Pseudo Strain Energy Research Articles

Feasibility study on model-based damage detection in shear frames using pseudo modal strain energy

This paper proposes a model-based approach for structural damage identification and quantification. Using pseudo modal strain energy and mode shape vectors, a damage-sensitive objective function is introduced which is suitable for damage estimation and quantification in shear frames. Whale optimization algorithm (WOA) is used to solve the problem and report the optimal solution as damage detection results. To illustrate the capability of the proposed method, a numerical example of a shear frame under different damage patterns is studied in both ideal and noisy cases. Furthermore, the performance of the WOA is compared with particle swarm optimization algorithm, as one the widely-used optimization techniques. The applicability of the method is also experimentally investigated by studying a six-story shear frame tested on a shake table. Based on the obtained results, the proposed method is able to assess the health of the shear building structures with high level of accuracy.

Kinetics of healing of asphalt mixtures

Abstract Promotion of healing of asphalt mixtures is significant to enhance the resiliency and extend the service life of asphalt pavements. Extensive laboratory measurements of effects of healing and field observations have proven its impact. Many approaches have been developed to explain and model healing of asphalt mixtures based on its mechanisms and/or mechanical features. However, due to the complexity caused by the co-existence of several coordinated rate processes during healing, there are still unclear aspects in terms of mechanisms and appropriate representation of each rate process. Target this issue, this study proposes to investigate healing of asphalt mixtures using kinetic and thermodynamic quantities and formulations, aiming at clarifying the relationships among the coordinated processes involved in healing and developing an approach to predict the rate of each process. Healing is found to contain two coordinated rate processes: free energy change and bond restoration. Healing rate is proportional to the rates of these two processes, and the healing activation energy is the product of the activation energy of the free energy change and that of the bond restoration. In order to calculate each activation energy and rate constant, the recoverable strain energy (RSE) and recoverable pseudo strain energy (RPSE) measured in the rest time of a creep and step-loading recovery (CSR) test are used. The RPSE in the intact material and the surface energy constitute the total free energy change for healing. A three-parameter model is proposed to simulate a rate process like the change of the RSE or free energy change with time, and a dimensionless logarithmic rate is defined to obtain a representative change rate. This representative rate is ideal to be used as the rate constant in the Arrhenius equation to compute the activation energy. The activation energies for viscoelastic recovery, healing, free energy change, and bond restoration are determined for two types of asphalt mixtures at unaged and aged states. The relations between different activation energies are clarified so as the relationships among different rate processes. Furthermore, the healing activation energy obtained from this kinetic approach is proven to be the same as that calculated using the damage density from a mechanistic approach. A method to generate a damage density-based healing curve at any rest time at any temperature using just energy measurements is proposed in this study.

A dissipated pseudo strain energy-based failure criterion for thermal cracking and its verification using thermal stress restrained specimen tests

Low-temperature cracking is one of the most prevalent types of distress in asphalt concrete pavements in regions where the air temperature undergoes a significant daily drop. This paper proposes a failure criterion that correlates the dissipated pseudo strain energy (DPSE) at the time of failure with the reduced strain rate. Uniaxial direct tension monotonic tests, axial compression dynamic modulus tests, and direct tension cyclic fatigue tests were performed using the Asphalt Mixture Performance Tester (AMPT) for a wide range of asphalt mixtures with different reclaimed asphalt pavement (RAP) contents, binder contents, virgin binder performance grades, and aging levels. The results show that the simplified viscoelastic continuum damage (S-VECD) model, which is characterized by the dynamic modulus and cyclic fatigue test results, can predict the stress-strain behavior of a given mixture subjected to monotonic tests at different temperatures and loading rates. This finding allows the prediction of DPSE in monotonic tension tests using the S-VECD model. The thermal stress restrained specimen test (TSRST) was then used to verify the DPSE-based failure criterion and the ability of the S-VECD model to predict thermal fracture behavior. The study results show that the predicted fracture temperatures match the measured ones for the study mixtures with reasonable accuracy. The study also used data from mixtures whose RAP contents, binder contents, virgin binder grades, and aging levels were systematically altered to verify the reasonableness of the proposed procedure to evaluate the differences in thermal fracture performance that are due to changes in these factors. The ability to predict the fracture stress and fracture temperature measured via the TSRST using the S-VECD model and the suggested DPSE failure criterion is of substantial practical and technical importance because it allows the prediction of both fatigue cracking and thermal cracking using a single set of tests, i.e., AMPT dynamic modulus and cyclic fatigue tests.

Quantification of Viscous and Fatigue Dissipation of Asphalt Concrete in Four-Point Bending Tests

Different methods are available to quantify the fatigue damage of the asphalt mixtures. Among these, methods based on the concept of dissipated energy are used predominantly. Characterizing fatigue damage using the concept of dissipated energy is complicated due to the presence of other modes of dissipation, for instance, viscous dissipation. Hence, most of the investigations attempt to separate the dissipation due to damage from the viscous dissipation. One of the widely used approaches to separate fatigue dissipation involves the use of a parameter called pseudostrain. The area under the stress-pseudostrain curve, called the dissipated pseudostrain energy, is used to characterize fatigue. In this study, the usefulness or otherwise of this approach to separate fatigue and viscous dissipation is explored. Toward this, experimental investigations were conducted using four-point bending for four types of asphalt mixtures at two different temperatures and four strain levels. It was observed that although the concept of pseudostrain to characterize the fatigue damage holds good in some specific cases, it cannot be adopted for all experimental data collected in this study. In view of this, a new strategy to separate the total dissipation into viscous and fatigue dissipation is proposed based on a constitutive assumption for the viscous dissipation of damaged asphalt concrete. This new method is then used to quantify fatigue damage in this study.

Investigating impacts of warm-mix asphalt technologies and high reclaimed asphalt pavement binder content on rutting and fatigue performance of asphalt binder through MSCR and LAS tests

The combined use of warm-mix asphalt (WMA) technologies and high percentages of reclaimed asphalt pavement (RAP) has become increasingly prevalent in asphalt paving industry due to its promising environmental and economic benefits; however, there remain significant concerns about the performance of WMA-high RAP mixtures. This study was focused on a laboratory investigation that evaluated the effects of two typical WMA additives, i.e., the wax based R and surfactant based M, and various high percentages (from 30% to 70%) of artificial RAP binder on the rutting and fatigue performance of asphalt binders through the recently developed multiple stress creep and recovery (MSCR) and linear amplitude sweep (LAS) tests, respectively. Five asphalt mixtures with different WMA technologies and RAP contents were used to verify the findings from the binder tests through the rutting and flexural fatigue tests. The results showed that the virgin binder always yielded the poorest rutting and fatigue performance. Both RAP binder and M improved the rutting resistance and traffic loading grades of the binders; R remarkably lowered the binder rutting performance, but this impact could be alleviated by properly increasing the RAP binder content. The inclusion of RAP binder enhanced the fatigue resistance of the binders, and so did R and M under most combinations of RAP contents and strain amplitudes. Generally, R performed better than M in improving the binder fatigue resistance. Besides, the LAS predicted results from the dissipated energy based approach generated slightly more conservative predictions than those from the pseudo strain energy based approach. Finally, most of the results for the mixtures exhibited similar trends to those for the binders, but M had different effects on the fatigue performance of the mixtures and binders.

Evaluation of fatigue behavior of asphalt binders containing reclaimed asphalt binder using simplified viscoelastic continuum damage approach

Several fatigue damage analysis approaches have been introduced for asphalt binders and mixtures. In this study, using three modifiers including softer bitumen, a rejuvenator and waste polymer modified bitumen, fatigue behavior of RAB-containing binder mixes was evaluated based on the simplified viscoelastic continuum damage mechanics (S-VECD). In addition, correlations between the S-VECD parameters and the other fatigue failure criteria were investigated. For this purpose, the time sweep test was used to evaluate fatigue behavior of various asphalt binders in controlled-strain mode. Results showed that the rejuvenator and softer bitumen had the greatest effect in terms of prioritization on the improvement of the fatigue resistance of the RAB-containing binder mixes. Moreover, the results showed that good unique relationships between plateau value (PV) and Nf50 and between rate of change of total released pseudo strain energy (GR) and Nf50 were established in the RAB-containing binder mixes. Furthermore, there was a good relationship between the two concepts of the dissipated energy approach used for determination of the PV and the dissipated pseudo strain energy approach which used for calculation of the GR values.

Fatigue performance predication model based on dissipated energy criteria using DSR under controlled-strain mode

Fatigue cracking is one of the primary modes of distress in flexible pavements that has an important economic impact. This paper describes the use of a dynamic shear rheometer (DSR) for fatigue performance testing of hot asphalt mixture under controlled-strain mode. 150 mm-diameter and 50 mm-height HMA finger samples used for the fatigue sequence procedure were developed and adopted to prepare the DSR samples. This paper reports the evaluation of fatigue resistance of asphalt mixture finger sample cores that were recovered from the field sections from Samawah–Nasiriyah City atrial road (97 km in the middle region of Iraq) using different continuum damage mechanics approach. The analysis has focused on comparing the dissipated pseudo strain energy (DPSE), energy ratio (ER) and energy stiffness ratio (ESR) in addition to the traditional approach under the controlled-strain mode. The results are used to develop guidelines for the design of fatigue-resistant mixtures in Iraq and to relate the mixture design to the structural design to optimize performance.

Predicting fatigue performance of hot mix asphalt using artificial neural networks

Developing predictive models for fatigue performance is a complex process and can depend on variables including material properties, test conditions and sample geometry. Several models have been developed in this regard; some of these are regression models and are related to mechanistic properties in addition to volumetric properties. In this work, a computational model, based on artificial neural networks (ANNs), is used to predict the fatigue performance of hot mix asphalt (HMA) tested in a dynamic shear rheometer (DSR) technique. Fatigue performance was evaluated according to three approaches: traditional, energy ratio and dissipated pseudo-strain energy. For predicting fatigue performance, two types of ANN models were developed: those dependent on test modes, that is, based on controlled test modes, and those independent of test modes, that is, irrespective of controlled test modes, using fundamental parameters, for example, stiffness modulus, phase angle and volumetric properties. In this work, limestone (L) and granite (G) aggregates were used with two binder grades (40/60 and 160/220) to prepare four mixtures with two different gradations: gap-graded hot rolled asphalt (HRA) and continuously graded dense bitumen macadam (DBM). The results revealed an excellent correlation between the predicted and experimental data. It was found that the prediction accuracy of the strain test mode was better than that of the stress test mode.

Comparative evaluation of fatigue resistance of warm fine aggregate asphalt mixtures

Fatigue cracking is one of the crucial distresses in asphalt pavements that affect its service life and rehabilitation process. The resistance of asphalt mixtures to fatigue failure in the laboratory experiments is influenced by several factors such as temperature, loading frequency, loading mode, sample type and geometry. This study focused on the evaluation of fatigue performance of different types of warm mix asphalt (WMA) mixture and comparing them with a hot asphalt mixture (control mixture). Warm fine aggregate mixtures (W-FAM) were fabricated using three different WMA additives: Advera, Sasobit, and Rediset which were short-term aged in the laboratory. Then, the W-FAM specimens were exposed to shear stress oscillation test by applying damaging stress level in the dynamic mechanical analyser (DMA) to examine the material fatigue resistance. The test results were analysed using the viscoelastic continuum damage (VECD) approach. The W-FAM exhibited lower dissipated pseudo-strain energy (DPSE) than the control mixture. However, there was no statistical significant difference between the W-FAM and control mix in terms of the number of cycles to failure resulted from the VECD analysis.

Reliability Analysis of Fatigue Life Prediction from the Viscoelastic Continuum Damage Model

The fatigue resistance of asphalt concrete materials plays an important role in the service life of a pavement. Several empirical and mechanistic models and efforts are under way toward improving these models for accurate prediction of fatigue life. The reliability of predictions with these models has not received substantial attention. This study used the simplified viscoelastic continuum damage model to analyze the reliability of fatigue predictions. Modulus and fatigue tests were conducted on a standard dense graded asphalt mixture to characterize the model and create deterministic fatigue life predictions. Monte Carlo simulations were then used to calculate the reliability of the fatigue predictions, given the variation in input parameters. The analysis was conducted for combinations of three experimental failure criteria and two model failure criteria at two strain levels for a total of 12 study cases. Differences in reliability between the combinations of failure conditions are identified and discussed. There are three major findings of this study. First, depending on the selection of failure criteria, the prediction errors could range from ±22% to ±52% at a 50% level of reliability, depending on the exact combination of failure criterion and strain level. Second, with an experimental failure criterion of 50%, modulus reduction shows better reliability regardless of the model failure criterion chosen to predict fatigue life. Third, the model failure criterion based on constant pseudostiffness at failure was found to be more reliable than was the pseudostrain energy release rate criterion when characterization was performed with three tests.

Evaluation of Fatigue Cracking in Asphalt Mixtures Based on Surface Energy

AbstractFatigue cracking in an asphalt mixture is a process whereby microcracks in the asphalt–aggregate interface propagate into extensive interconnected cracks under repeated loads. The fatigue performance of asphalt is influenced by the load as well as the intrinsic nature of the asphalt–aggregate system. This study used the surface energy concept of asphalt and aggregate systems to characterize the fatigue behavior of asphalt mixtures. The surface energy of asphalt and aggregate at different temperatures were measured using Wilhelmy plate method and contact angle meter, respectively. By using dissipated pseudostrain energy of nonlinear viscoelastic material and micromechanics cracking model, the effect of surface energy on fatigue life of the asphalt mixtures was analyzed. Laboratory test indicated that the surface energy of the asphalt generally decreased with an increase of temperature. Compared with AH70 grade asphalt, the surface energy of styrene-butadiene-styrene block copolymer (SBS)-modified a...

Fatigue resistance of asphalt binders: Assessment of the analysis methods in strain-controlled tests

Fatigue testing of binders is an important subject in asphalt research and in recent decades several test procedures and analysis methods have been proposed. This paper discusses the application of several analysis methods to two different strain-controlled tests, implemented with the DSR.The fatigue laws obtained from the time sweep (TST) and the linear amplitude sweep (LAS) tests with the traditional failure limits, based on a fixed stiffness reduction value, are quite different. Using LAS, with maximum shear stress as failure criterion, gives rise to better results that can be further improved when changing the failure criterion to one based on the dissipated pseudo strain energy evolution.

Unified failure criterion for asphalt binder under cyclic fatigue loading

Defining failure and developing a unified failure criterion for the fatigue testing of asphalt materials remain a challenge. This study seeks to develop a failure criterion for the fatigue testing of asphalt binders under cyclic loading in the dynamic shear rheometer. Newly developed pseudo-strain energy (PSE)-based failure analysis is introduced for both the time sweep fatigue test and the accelerated linear amplitude sweep (LAS) test (AASHTO TP101). The presented methodology builds upon recent advances in the simplified viscoelastic continuum damage (S-VECD) modelling of asphalt mixtures. Trends in stored PSE have been proven to be effective in defining failure for the LAS tests of asphalt binders. This new proposed failure definition is material-dependent and, thus, is effective in capturing the benefits of asphalt modification for binder fatigue resistance. In addition, it is found that a unique relationship that is independent of loading history exists between the PSE release rate and fatigue life. The fatigue life predictions using this relationship and the S-VECD model are in reasonable agreement with the laboratory-measured fatigue life data and also generally relate well with the field fatigue performance measured in the FHWA-ALF (Federal Highway Administration – Accelerated Loading Facility) pooled fund study.

A New Failure Criterion for Asphalt Mixtures under Fatigue Loading

In this paper a new criterion for determination of cycle number to failure of asphalt mixture at test in controlled strain mode is proposed. The proposed criterion is based on equality of total dissipated energy and total dissipated pseudo strain energy at failure. The proposed failure criterion is presented in three forms: in energy balance form, in terms of linear viscoelasticity theory and continuum damage mechanics. A new criterion applicability is shown by testing of hot mix asphalt mixture samples on four point bending equipment in controlled strain mode. Comparison of loading cycle numbers to failure of asphalt mixture obtained using the proposed and other often used criteria are carried out.

Noninvasive in vivo determination of residual strains and stresses.

Vascular growth and remodeling during embryonic development are associated with blood flow and pressure induced stress distribution, in which residual strains and stresses play a central role. Residual strains are typically measured by performing in vitro tests on the excised vascular tissue. In this paper, we investigated the possibility of estimating residual strains and stresses using physiological pressure-radius data obtained through in vivo noninvasive measurement techniques, such as optical coherence tomography or ultrasound modalities. This analytical approach first tested with in vitro results using experimental data sets for three different arteries such as rabbit carotid artery, rabbit thoracic artery, and human carotid artery based on Fung's pseudostrain energy function and Delfino's exponential strain energy function (SEF). We also examined residual strains and stresses in the human swine iliac artery using the in vivo experimental ultrasound data sets corresponding to the systolic-to-diastolic region only. This allowed computation of the in vivo residual stress information for loading and unloading states separately. Residual strain parameters as well as the material parameters were successfully computed with high accuracy, where the relative errors are introduced in the range of 0-7.5%. Corresponding residual stress distributions demonstrated global errors all in acceptable ranges. A slight discrepancy was observed in the computed reduced axial force. Results of computations performed based on in vivo experimental data obtained from loading and unloading states of the artery exhibited alterations in material properties and residual strain parameters as well. Emerging noninvasive measurement techniques combined with the present analytical approach can be used to estimate residual strains and stresses in vascular tissues as a precursor for growth estimates. This approach is also validated with a finite element model of a general two-layered artery, where the material remodeling states and residual strain generation are investigated.

Crack initiation in asphalt mixtures under external compressive loads

Crack initiation was studied for asphalt mixtures under external compressive loads. High tensile localized stresses near the edges of compressed air voids lead to the growth of wing cracks in the direction of the external loads. A quantitative crack initiation criterion was derived using pseudostrain energy balance principle. Bond energy is determined and it increases with aging and loading rate while decreases with temperature. Cohesive and adhesive cracking occur simultaneously and a method was proposed to determine the individual percentage. The crack initiation criterion is simplified and validated through comparing the predicted and measured compressive strength of the asphalt mixtures.

A multilevel hierarchical finite element model for capillary failure in soft tissue.

Bruising, the result of capillary failure due to trauma, is a common indication of abuse. However, the etiology of capillary failure has yet to be determined as the scale change from tissue to capillary represents several orders of magnitude. As a first step toward determining bruise etiology, we have developed a multilevel hierarchical finite element model (FEM) of a portion of the upper human arm using a commercial finite element tool and a series of three interconnected hierarchical submodels. The third and final submodel contains a portion of the muscle tissue in which a single capillary is embedded. Nonlinear, hyperelastic material properties were applied to skin, adipose, muscle, and capillary wall materials. A pseudostrain energy method was implemented to subtract rigid-body-like motion of the submodel volume experienced in the global model, and was critical for convergence and successful analyses in the submodels. The deformation and hoop stresses in the capillary wall were determined and compared with published capillary failure stress. For the dynamic load applied to the skin of the arm (physiologically simulating a punch), the model predicted that approximately 8% volume fraction of the capillary wall was above the reference capillary failure stress, indicating bruising would likely occur.

Development of a Failure Criterion for Asphalt Mixtures under Different Modes of Fatigue Loading

In the study reported in this paper, the previously developed failure criterion for the viscoelastic continuum damage (VECD) model (referred to here as GOR, where O indicates old and GR is the rate of release of the pseudostrain energy) was applied to different modes of fatigue loading. The research team found that this criterion was mode-of-loading dependent and therefore considered insufficient. To mitigate this limitation, the GOR criterion was refined to become a new failure criterion, the GR method, which resolved the mode-of-load dependency issue. A characteristic relationship, which was found to exist in recycled asphalt pavement (RAP) and non-RAP mixtures between the rate of change of the averaged released pseudostrain energy during fatigue testing and the final fatigue life was derived in this study. This relationship is independent of mode of loading, strain amplitude, and temperature. The proposed failure criterion combines the advantages of the VECD model and this characteristic relationship, which originate from fundamental mixture properties. This proposed method can predict the fatigue life of asphalt concrete mixtures across different modes of loading, temperatures, and strain amplitudes within typical sample-to-sample variability that is observed in fatigue testing.

Anisotropic Characterization of Crack Growth in the Tertiary Flow of Asphalt Mixtures in Compression

Asphalt mixtures exhibit primary, secondary, and tertiary stages in sequence during a rutting deterioration. Many field asphalt pavements are still in service even when the asphalt layer is in the tertiary stage, and rehabilitation is not performed until a significant amount of rutting accompanied by numerous macrocracks is observed. The objective of this study was to provide a mechanistic method to model the anisotropic cracking of the asphalt mixtures in compression during the tertiary stage of rutting. Laboratory tests including nondestructive and destructive tests were performed to obtain the viscoelastic and viscofracture properties of the asphalt mixtures. Each of the measured axial and radial total strains in the destructive tests were decomposed into elastic, plastic, viscoelastic, viscoplastic, and viscofracture strains using the pseudostrain method in an extended elastic-viscoelastic correspondence principle. The viscofracture strains are caused by the crack growth, which is primarily signaled by the increase of phase angle in the tertiary flow. The viscofracture properties are characterized using the anisotropic damage densities (i.e., the ratio of the lost area caused by cracks to the original total area in orthogonal directions). Using the decomposed axial and radial viscofracture strains, the axial and radial damage densities were determined by using a dissipated pseudostrain energy balance principle and a geometric analysis of the cracks, respectively. Anisotropic pseudo J-integral Paris' laws in terms of damage densities were used to characterize the evolution of the cracks in compression. The material constants in the Paris' law are determined and found to be highly correlated. These tests, analysis, and modeling were performed on different asphalt mixtures with two binders, two air void contents, and three aging periods. Consistent results were obtained; for instance, a stiffer asphalt mixture is demonstrated to have a higher modulus, a lower phase angle, a greater flow number, and a larger n1 value (exponent of Paris' law). The calculation of the orientation of cracks demonstrates that the asphalt mixture with 4% air voids has a brittle fracture and a splitting crack mode, whereas the asphalt mixture with 7% air voids tends to have a ductile fracture and a diagonal sliding crack mode. Cracks of the asphalt mixtures in compression are inclined to propagate along the direction of the external compressive load.

Asphalt damage characterisation from cyclic test and X-ray computed tomography

Imaging techniques have been used to characterise laboratory fatigue testing on asphalt mixtures. Specimens were tested in tension-compression cyclic testing at different temperatures. Testing was stopped at predefined stages, and specimens were scanned in X-ray computed tomography. A three-dimensional image of the original specimens was developed for analysis. It was found from the image analysis that the damage (air voids) were found to be increasing with an increase in strain as damage accumulated in the specimens. An energy-based damage mechanics model was used to calculate the increase in damage. Dissipated pseudo-strain energy and adhesion between binder and aggregate were used in the model. Pseudo-strain energy was calculated from laboratory testing, and the adhesion parameter was determined from surface energies of aggregate and bitumen (binder). Values obtained from a numerical model were found to have a similar trend as that of the data from X-ray computed tomography and image analysis.