Number Of Load Applications Research Articles

Elastic shakedown limit of a steel lattice girder

This paper presents a solution for the problem concerning the behaviour of a steel lattice girder subjected to dynamic load pulses. The theory of shakedown is used in the analysis. It is assumed that such loads cause a non-elastic response which includes dissipation of energy causing deformations and residual forces developed in the structural members of the girder. At a certain intensity of these forces, the girder can react to subsequent load pulses without further dissipation of energy, behaving in the elastic region after shakedown. This condition is referred to as adaptation of the structure to assumed cyclic loading. Elastic shakedown limit is determined through a direct analysis of the girder's dynamic behaviour, i.e. by checking if energy dissipation decreases with loading cycles. This gives the number of load applications after which no further increase of the energy dissipation is observed. The existing permanent deformations persist and residual forces remain in the same state. The analysis takes into account the possibility that compressed members can buckle which may result in non-elastic, longitudinal and transverse vibrations of these members. Non-linear geometry of members is taken into account. Then a perfectly elastic-viscoplastic model of the material is used. The main goal is to determine the state of the non-elastic movements of the girder joints and the residual internal forces developed in the girder members after each load application. The values obtained in this way serve as the basis for describing the next loading cycle. It is possible to use the approach presented in the paper to evaluate the effects of accidental loads. Then it is checked whether a small number of repetitions of accidental load would result in exceeding the serviceability limit state criteria of the maximum permanent deformation or displacement and/or strain amplitudes. If so, the magnitude of accidental load is greater than the elastic shakedown limit. Some examples are given to illustrate the application of the theory of shakedown.

Evaluating the mechanical performance of asphalt mixtures in cyclic torsional shear test

In this paper, the mechanical performance of asphalt mixtures was examined in cyclic torsional shear test, in which the relationship between the averaged shear strain, γav, and the number of cyclic loading, N, was obtained by using a short, about 25mm height, specimen. In these tests, the effects of some influencing factors such as the type of asphalt mixture, the thickness of specimen and the temperature were examined. In each test, four indices; i.e., the slope of plastic flow line, the slope of stripping line, the number of load applications at the inflection point for stripping and the averaged shear strain at the inflection point for stripping, were defined for the relationship between γav and N. As a result of this study, we clarified that various performances such as rutting resistance, fatigue failure resistance and the stripping resistance of asphalt mixture can be appropriately evaluated by using the cyclic torsional shear test.

Analysis of the distribution of the number of applications of the estimated load on the Federal roads during the year

The article is devoted to the statistical processing of traffic intensity and composition of traffic flow obtained from the points of automated traffic intensity accounting for 2010-2018 in order to determine the distribution of the number of applications of the calculated load by months. The main source of information for statistical processing was the results of traffic accounting on highways M-1 «Belarus», a-107 MMK Mozhaisk-Volokolamsk highway, M-3 «Ukraine», M-4 «don», M-4 «don». The correct determination of the traffic intensity and composition of the traffic flow is an important task that allows you to make adequate decisions at the design stage of roads, namely to choose a road structure that can operate under load from the actual traffic flow for the entire service life. The authors calculated the total number of applications of the calculated load to the point on the surface of the coating, using the coefficients of reduction of vehicles to the calculated load of 115 kN. After calculating the total number of applications, the resulting value was divided by the number of days in the month in question. According to the data obtained, the total total number of applications of the calculated load at all points of accounting, by month, was found. The minimum values of the number of load applications are observed in winter (January, February, March), when the situation on the road deteriorates due to weather conditions. The values range from 4.75 % to 8 % for roads M-1 «Belarus», M-3 «Ukraine», M-4 «Don», M-4 «Don». The maximum values of the number of load applications observed in the warmer months (July, August, September, October), due to the fact that there are favorable weather conditions for recreation and the most active agricultural industry. The values range from 7.6 % to 11.3 % for the roads M-1 «Belarus», M-3 «Ukraine», M-4 «Don», M-4 «Don».

Analiza odkształceń trwałych warstw z kruszywa w konstrukcji nawierzchni drogowej

Models of permanent deformation in soils and granular materials are analysed in the article. Power, logarithmic and exponential functions that connect permanent deformation with the deformation caused by the first loading or with the one accumulated as a result of a certain number of load applications are found to be most often used. Due to the application of a hereditary creep theory some generalizing models for the analysis of permanent deformations under cyclic loading were obtained. As a result, a new method based on the integration of power functions describing the increment of permanent deformation was proposed. The experimental data on the dependence of residual deformation upon the amount of loads, maximum and minimum stresses were obtained, coefficients of equations derived were defined. The results of the calculations and the experimental data of a triaxial test of sand-gravel mix and granodiorite crushed stone were compared.

Rutting prediction in airport pavement granular base/subbase: A stress history based approach

Abstract Test data from full-scale aircraft gear loading conducted at the National Airport Pavement Test Facility (NAPTF) by the US Federal Aviation Administration (FAA) were analyzed to investigate the effects of wander (offset loads) and channelized traffic loadings on the deformation behavior of unbound aggregate layers in asphalt pavement test sections. Insights were drawn on the complex rebound (recovered) and residual (unrecovered) deformation trends of granular materials due to passing of each of the 6-wheel Boeing 777 (B777) and the 4-wheel Boeing 747 (B747) gears for various combinations of loading (stress history effects), wander positions, and wander sequences. Measured field layer deformations and the accumulation rates could only be achieved when the magnitudes and variations of stress states in the granular layers, number of load applications, gear load wander patterns, previous loading stress history effects, trafficking speed or loading rate effects, and finally, principal stress rotation effects due to moving wheel loads were properly accounted for. Accordingly, measured transverse profiles and multi-depth deflectometer data were used to create individual pass residual deformation transverse profiles. The created transverse profiles were then combined with stress history effects to predict the residual transverse profiles for the test sections with P209/P154 granular base/subbase layers. The proposed method emphasizes the use of the previous load location and stress history of the pavement element to develop the residual deformation in that element. Calculation of the residual deformation in each element across the pavement surface results in the development of the complete permanent deformation transverse profile. This technique can be applied to estimate the transverse rutting profile of the pavement after trafficking based on any combination of applied wander and traffic direction.

Estimation of resilient modulus of unbound granular materials using Clegg impact value and field stress levels

Resilient modulus (Mr) is an important property that controls the performance of pavement materials under dynamic wheel loads. Mr can be determined in the laboratory from repeated load triaxial tests and is defined as the ratio of the deviator stress to the recoverable strain after a number of load applications. Inherently, it is a challenge to perform repeated load triaxial tests as routine tests due to their rather complicated, time-consuming and expensive procedure. Hence, researchers have attempted to develop empirical estimation models based on the mechanical properties of pavement materials, such as the California bearing ratio and the unconfined compressive strength or physical properties of materials. This study examines the correlation between the Clegg impact value (CIV) and the Mr of unbound granular materials (UGM) of pavements. The Clegg impact hammer test provides a parameter based on the response of the material to dynamic, rather than static or gradual, loading. Fourteen different unbound granular materials with particle sizes ranging from 7 mm to 19 mm used in the study. The results indicate that there exist a good to strong correlation between the resilient modulus Mr and Clegg impact hammer value, CIV, with the highest R2 value of 0.82 and the average R2 value of 0.76, from 48 stress levels used in Mr tests.

A Framework to Utilize Shear Strength Properties for Evaluating Rutting Potentials of Unbound Aggregate Materials

This paper presents shear strength and permanent deformation trends of four unbound aggregate materials, commonly used for base and subbase layers in the state of North Carolina, USA, studied through repeated load triaxial testing, using the University of Illinois FastCell equipment. A testing and modeling framework has been established to develop a proper permanent deformation prediction model, referred to herein as the UIUC rutting model, with number of load applications. According to the framework, the unbound aggregate shear strength properties are incorporated into the model using the ratio of the applied wheel load shear stress to the mobilized shear strength, i.e., the Shear Stress Ratio (SSR). This requires conducting repeated load permanent deformation tests at SSR values of 0.25, 0.5 and 0.75 to determine the trends in permanent deformation accumulation. The prediction ability of the developed UIUC rutting model is evaluated in this paper for the four materials tested at both an engineered target gradation and source gradations.

Fatigue Performance of Asphalt Mixture under Actual Loading Patterns at Different Pulse Durations

Abstract The fatigue performance of an asphalt mixture under actual loading patterns corresponding to single, tandem, and tridem axle configurations at three different pulse durations corresponding to axle speeds with constant rest periods was examined using an indirect tensile cyclic load test. This research was conducted at two temperatures, 25°C and 35°C. Considering our sets of variables and three repetitions for each set, in total 54 specimens were tested. The actual loading patterns applied to the specimens were determined using the KENLAYER software program. After testing and data acquisition, the cumulative vertical plastic strain approach was utilized to determine the number of load applications at two points of deformation on the fatigue curves, the hardening and softening starting points. The results at these two points show the following: (1) force repetition depends on loading patterns and, at a constant speed, varies from maximum to minimum with tridem, tandem, and single loading patterns, except at the hardening starting point; (2) force repetitions are strongly related to pulse duration in such a way that fatigue life increases with a decrease in pulse duration; and (3) the effect of temperature depends on pulse durations and loading patterns. It can be stated, in general, that when comparing the effects of different loading patterns, pulse duration must be considered. Based on the findings of this study, at different temperatures the results follow the same trends and are not temperature dependent.

Assessment of the Mechanical Properties of ProTaper Next Nickel-Titanium Rotary Files

IntroductionThe purpose of this study was to compare the torsional resistance, flexibility, and surface microhardness of ProTaper Next files (PTN) with Twisted Files (TF) and RaCe (RC). MethodsA metal block with a cubical hole was used to evaluate the torsional resistance. Five millimeters of the tip of each file was securely held in place by filling the mold with a resin composite, and the files were driven clockwise at 300 rpm. The number of load applications before fracture was recorded for each file. A scanning electron microscope was used to characterize the topographic features of the fracture surfaces of the broken files. The files were tested for bending resistance by using cantilever-bending test. Vickers microhardness was measured on the cross section of instruments with 300-g load and 15-second dwell time. Torsional resistance data were analyzed by using the nonparametric Kruskal-Wallis and Mann-Whitney U tests. Bending resistance and microhardness data were analyzed by using analysis of variance and Tukey tests. ResultsPTN showed the highest torsional resistance and microhardness, followed by RC (P < .05). The fracture cross sections of all brands showed dimpling near the center of fracture surface. The ranking in the bending resistance values was as follows: RC > PTN > TF. ConclusionsPTN improved its resistance to torsional stresses and wear compared with TF and RC. TF showed improved flexibility compared with other tested brands.

Framework for Development of an Improved Unbound Aggregate Base Rutting Model for Mechanistic–Empirical Pavement Design

This paper presents findings from an ongoing research study at the University of Illinois that aims to develop and calibrate improved models for unbound aggregate rutting through laboratory characterization of aggregate materials used for unbound base and subbase applications in the state of North Carolina. Extensive triaxial laboratory testing was performed to establish a robust link between the number of load applications, stress levels, shear stress and sheer strength ratios, and permanent deformation responses. A framework was established for considering the strong correlation that commonly exists between permanent deformation and shear strength characteristics, as opposed to resilient modulus properties, in the laboratory characterization of the permanent deformation behavior of various types of aggregate materials. Trends of permanent strain accumulations from repeated load triaxial tests were adequately captured in a new rutting model whose development took into account the shear stresses applied at 25%, 50%, and 75% of the shear strength properties of these materials under similar field loading confinement conditions. The research shows that this model is an improvement on the rutting damage model for unbound aggregate currently used in AASHTO's mechanistic–empirical pavement design approach because it offers better material characterization and rutting prediction of the unbound base or subbase layer.

Resilient modulus of unsaturated subgrade soil: experimental and theoretical investigations

The resilient modulus, MR, of subgrade soil is an important stiffness parameter for analysing fatigue cracking in either the asphalt or concrete layer of a pavement. Although subgrade soil is often unsaturated and subject to seasonal variations of moisture content and hence suction in the field, effects of soil suction on the resilient modulus are generally not accounted for in existing testing methods. In this study, MRvalues of a subgrade soil under various stress and suction conditions were investigated using a suction-controlled cyclic triaxial apparatus. To enhance the accuracy of measurements, Hall-effect transducers were employed to monitor the local axial and radial deformation of each specimen. It was found that MRincreases with number of load applications when a soil contracts, but decreases slightly when a soil dilates. When suction increases, the soil response tends to change from contractive to dilative due to suction-induced dilatancy. Moreover, the measured MRis highly dependent on the stress state. It decreases with cyclic stress due to the nonlinearity of the soil stress–strain behaviour, but increases significantly with suction due to the presence of water tension. At the same stress and suction conditions, MRmeasured along the wetting path is generally larger than that measured along the drying path. A new semi-empirical equation representing the stress-dependency of MRis proposed and was verified using experimental results of four different soils.

Pavement Deterioration and Maintenance Model for Low Volume Roads

Development of an intelligent flexible pavement deterioration and maintenance management model is the need of implementing organizations to prioritize pavement maintenance and rehabilitation works, as this involves cost economics. Pavement deterioration model, is an equation that relates to some extrinsic 'time factor' (age or number of load applications) to a combination of intrinsic factors (structural responses, etc.) and performance indicators which simulate the deterioration process of pavement condition and provide forecasting of pavement condition over a period of time. These pavement deterioration or performance models play a pivotal role in pavement management systems. To develop these models structural and functional response measurement of 18 sections of low volume pavements were carried out for continuous two years in Uttarakhand and Uttar Pradesh states of India. Statistical analysis tools and Artificial Neural Network (ANN) are used to develop the models. Statistical performance indicators and logical relationships between input parameters and output parameters are used to select the best fit model. Polynomial relationship best relates to the input parameters such as pavement age, CBR of subgrade, traffic, pavement thickness and also to the output parameters i.e. pavement condition indicators such as deflection, riding quality, surface roughness. Paired t-test is also carried out for the validation purpose of chosen best fit models. Maintenance Priority Index (MPI) is developed using three parameters named as deflection, riding quality and traffic to decide the priority.

Validation of a Three-Dimensional Finite Element Model using Airfield Pavement Multiple Wheel Load Responses

ABSTRACT Various highway vehicle axle/wheel arrangements and aircraft gear configurations adopted nowadays to accommodate increasing load levels impact flexible pavement response and performance in accordance with different multiple wheel loading scenarios. As the demand for heavier wheel loads and number of load applications continually increases, it is essential to properly characterize the nonlinear behavior of the pavement subgrade and unbound aggregate base/subbase layers. This paper focuses on the validation of a recently developed three-dimensional (3D) nonlinear finite element (FE) model using the measured responses of airfield flexible pavement test sections trafficked under 4-wheel and 6-wheel aircraft gear configurations. For this purpose, realistic nonlinear, stress-dependent pavement subgrade and base/subbase resilient modulus models were employed in a programmed User MATerial (UMAT) subroutine of the general purpose ABAQUSTM FE program. The predicted pavement responses matched closely with the displacements and stresses measured in the field and the FE model could be reasonably applied to the design of airfield pavements serving multiple wheel gear loads when the nonlinear pavement geomaterials were considered. In addition, comparisons made between the single wheel superposition and the full 3D loading results proved the need and importance of 3D FE nonlinear analyses of thinly surfaced flexible pavements to properly consider both the stress dependent modulus behavior and the implications of multiple wheel loads and their interaction.

Deformation Properties of Untreated and Enzyme-Treated Bottom Ash Waste for Use in Foundations

The use of waste and recycled materials in different construction applications is a widespread approach. In this work, incinerator bottom ash (IBA) waste was mixed with limestone at different levels, namely, 0%, 30%, 50%, and 80%, to produce blends for use as pavement foundation layers. The study focused on evaluating the resistance to permanent deformation of IBA–limestone blends, which is vital to prevent or minimize pavement rutting. An experimental program was undertaken to investigate the influence of plant-based enzyme treatment on the behavior of these blends. Cyclic and static triaxial compression tests were adopted to determine the materials’ mechanical characteristics. Emphasis was on examining the effect of various parameters, such as IBA content, enzyme content, moisture content, curing time, stress level, and number of load applications, on the behavior of the investigated blends. The accumulated permanent strain and strain rate were used to describe the blends’ shakedown stress limits. Results showed that IBA blends gave a favorable performance as foundation layers in comparison with the control limestone blend. Enzyme addition improved the permanent deformation resistance for the control limestone blend; however, it did not have any noticeable effect on the IBA blends. According to the shakedown concept analysis, all blends, at a cyclic stress level of more than 21% of the static failure stress, underwent excessive plastic strain.

Field Validation of Airport Pavement Granular Layer Rutting Predictions

This paper presents research findings on the prediction performances and field validations of the recently developed granular base–subbase layer permanent deformation models using the full-scale pavement test section data from the FAA's National Airport Pavement Test Facility (NAPTF). The FAA-designated P209/P154 aggregate materials were used in the construction and testing of the NAPTF flexible pavement test sections with variable-thickness base and subbase courses. To account for the rutting performances of these substantially thick granular layers, a comprehensive set of repeated load triaxial tests, considering both constant and variable confining pressure (CCP and VCP) conditions, were conducted on the P209 base and P154 subbase granular materials. On the basis of the laboratory test results, both CCP- and VCP-type permanent deformation models were developed to predict maximum ruts that occurred at the NAPTF under both six-wheel and four-wheel gear loadings applied following a wander pattern. The developed rutting models were first calibrated for the field conditions and then evaluated for predicting the field accumulation of permanent deformations by properly taking into account the NAPTF trafficking data, effects of stress rotation due to moving wheel loads, and loading stress history effects. A comparison of the measured and predicted permanent deformations indicated that a good match for the measured rut magnitudes and the accumulation rates could be achieved only when the magnitudes and variations of stress states in the granular layers, number of load applications, gear load wander patterns, previous loading stress history effects, trafficking speed or loading rate effects, and finally, principal stress rotation effects due to moving wheel loads were properly accounted for in the laboratory testing and permanent deformation model development.

Enhanced Portland Cement Concrete Fatigue Model for StreetPave

The Portland Cement Association (PCA) pavement thickness design method for jointed concrete pavements is mechanistically based and consists of both fatigue and erosion analyses. It determines the minimum slab thickness required for a given set of site and design conditions on the basis of both fatigue and erosion criteria. At the heart of the fatigue analysis is the fatigue model, which establishes the number of allowable load repetitions for a given stress ratio [ratio of flexural edge stress caused by the application of wheel loads to the portland cement concrete (PCC) slab flexural strength]. The PCA fatigue model is based on data derived from beam fatigue tests conducted in the early 1950s and 1960s. The model estimates the conservative lower-bound estimate of the allowable number of load applications at a given stress ratio (i.e., it incorporates a high degree of reliability–-approximately 90% or higher). Although this may be desirable for high-volume, high-traffic pavements, it is too conservative for low-volume roads or street pavements. The PCA pavement thickness design method currently is being used in the American Concrete Pavement Association (ACPA) pavement design software, StreetPave. StreetPave incorporates the PCA's pavement thickness design methodology in a Windows-based user platform. ACPA commissioned a study to expand, improve, and broaden the current PCA fatigue model by including reliability as a parameter for predicting PCC fatigue damage and by calibrating the enhanced model with additional fatigue data from recently completed studies. An enhanced fatigue model was then developed.

Simple Model for Pavement Damage

A simple phenomenological damage model based on the number of load applications, the critical response, and the material modulus was used with three sets of experimental data: (a) the decrease in the modulus of an asphalt concrete (AC) under laboratory, direct tension fatigue testing; (b) the decrease in the modulus of a pozzolan–lime-stabilized sand under accelerated loading in a full-scale pavement testing facility; and (c) the increase in the permanent strain at three levels of two subgrade materials, also under full-scale accelerated loading. The model is shown to be capable of describing the damage reasonably well for all three cases, though with some limitations. For the direct tension tests with AC, the rate of damage was underpredicted for two of six samples under controlled stress testing, whereas the prediction for all 10 controlled strain tests was good. For freeze–thaw conditions, the model for permanent strain in the subgrade also tended to underpredict the damage rate. The simple damage model may be useful for incremental–recursive pavement design or for pavement management systems.

Simple Model for Pavement Damage

A simple phenomenological damage model based on the number of load applications, the critical response, and the material modulus was used with three sets of experimental data: (a) the decrease in the modulus of an asphalt concrete (AC) under laboratory, direct tension fatigue testing; (b) the decrease in the modulus of a pozzolan–lime-stabilized sand under accelerated loading in a full-scale pavement testing facility; and (c) the increase in the permanent strain at three levels of two subgrade materials, also under full-scale accelerated loading. The model is shown to be capable of describing the damage reasonably well for all three cases, though with some limitations. For the direct tension tests with AC, the rate of damage was underpredicted for two of six samples under controlled stress testing, whereas the prediction for all 10 controlled strain tests was good. For freeze–thaw conditions, the model for permanent strain in the subgrade also tended to underpredict the damage rate. The simple damage model may be useful for incremental–recursive pavement design or for pavement management systems.

Enhanced Portland Cement Concrete Fatigue Model for StreetPave

The Portland Cement Association (PCA) pavement thickness design method for jointed concrete pavements is mechanistically based and consists of both fatigue and erosion analyses. It determines the minimum slab thickness required for a given set of site and design conditions on the basis of both fatigue and erosion criteria. At the heart of the fatigue analysis is the fatigue model, which establishes the number of allowable load repetitions for a given stress ratio [ratio of flexural edge stress caused by the application of wheel loads to the portland cement concrete (PCC) slab flexural strength]. The PCA fatigue model is based on data derived from beam fatigue tests conducted in the early 1950s and 1960s. The model estimates the conservative lower-bound estimate of the allowable number of load applications at a given stress ratio (i.e., it incorporates a high degree of reliability-approximately 90% or higher). Although this may be desirable for high-volume, high-traffic pavements, it is too conservative fo...

Resilient Modulus Measurement of Fine-Grained Subgrade Soils

The effects of several variables that may influence the resilient modulus of fine-grained subgrade soils have been studied using two different soils. The number of load applications, the rest period, and the load sequence are shown to have no significant effect on the measured resilient modulus. It is also demonstrated that confining pressure in the range of 0 to 69 kPa (0 to 10 psi) has less than a 5 percent effect on the measured resilient modulus of the investigated soils. However, the condition of specimen ends is shown to influence the measured resilient modulus. A comparison between the measured resilient modulus for both soils using impact and kneading compaction methods is also presented.