Back-calculation of transition probabilities for Markovian-based pavement performance prediction models

This paper presents a new technique to estimate the transition probabilities used in the Markovian-based pavement performance prediction models. The proposed technique is based on the ‘back-calculation’ of the discrete-time Markov model using only two consecutive cycles of pavement distress assessment. The transition probabilities, representing the pavement deterioration rates, are the main elements of the Markov model used in predicting future pavement conditions. The paper also presents a simplified procedure for evaluating the pavement state of distress using the two major pavement defect groups, namely cracking and deformation. These two defect groups are to be identified and evaluated for pavement sections using visual inspection and simple linear measurements. The extent of these two major defect groups is measured using the defected pavement areas (or lengths) and the defect severity is measured based on the average crack width and average deformation depth. A case study is presented to demonstrate the ‘back-calculation’ of transition probabilities. In particular, the impacts of the pavement section length on the distress rating and on the estimation of the transition probabilities have been investigated. The results have indicated that the estimated transition probabilities become highly unstable as the section length gets larger and the sample size becomes smaller.     

Risk based probabilistic pavement deterioration prediction models for low volume roads

Accurate prediction of pavement performance is important for efficient management of road infrastructure. Pavement performance prediction models developed for low-volume roads are mainly based on deterministic approach. The deterministic prediction models are inadequate to completely capture the deterioration mechanism. Uncertainties may occur in pavement behaviour under changing traffic loads and environment conditions, which may not be realistically represented by deterministic model. The objective of this paper is to develop pavement deterioration prediction models by probabilistic approach, for various distresses observed on low-volume roads in the state of Kerala in India, with the help of existing deterministic models. The major distresses observed on low-volume roads were ravelling, pothole and edge failure. Load-associated distresses were rarely observed on these roads as the maximum cumulative standard axle observed was only one million standard axle (msa). Hence, lack of proper drainage and construction quality (CQ) could be attributed as the major reasons for the pavement deterioration. Progression of deterioration of pavements with age has been studied and the intensity of distresses along with corresponding probabilities was arrived at. The distresses predicted by probabilistic models were compared with those predicted by deterministic models and the actual distress values observed in the field. The prediction models were validated using Mean Absolute Percentage Error, a statistical method for accuracy measurement of forecasting models. A risk analysis was then conducted to select the critical percentile value for each type of distress corresponding to varying pavement age. A sensitivity analysis was also carried out to study the effect of pavement age and CQ on the progression of pavement deterioration.     

Computing Transition Probability in Markov Chain for Early Prediction of Software Reliability

Early prediction of software reliability provides basis for evaluating potential reliability during early stages of a project. It also assists in evaluating the feasibility of proposed reliability requirements and provides a rational basis for design and allocation decisions. Many researchers have proposed different approaches to predict the software reliability based on a Markov model. The transition probabilities in between the states of the Markov model are input parameters to predict the software reliability. In the existing approaches, these probabilities are either assumed on some knowledge or computed using analytical method, and hence, it does not give accurate predicted reliability figure. Some authors compute them using operational profile data, but that is possible only after the deployment of the software, and this is not early prediction. The work in this paper is devoted to demonstrate the computation of transition probability in the Markov reliability model taking a case study. The proposed approach has been validated on 47 sets of real data. Copyright © 2015 John Wiley & Sons, Ltd.     

Dynamic analyses of traffic speed deflection devices

Two traffic speed deflection devices (TSDDs) that measure surface deflections at posted traffic speeds (up to 80–96 kph) were evaluated through a recent Federal Highway Administration project that included field trials at the MnROAD facility. Four geophones were embedded near the pavement surface to measure surface deflections during field trials at each of three MnROAD cells. In addition, the MnROAD facility counted with numerous other sensors such as strain gauges to measure pavement responses and thermocouple trees to collect pavement temperature at various depths. For the implementation of TSDDs in any network-level pavement management system, it is important to utilise a proper analytical model that can accommodate moving load and viscoelastic properties of pavement layers in the simulation of TSDD measurements. The 3D-Move software was chosen for this purpose. The viscoelastic properties used for the asphalt concrete (AC) layer include dynamic modulus and damping coefficient as a function of frequency relevant to the temperature at the time of the MnROAD field trials. The field trials and available data represented realistic field case scenarios to validate once more 3D-Move specifically for TSDD measurements. The proposed dynamic analytical model provided a good match with a variety of independent pavement responses that included surface deflection bowls (measured using embedded geophone sensors) as well as horizontal strains at the bottom of the AC layers (measured using MnROAD sensors).     

Probabilistic prediction models for crack initiation and progression of spray sealed pavements

Cracking is one of the primary distress modes in spray (chip)-sealed pavement surface performance and its prediction is a major concern for pavement engineers. In order to identify, manage and asses effectively and efficiently cracked pavement at a network level, a probabilistic modelling approach is utilised to develop cracking initiation and progression models. This study aims to predict the probability of pavement cracks occurring using a binary logistic model and cracks progression over time using an ordinal logistic regression model. These models have been developed to take into account the effect of variations among observations, among sections and among highways. Readily available historical time series data (from 2004 to 2011) from 40 highway segments have been collected and prepared for modelling. These time series include surface cracking as a performance parameter and traffic loading, expansion potential of subgrade soil, climate condition, condition of drainage system and pavement strength as predictor parameters. Cracking data include all types of cracking: transverse, longitudinal and crocodile cracking and is reported as a percent of the affected area. The study estimates the probability of crack initiation at a certain time and predicts the probability of a pavement maintaining its current level of cracking. It is found that with the 50% estimated probability, about 82% of the observations are correctly predicted by the crack initiation model and 65% of the observations are correctly predicted by the crack progression model. The study has concluded that the effect of time is stronger than the other variables on crack initiation and progression. Also, the effect of traffic loading is stronger than the effect of initial pavement strength in crack initiation phase. However, the effect of pavement strength at any time is stronger than the effect of traffic loading in crack progression phase. The predicted probabilities have been successfully validated using another data-set from the same network and the results indicate that the developed probability models are well estimating the crack conditions and have the ability to predict future conditions accurately.     

Quantitative reliability analysis of different design alternatives for steer-by-wire system

For a fault-tolerant SBW (Steer-By-Wire) system, two structural designs with and without a backup mechanical coupling are proposed and assessed by a unified approach from a reliability point of view. An operation procedure to cope with partial system degradations prior to a complete loss of steering is presented for each design. The procedure can be represented by a transition diagram that, in turn, is converted into a layered Markov state transition diagram by introduction of augmented states. Reliabilities of the two designs are quantitatively compared by numerical integration of the Markov diagrams based on realistic failure rate data; system degradation probabilities are obtained as well as the complete steering loss probability. A power source is identified as a key component for the SBW to function without a mechanical backup.     

Development of degradation model for urban asphalt pavement

There is a lack of a profound understanding of urban pavement deterioration pattern. This is due to the complexity of traffic conditions and the variety of pavement structures in urban roads. The lack of a suitable deterioration model for the urban pavements limits the possibility of making any scientific and cost-effective repair and maintenance strategy. There is a need for a better understanding of the long-term behaviour of urban pavements by which predictive pavement condition models can be derived and consequently a suitable maintenance management system can be built. In response to this need, a comprehensive field study was performed in three Iranian cosmopolitan cities. Pervasive pavement damages were defined and an urban pavement condition index was established. A deterioration model was developed by monitoring and analysing the conditions of road pavements in a period of four years. This model varies as the structural and loading conditions of the pavement change. The efficiency and practicability of the model in predicting the conditions of the pavements were illustrated.     

Sensitivity of flexible pavement design to Michigan’s climatic inputs using pavement ME design

Climate condition is an important factor that affects the performance of pavements and distress predictions using mechanistic-empirical analyses. This study aims to analyse the sensitivity of flexible pavement distress predictions to climatic inputs using the AASHTOWare Pavement ME Design software in the state of Michigan. Typical traffic parameters, pavement structures and material properties for the state of Michigan were used as inputs for the analysis of flexible pavement performance. Six representative sites geographically distributed throughout Michigan and two typical traffic levels (high and medium) were incorporated in a comprehensive analysis of the effects of climate on flexible pavement performance predictions. A normalised sensitivity index was adopted to quantitatively evaluate the sensitivity of distress predictions to the five individual climatic variables: temperature, wind speed, precipitation, percent sunshine and relative humidity. The results of this study showed that the prediction of flexible pavement performance in Michigan is most sensitive to changes in temperature with other climatic factors such as wind speed, percent sunshine, precipitation and relative humidity impacting predictions to a lesser extent. Higher temperature and percent sunshine at a given location increased rutting and International Roughness Index (IRI) predictions, but reduced the likelihood of fatigue cracking. An increase in wind speed or precipitation reduced rutting and IRI predictions, but increased fatigue cracking predictions. Ambient relative humidity had a negligible effect on all flexible pavement distress predictions. These findings provide insights into the sensitivity of flexible pavement designs under different climate conditions. The sensitivity results are also beneficial for the Michigan Department of Transportation as they seek to improve the existing climatic files in PMED through evaluation of new climatic data sources.     

In-situ assessment of the stress-dependent stiffness of unbound aggregate bases: application in inverted base pavements

Unbound aggregate bases are the primary structural components in many flexible pavements. The response of the unbound aggregate base is critical to the overall performance of the pavement, particularly in inverted base pavements given the proximity of the base to the traffic loads. The behaviour of granular materials such as unbound aggregate bases is inherently nonlinear and anisotropic. An experimental methodology is developed to assess the in-situ stress-dependent small-strain stiffness of unbound aggregate bases under controlled load using wave propagation techniques. CODA wave analysis is used to detect small changes in travel time. The methodology is applied in two distinct case histories of inverted base pavements. Results show that field-compacted granular bases exhibit higher stiffness, lower stress sensitivity and more pronounced anisotropy than laboratory-compacted specimens. The discrepancy in stiffness observed among the two field case histories is primarily attributed to traffic preconditioning sustained by the older pavement. Additional results show that the effect of suction on the stiffness of coarse-grained granular bases is insignificant.     

Experimental investigation on skid resistance of asphalt pavement under various slippery conditions

The skid resistant performance of slippery pavement is one of the most important pavement surface characteristics, as it is associated with both pavement serviceability and traffic safety. Through simulating different pavement conditions in the freezing laboratory, skid resistance of asphalt pavement under various slippery conditions is measured with pendulum friction coefficient tester. Then, the effects of pavement temperature on skid resistance of dry, wet, icing and snowy pavements are quantitatively analysed. Furthermore, factors exerting effects on test results are taken into account, such as thicknesses of ice and water film on pavement. Through quantitative analysis, empirical evaluation model of pavement friction coefficient (PFC) under different conditions is established. To facilitate practical engineering application, reference standard values of PFC are recommended. Finally, the PFC is classified into seven levels, which illustrates the corresponding relationships of friction rank, skid resistance assessment, PFC range and pavement conditions.     

Introduction of a new continuous time and state space stochastic process in condition prediction

Periodic condition assessments of pavements together with condition predictions are the basis for investment decisions in every pavement management system (PMS). Typical approaches include surveys of distress types every 3–6 years with analysis rating and calculation of condition indices for road safety and/or structural health. Furthermore, advanced PMS prediction models allow a comparison of maintenance alternatives and an optimisation of investment strategies. This paper presents an overview of current survey and rating approaches in Germany, Switzerland and Austria, together with an impact analysis of different methods, utilised deterministic performance functions and condition threshold (trigger) values for all major distress types. The core of this paper is a comparison of common deterministic condition prediction models with discrete stochastic approaches and prediction models based on advanced regression techniques mainly from scientific literature and an innovative stochastic continuous time and continuous state space process (HOFFMANN – Process). All prediction models are applied to real-world data from condition surveys in Austria and the long-term pavement performance Database (USA) at single-section and network level. The paper provides evidence why deterministic prediction approaches are leading to substantial bias in condition distribution and remaining service life as they do not account for the stochastic nature of pavements. Classic Markov-chain approaches do not account for censoring of survey data and neglect changes in transition probabilities with increasing age. Applying common bivariate and multiple regression techniques may also lead to certain bias due to collinearity effects and specification bias. The paper provides mathematical evidence on ways to avoid these shortcomings based on the presented innovative stochastic process leading to a higher reliability in condition assessment, rating and accuracy of condition predictions. The aspects of censoring, distress-specific assignment and optimisation of treatments with this new HOFFMANN-process will be covered in forthcoming papers.     

Rutting progression models for light duty pavements

Deterioration models allow road managers to assess current condition and to predict future conditions of their road networks. Due to heavy vehicle axle repetitions and the effect of environmental factors, permanent deformation (rutting) develops gradually in the wheel paths and impacts on structural and surface performance of flexible pavements. This paper reports the approach adopted to develop absolute deterministic models for permanent deformation of low volume roads. A representative large sample network (23 highways) of light duty pavements was selected. For each section, time series data from four consecutive condition surveys were collected. Multiple regression analysis was carried out to develop models to predict pavement rutting progression over time as a function of a number of contributing variables. They include traffic loading, pavement strength, climate and drainage condition. For more powerful prediction, family group data-fitting approach was utilised to estimate future rutting progression based on the average rut depth curve for a series of pavements with similar characteristics. This study highlighted that separate family deterioration models are preferred and needed for more realistic results. The paper concludes that the analysis approach used for developing the models confirmed their accuracy and reliability by well-fitting to the validation data with low standard error values. Also, study results show that higher traffic loading, lower pavement strength, poor drainage and climates with high seasonal variation contribute to increasing rutting progression rate.     

Effects of mean annual temperature and mean annual precipitation on the performance of flexible pavement using ME design

The purposes of this study were to establish the difference between empirical and mechanistic–empirical approaches in the flexible pavement design and to quantify the effects of mean annual precipitation and temperature on the flexible pavement distresses using the Mechanistic-Empirical Pavement Design Guide (MEPDG) software. Seventy-six specific locations from 13 states throughout the USA were selected based on different climate conditions using virtual climate stations based on the interpolation from the nearest weather stations prior to meeting the objectives. Subsequently, analysis was conducted based on the predicted distresses, including longitudinal cracking, transverse cracking, alligator cracking, asphalt concrete rutting and total pavement permanent deformation. Generally, the pavement structure and materials have been set as constant to control the effects of material on the results. On the basis of the MEPDG analysis, the longitudinal cracking of flexible pavement is significantly affected by both factors (temperature and precipitation), particularly in wet climatic regions. The mean annual temperature has a great influence on the alligator cracking, transverse cracking and permanent deformation of flexible pavement. However, neither factors demonstrated a significant impact on the predicted International Roughness Index of flexible pavement surfaces.     

Possible estimation of resilient modulus of fine-grained soils using a dynamic lightweight cone penetrometer

Resilient modulus is an important parameter to characterise the resilient behaviour of pavement materials. Resilient modulus can be determined in the laboratory from repeated load triaxial test and is defined as the ratio of deviator stress to recoverable strain. Inherently, it is a challenge to perform repeated load triaxial tests as a routine basic test due to its complicated, time-consuming and expensive procedure; hence, several empirical approaches to estimate the resilient modulus from other soil mechanical properties – California bearing ratio, unconfined compressive strength or physical properties – have been proposed. This study has investigated the application of a dynamic lightweight cone penetrometer for the estimation of the resilient modulus in the laboratory and field conditions for some Victorian fine-grained subgrade soils. The results show the possibility to estimate the resilient modulus of fine-grained soils using the dynamic lightweight penetration index at any moisture content (MC) from optimum MC to soaked conditions.     

Optimal design for concrete pavement situated above box culvert: experimental and numerical study

This study examined the pavement distress data obtained from the field as well as the effects of the soil cover depth, joint position and reinforced slab length on the behaviour of concrete pavement using the finite element method. An ultimate strength model with a similarity of 1/2 was designed and constructed. Finite element analysis incorporating an implicit direct numerical integration scheme was conducted to obtain an optimal design for the pavement structure above a box culvert. An accelerated pavement test was conducted for validation, in which a realistic traffic load was imposed on the pavement model constructed in the laboratory. The strain histories were measured at each section and compared with those of numerical analysis. The optimal joint position and reinforced slab length that can minimise the damage to the pavement structure above a box culvert were also determined.     

A stochastic model of empty-vehicle travel time and load request service time in light-traffic material handling systems

Empty-vehicle travel time plays an important role in the design and control of automated guided vehicle systems (AGVSs). However, many analytical models of these systems assume the amount of empty-vehicle travel time is the same as the loaded-vehicle travel time. This paper examines empty-vehicle travel time in AGVSs with low traffic intensity. The model uses a discrete-time Markov chain based on vehicle location and represents dispatching rules in the one-step transition matrix. The model can be used to compute moments and cumulative probabilities for the empty-vehicle travel time. Coupled with the loaded-vehicle travel time and the loading/unloading time, similar results can be obtained for the time to service a load request.     

Analysis of effect of overloaded vehicles on fatigue life of flexible pavements based on weigh in motion (WIM) data

Overloaded vehicles have a significant impact on pavement fatigue life and distress. As the studies show, the phenomena intensify when the control of traffic is poor. The paper presents the results of the research including analysis of weigh in motion data from eight stations and analysis of asphalt pavement fatigue caused by mixed traffic. Distributions of vehicles axles load including the multiple axles effects are presented. Mixed axle loads were transformed into equivalent number of standard 100 kN axle loads. The regression model of load equivalency factor depending on the axle load distribution and the percentage of overloaded vehicles is presented. The analysis of the effect of overloaded vehicles on decrease of fatigue life of a pavement structure is presented. The analysis has shown that the increase of percentage of overloaded vehicles from 0% to 20% can reduce the fatigue life of asphalt pavement upto 50%.     

移动载荷下粘弹性道路瞬态响应解析解

为了研究沥青路面动力响应,本文同时考虑道路基层和面层的粘弹性,将道路面层看作具有粘弹性的无限长梁作用在Kelvin粘弹性地基上,建立了移动载荷作用下路面动力学模型,利用Green函数法、Laplace变换和Fourier变换等方法,推导出了基于面层和基层粘弹性的移动载荷作用下路面瞬态响应解析解。由于该模型考虑了面层的粘弹性,从而能更全面的考虑车速、温度、道路材料等因素对路面动力响应的影响。     

Fourier-finite element analysis of pavements under moving vehicular loading

With the goal of predicting progressive pavement distress (damage and rutting) under millions of cycles of moving vehicular loading, an efficient analysis framework is developed by combining the ideas of Fourier transform, finite element discretisation and time-scale separation. Using the simple observation of time-scale separation between evolution of pavement damage/rutting, temperature variation and traffic load variation, the analysis under millions of cycles is reduced to a few hundred analyses of stress and strain evolution under a single cycle of moving load. A new method called Fourier-finite element (FFE) method is proposed for each independent stress analysis. Essentially, Fourier analysis is used to eliminate the time dimension as well as the spatial dimension in the direction of traffic, reducing the problem to a set of two-dimensional problems, which are in turn solved using the finite element method (FEM). The FFE method is more efficient than direct three-dimensional (3D) FEM by orders of magnitude, but captures the 3D effects in an accurate manner. The FFE stress analysis technique is combined with time-scale separation-based ideas to develop a pavement performance modelling framework. A 20-year pavement simulation is presented to illustrate the efficiency of the proposed framework.