigue reliability quantitative analysis of cement concrete for highway pavement under high stress ratio

In order to obtain the change law of the fatigue reliability of cement concrete for highway pavement under high stress ratios, first, the probability densities of monotonic random variables including concrete fatigue life are deduced. And then, the fatigue damage probability densities of the Miner and Chaboche-Zhao models are deduced. By virtue of laboratory fatigue test results, the fatigue damage probability density functions of the two models can be obtained, considering different stress ratios. Finally, substituting load cycles into them, the change law of cement concrete fatigue reliability about load cycles can be acquired. The results show that under the same stress ratio, with the increase in the load cycle, the fatigue reliability declines from almost 100% to 0% gradually. No matter under what stress ratio, during the initial stage of the load action, there is always a relatively stable phase for fatigue reliability. With the increase in the stress ratio, the stable phase gradually shortens and the load cycle corresponding to the reliability of 0% also decreases. In the descent phase of reliability, the higher the stress ratio is, the lower the concrete reliability is for the same load cycle. Besides, compared with the Chaboche-Zhao fatigue damage model, the Miner fatigue damage model is safer.

Use of piezocone tests to predict consolidation yield stress and overconsolidation ratio of lagoonal deposit soil

Existing empirical methods for interpreting the consolidation yield stress and the overconsolidation ratio （OCR） in clays from piezocone tests are briefly reviewed. It can be seen that no universal correlation exists for all worldwide sites. However, for a given clay deposit, there does exist a most appropriate method to reflect the consolidation yield stress and the OCR based on piezocone test data. Three empirical methods are compared based on the piezocone test data collected on Lixia River lagoonal deposit soil sites in the north of Jiangsu province. The objective of this study is to evaluate the validity of the existing relationships linking the consolidation yield stress to piezocone test data and identify the appropriate method for Lixia River lagoonal deposit soil. It is shown that the correlation based on the net tip resistance has much higher accuracy for estimating the consolidation yield stress of lagoonal deposit soil than other methods.