Coupled Eulerian-Lagrangian simulation of a modified direct shearapparatus for the measurement of residual shear strengths

The simulation of large-strain geotechnical laboratory tests with conventional Lagrangian finite element method(FEM)techniques is often problematic due to excessive mesh distortion.The multiple reversal direct shear(MRDS)test can be used to measure the residual shear strength of soils in a laboratory setting.However,modelling and simulation generally require advanced numerical methods to accommodate the large shear strains concentrated in the shear plane.In reality,when the standard direct shear(DS)apparatus is used,the MRDS method is prone to two major sources of measurement error:load cap tilting and specimen loss.These sources of error make it difficult or even impossible to correctly determine the residual shear strength.This paper presents a modified DS apparatus and multi-reversal multi-stage test method,simulated using the coupled Eulerian-Lagrangian(CEL)method in a finite element environment.The method was successful in evaluating equipment and preventing both load cap tilting and specimen loss,while modelling large-deformation behaviour that is not readily simulated with the conventional FEM or arbitrary Lagrangian-Eulerian(ALE)analysis.Thereafter,a modified DS apparatus was created for the purpose of analysing mixtures of organic materials found in an Australian clay.The results obtained from the modified DS CEL model in combination with laboratory tests show a great improvement in the measured residual shear strength profiles compared to those from the standard apparatus.The modified DS setup ensures that accurate material residual shear strengths are calculated,a factor that is vital to ensure appropriate soil behaviour is simulated for numerical analyses of large-scale geotechnical projects.

Influence of dent on residual ultimate strength of 2024-T3 aluminum alloy plate under axial compression

Drop-weight impact tests were conducted on 2024-T3 aluminum plates with five types of impactors, and then the effects of the dent on the residual ultimate strength of the 2024-T3 specimens were investigated through axial compression tests. Results indicate that with increase in dent depth, the five types of dents affect the ultimate strength of the plate in different trends. Nevertheless, other than the plate global deflection caused by impacting, the dent itself has unremarkable effect on the ultimate strength. The mathematical expressions are derived regarding the relationship between impact energy factor and the dent depth factor as well as the compressive ultimate strength reduction rate and the dent depth factor.

Residual Strength of Stiffened LY12CZ Aluminum Alloy Panels with Widespread Fatigue Damage

Experimental and analytical investigations on the residual strength of the stiffened LY12CZ aluminum alloy panels with widespread fatigue damage （WFD） are conducted. Nine stiffened LY12CZ aluminum alloy panels with three different types of damage are tested for residual strength. Each specimen is pre-cracked at rivet holes by saw cuts and subjected to a monotonically increasing tensile load until failure is occurred and the failure load is recorded. The stress intensity factors at the tips of the lead crack and the adjacent WFD cracks of the stiffened aluminum alloy panels are calculated by compounding approach and finite element method （FEM） respectively. The residual strength of the stiffened panels with WFD is evaluated by the engineering method with plastic zone linkup criterion and the FEM with apparent fracture toughness criterion respectively. The predicted residual strength agrees well with the experiment results. It indicates that in engineering practice these methods can be used for residual strength evaluation with the acceptable accuracy. It can be seen from this research that WFD can significantly reduce the residual strength and the critical crack length of the stiffened panels with WFD. The effect of WFD crack length on residual strength is also studied.

Thermal damage constitutive model for rock considering damage threshold and residual strength

With the gradual depletion of mineral resources in the shallow part of the earth,resource exploitation continues to move deeper into the earth,it becomes a hot topic to simulate the whole process of rock strain softening,deformation and failure in deep environment,especially under high temperature and high pressure.On the basis of Lemaitre’s strain-equivalent principle,combined with statistics and damage theory,a statistical constitutive model of rock thermal damage under triaxial compression condition is established.At the same time,taking into account the existing damage model is difficult to reflect residual strength after rock failure,the residual strength is considered in this paper by introducing correction factor of damage variable,the model rationality is also verified by experiments.Analysis of results indicates that the damage evolution curve reflects the whole process of rock micro-cracks enclosure,initiation,expansion,penetration,and the formation of macro-cracks under coupled effect of temperature and confining pressure.Rock thermal damage shows logistic growth function with the increase of temperature.Under the same strain condition,rock total damage decreases with the rise of confining pressure.By studying the electron microscope images(SEM)of rock fracture,it is inferred that 35.40 MPa is the critical confining pressure of brittle to plastic transition for this granite.The model parameter F reflects the average strength of rock,and M reflects the morphological characteristics of rock stress–strain curves.The physical meanings of model parameters are clear and the model is suitable for complex stress states,which provides valuable references for the study of rock deformation and stability in deep engineering.

Prediction of the residual strength of clay using functional networks

Landslides are common natural hazards occurring in most parts of the world and have considerable adverse economic effects. Residual shear strength of clay is one of the most important factors in the determination of stability of slopes or landslides. This effect is more pronounced in sensitive clays which show large changes in shear strength from peak to residual states. This study analyses the prediction of the residual strength of clay based on a new prediction model, functional networks（FN） using data available in the literature. The performance of FN was compared with support vector machine（SVM） and artificial neural network（ANN） based on statistical parameters like correlation coefficient（R）, Nash–Sutcliff coefficient of efficiency（E）, absolute average error（AAE）, maximum average error（MAE） and root mean square error（RMSE）. Based on R and E parameters, FN is found to be a better prediction tool than ANN for the given data. However, the R and E values for FN are less than SVM. A prediction equation is presented that can be used by practicing geotechnical engineers. A sensitivity analysis is carried out to ascertain the importance of various inputs in the prediction of the output.

Estimation of residual shear strength ratios of liquefied soil deposits from shear wave velocity

For sites susceptible to liquefaction induced lateral spreading during a probable earthquake, geotechnical engineers often need to know the undrained residual shear strength of the liquefied soil deposit to estimate lateral spreading displacements, and the forces acting on the piles from the liquefied soils in order to perform post liquefaction stability analyses. The most commonly used methods to estimate the undrained residual shear strength （Su~） of liquefied sand deposits are based on the correlations determined from liquefaction induced flow failures with SPT and CPT data. In this study, 44 lateral spread case histories are analyzed and a new relationship based on only lateral spread case histories is recommended, which estimates the residual shear strength ratio of the liquefiable soil layer from normalized shear wave velocity. The new proposed method is also utilized to estimate the residual lateral displacement of an example bridge problem in an area susceptible to lateral spreading in order to provide insight into how the proposed relationship can be used in geotechnical engineering practice.

A predictive equation for residual strength using a hybrid of subset selection of maximum dissimilarity method with Pareto optimal multi-gene genetic programming

More accurate and reliable estimation of residual strength friction angle(/r)of clay is crucial in many geotechnical engineering applications,including riverbank stability analysis,design,and assessment of earthen dam slope stabilities.However,a general predictive equation for/r,with applicability in a wide range of effective parameters,remains an important research gap.The goal of this study is to develop a more accurate equation for/r using the Pareto Optimal Multi-gene Genetic Programming(POMGGP)approach by evaluating a comprehensive dataset of 290 experiments compiled from published literature databases worldwide.A new framework for integrated equation derivation proposed that hybridizes the Subset Selection of Maximum Dissimilarity Method(SSMD)with Multi-gene Genetic Programming(MGP)and Pareto-optimality(PO)to find an accurate equation for/r with wide range applicability.The final predictive equation resulted from POMGGP modeling was assessed in comparison with some previously published machine learning-based equations using statistical error analysis criteria,Taylor diagram,revised discrepancy ratio(RDR),and scatter plots.Base on the results,the POMGGP has the lowest uncertainty with U95=2.25,when compared with Artificial Neural Network(ANN)(U95=2.3),Bayesian Regularization Neural Network(BRNN)(U95=2.94),Levenberg-Marquardt Neural Network(LMNN)(U95=3.3),and Differential Evolution Neural Network(DENN)(U95=2.37).The more reliable results in estimation of/r derived by POMGGP with reliability 59.3%,and resiliency 60%in comparison with ANN(reliability=30.23%,resiliency=28.33%),BRNN(reliability=10.47%,resiliency=10.39%),LMNN(reliability=19.77%,resiliency=20.29%)and DENN(reliability=27.91%,resiliency=24.19%).Besides the simplicity and ease of application of the new POMGGP equation to a broad range of conditions,using the uncertainty,reliability,and resilience analysis confirmed that the derived equation for/r significantly outperformed other existing machine learning methods,including the ANN,BRNN,LMNN,and DENN equations。

Residual Tensile Strength of Plain Concrete Under Tensile Fatigue Loading

The functional relation between the residual tensile strength of plain concrete and number of cycles was determined. 99 tappered prism specimens of plain concrete were tested under uniaxial tensile fatigue loading. Based on the probability distribution of the residual tensile strength, the empirical expressions of the residual tensile strength corresponding to the number of cycles were obtained. The residual tensile strength attenuating curves can be used to predict the residual fatigue life of the specimen under variable-amplitude fatigue loading. There is a good correlation between residual tensile strength and residual secant elastic modulus. The relationship between the residual secant elastic modulus and number of cycles was also established.

Residual strength model for composite laminates

To research the approach of predicting composites fatigue life,the cumulative fatigue damage of fiber-reinforced plastic laminates(FRP) was investigated,and based on the complex exponential function,the residual strength model was obtained. This model can accurately describe the propagation of cumulative fatigue damage of FRP in three stages,especially in the initial stage and the ceasing stage. Applying this model in the experiment with two loading cycles,it can be found that the prediction result has good coincidence with experimental data. So a reliable residual strength model can be provided for studying the cumulative fatigue damage of FRP.

Validity of continuous-failure-state unloading triaxial tests as a means to estimate the residual strength of rocks

The residual strength of rocks and rock masses is an important parameter to be constrained for analysis and design purposes in many rock engineering applications.A residual strength envelope in principal stress space is typically developed using residual strength data obtained from compression tests on many different specimens of the same rock type.In this study,we examined the potential for use of the continuous-failure-state testing concept as a means to constrain the residual strength envelope using a limited number of specimens.Specifically,cylindrical specimens of three rock types(granodiorite,diabase,and Stanstead granite)were unloaded at the residual state such that a full residual strength envelope for each individual specimen was obtained.Using a residual strength model that introduces a single new strength parameter(the residual strength index,or RSI),the results of the continuous-failurestate unloading tests were compared to conventionally obtained residual strength envelopes.Overall,the continuous-failure-state residual strength data were found to be consistent with the conventional residual strength data.However,it was identified that the primary factor limiting an accurate characterization of the residual strength for a given rock type is not the amount of data for a given specimen,but the variety of specimens available to characterize the inherent variability of the rock unit of interest.Accordingly,the use of continuous-failure-state testing for estimation of the residual strength of a rock unit is only recommended when the number of specimens available for testing is very limited(i.e.<5).

Experimental and theoretical research on residual strength of plain concrete under compressive fatigue loading

To investigate the residual strength of concrete under fatigue loading, experiments were conducted to determine the functional relation between residual strength and the number of cycles. 80 100mm×100mm×100mm specimens of plain concrete were tested under uniaxial compressive fatigue loading. Based on probability distribution of the residual strength of concrete under fatigue loading, the empirical expressions of the residual strength corresponding to the number of cycles were obtained. There is a good correlation between residual strength and residual secant elastic modulus. Thus the relationship between residual secant elastic modulus and the number of cycles is established. A damage variable based on the longitudinal maximum strain is defined, and a good linearity relationship between residual strength and damage is found out.

Corrosion damage evolution and residual strength of corroded aluminum alloys

The LY12CZ aluminum alloy specimens were corroded under the conditions of different test temperatures and exposure durations. After corrosion exposure, fatigue tests were performed. Scanning electron microscopy and optical microscope analyses on corrosion damage were carried out. The definition of surface corrosion damage ratio was provided to describe the extent of surface corrosion damage. On the basis of the measured data sets of the corrosion damage ratio, the probabilistic model of corrosion damage evolution was built. The corrosion damage decreased the fatigue life by a factor of about 1.25 to 2.38 and the prediction method of residual strength of the corroded structure was presented.

Fatigue reliability based on residual strength model with hybrid uncertain parameters

The aim of this paper is to evaluate the fatigue reliability with hybrid uncertain parameters based on a residual strength model. By solving the non-probabilistic setbased reliability problem and analyzing the reliability with randomness, the fatigue reliability with hybrid parameters can be obtained. The presented hybrid model can adequately consider all uncertainties affecting the fatigue reliability with hybrid uncertain parameters. A comparison among the presented hybrid model, non-probabilistic set-theoretic model and the conventional random model is made through two typical numerical examples. The results show that the presented hybrid model, which can ensure structural security, is effective and practical.

Inner damage identification and residual strength assessment of a 3D printed tunnel with marble-like cementitious materials using piezoelectric transducers

Quantitative damage identification of surrounding rock is important to assess the current condition and residual strength of underground tunnels.In this work,an underground tunnel model with marble-like cementitious materials was first fabricated using the three-dimensional(3D)printing technique and then loaded to simulate its failure mode in the laboratory.Lead zirconate titanate piezoelectric(PZT)transducers were embedded in the surrounding rock around the tunnel in the process of 3D printing.A 3D monitoring network was formed to locate damage areas and evaluate damage extent during loading.Results show that as the load increased,main cracks firstly appeared above the tunnel roof and below the floor,and then they coalesced into the tunnel boundary.Finally,the tunnel model was broken into several parts.The resonant frequency and the peak of the conductance signature firstly shifted rightwards with loading due to the sealing of microcracks,and then shifted backwards after new cracks appeared.An overall increase in the root-mean-square deviation(RMSD)calculated from conductance signatures of all the PZT transducers was observed as the load(damage)increased.Damage-dependent equivalent stiffness parameters(ESPs)were calculated from the real and imaginary signatures of each PZT at different damage states.Satisfactory agreement between equivalent and experimental ESP values was achieved.Also,the relationship between the change of the ESP and the residual strength was obtained.The method paves the way for damage identification and residual strength estimation of other 3D printed structures in civil engineering.

RESIDUAL STRENGTH AND FATIGUE LIFE OF 2-D AND 3-D CARBON FABRIC COMPOSITES

The fatigue behavior and damage mechanisms of 2 D and 3 D carbon/epoxy composites with approximately the same 51% fiber volume fraction were investigated. A test program was conducted on fatigue residual strength and fatigue life under constant amplitude tensile fatigue loading. Equations of predicting the fatigue life for both 2 D and 3 D composites were provided. Comparison of the 2 D and 3 D composites indicated that due to the through thickness reinforcement, the 3 D composite has considerably better fatigue performance. Comparison of experimental data with calculation results shows good agreement, thus confirming the usefulness of the predictions.

A STUDY OF RESIDUAL STRENGTH OF SISAL TEXTILE REINFORCED VINYL ESTER

In this study, the residual strength of sisal textile reinforced vinyl ester resin is studied using specimens with a central hole. Two kinds of chemicals, silane and permanganate, are used to treat sisal fibre surfaces. The effects of fibre surface treatments on the residual strength of sisal fibre reinforced composites with different central hole sizes are analysed. Optical microscopy （OM） surveys provide sound evidence for the relationship between residual strength properties and fracture morphologies of sisal textile reinforced vinyl ester. Several theoretical models used to predict the residual strength of laminated composites are briefly reviewed. Point stress criterion （PSC） and average stress criterion （ASC） models are used to analyze the mechanical properties of sisal textile reinforced polymers with a central hole in this research. Material constant, characteristic length （d0 or lc）, is obtained and used to analyze the mechanical behavior of the composites. The residual strength of the composites predicted by PSC and ASC models is in good agreement with the experimental results..

Numerical Analysis of Residual Strength in the Perforated Casing of Ultra Deep Wells

A three-dimensional model for the numerical simulation of casing-cement behavior is used to investigate residual strength in the perforated casing of ultra deep wells.The influence of the hole diameter,hole density and phase angle on the residual strength of the casing under non-uniform stress and fracturing conditions is revealed through the consideration of different perforation parameters.It is shown that the residual strength of the casing increases with the hole diameter and periodically changes with the hole density;the phase angle is the main factor that affects the residual strength of the perforated casing,and the perforation should be avoided in the direction of the minimum principal stress to reduce stress concentration at the perforation hole.Moreover,as shown by a companion orthogonal experiment,the descending order of influence of the different influential parameters is:phase angle,hole diameter,hole density and the thickness of casing.

A Model for the Determination of Semi-Circular Spot Corrosion Damage and Residual Strength in Oil Pipes

Pitting corrosion often occurs due to the presence of various corrosive substances,such as CO_(2) and H_(2)S,in the pipe service environment.As a result of this process,the residual strength of oil pipes is reduced and this can compromise the integrity of the entire pipe string.In the present work,a model is introduced on the basis of the API579 standard to determine the so-called stress concentration coefficient.The model accounts for pitting corrosion shapes such as shallow semi-circles,semi-circles,and deep semi-circles.The relationship between the corrosion pit depth and opening diameter and the residual strength of the oil casing is obtained.The results show that the influence of the pit opening diameter on the stress concentration coefficient is smaller than that of the pit depth.For a constant pit opening diameter,the coefficient increases gradually with increasing the pit depth.The compressive strength and internal pressure strength of the carbon steel oil casing decrease accordingly.When the depth of the corrosion pit is relatively small,the growth of the coefficient is slower;when the depth of the corrosion pit increases to a certain value,the increase in stress concentration coefficient becomes obvious.

An Application of the Modified Shear Lag Model to Study the Influence of Thermal Residual Stresses on the Stiffness and Yield Strength of Short Fiber Reinforced Metal Matrix Composites

The modified shear lag model proposed recently was applied to calculate thermal residual stresses and subsequent stress distributions under tensile and compressive loadings. The expressions for the elastic moduli and the yield strengths under tensile and compressive loadings were derived which take account of thermal residual stresses. The asymmetries in the elastic modulus and the yield strength were interpreted using the derived expressions and the obtained results of the stress calculations. The model predictions have exhibited good agreements with the experimental results and also with the other theoretical predictions

Crack patterns corresponding to the residual strength plateau of ceramics subjected to thermal shock

The formation strength plateau of ceramics is addressed. A set of of 99A1203 are conducted, mechanism of the residual subjected to thermal shock thermal shock experiments where the thin specimens of 1 mm× 10 mm×50 mm exhibit parallel through edge cracks, and thus permit quantitative measurements of the crack patterns. The cracks evolve with the severity of ther- mal shock. It is found that there is a correlation between the length and density of the thermal shock cracks. The increase of crack length weakens the residual strength, whereas the increase of crack density improves it. In a considerably wide temperature range, the two contrary effects just counteract each other; consequently a plateau appears in the variation curve of the residual strength. A comparison between the numerical and experimental results of the residual strength is made, and they are found in good agreement. This work is helpful to a deep understanding of the thermal shock failure of ceramics.