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92 IntroductIon Chapter five provides detailed findings on the modeling and analysis methods employed by the various researchers and the benefits and limitations of different approaches. It discusses the various models conceptually and specifically comments on the application of f-sAPT in the MEPDG and other M-E pavement design methods. All the models are not repeated, as this would require substantial detail on model parameter definitions, limitations of specific models, and related details that are well covered in the various references and would add to the volume of the current synthesis without adding to the main discussion. Most of the modeling and analysis work discussed in this chapter focuses on improving the materials models for the var- ious M-E design models, thereby reducing the risk of design as more appropriate parameters are incorporated into the design, and the effect of each of the parameters are better understood. The issues highlighted are the increased use of FEM for analysis of moving loads (as opposed to static load analysis), where factors such as mass inertia and stress rotation are incor- porated into the model; the increased use of materials models that are not simply linear elastic, but which incorporate the effects on nonlinearity, viscosity, and environmental sensitivity (i.e., moisture and temperature); the increased use of detailed definition of the applied loads in terms of both load history and contact stress patterns; and the increased cognizance given to the effects of the environment on pavement response. It appears as if a process is driven on several fronts where improved computers allow for increasingly complex calcula- tions without becoming too time- and resource-consuming, the understanding of materials properties are improving with the parallel development of appropriate laboratory and field instruments, and tests to obtain these parameters for different materials and the subsequent modeling is improved through the combination of these factors. Most of the M-E methods operate on a multilevel basis, where pavements of lesser importance where higher risk can be tolerated are designed using a simplified version of the system, and pavement where very little risk can be tolerated are designed using the most complex version of the M-E method. It does, unfortunately, appear that much of the modeling is still focused on the surfacing layers and that the effect and contribution of lower materials layers are generalized and simplified, although these effects may sometimes affect the surfacing and other upper layers significantly. It is specifi- cally the strength-balance of the pavement (providing a pave- ment structure where layers are not overstrained or -stressed owing to a lack of support or protection) that often appear to be ignored in test planning and modeling. The combination of f-sAPT data with laboratory, LTM, and field data differs between projects and depends mainly on the requirements of the specific project. F-sAPT is almost always combined with and supported by laboratory data, with field data used for calibration with real environment and traf- fic. It appears as if LTM data are not used by many respon- dents. Some respondents make use of replicate sections on public roads that become the field sections and almost play the role of LTM sections, although they are not monitored in the same way as the SHRP LTPP sections. F-sAPT is clearly viewed as one of the available tools and not as the ultimate answer to all questions. Some respondents indicated that the f-sAPT work focuses on specific materials (i.e., HMA layer testing) and that this knowledge is then combined with field response to obtain the information for typical structures. Response regarding the types of models used for back- calculation, deflection analysis, deformation, fatigue, load equivalence, pavement serviceability, stress, and strain are summarized in Figure 48. It indicates that the majority of respondents use elastic layer theory for most applications, with usage of FEM also significant. Iterative methods are mainly used for backcalculation, whereas elasto-plastic, sta- tistical, and visco-elastic layer theory are applied in fewer instances. This is probably because these model properties are typically material related (i.e., visco-elastic methods for asphalt materials). ModelIng and analysIs analysis Romanoschi and Metcalf (2000) evaluated statistical models for the determination of the probability distribution func- tion for time-to-failure of pavement structures using rutting data from the Louisiana f-sAPT facility. Determination of the probability distribution function for the time-to-failure is essential for the development of pavement life models as the probability distribution function reflects the variability chapter five ModelIng and analysIs
93 in pavement degradation. If the pavement life model has a known form the closed form solutions and Monte Carlo algo- rithms can be used. Both methods use degradation data and can be employed even for degradation levels below fail- ure levels. If the degradation model form is not known, the survival analysis method based on censored observations must be used to derive the pavement life model. This method cannot use only degradation data at levels below the failure level, because the failure of some structures must be recorded. Saleh et al. (2003) compared the 3-D FEM technique with isotropic and anisotropic multilayer elastic solutions when the unbound base layer is assumed to behave almost elastically. The 3-D FEM was found to provide the best match for the subgrade strains as it accounts for the elastic-plastic material behavior, modeling the plasticity using the DruckerâPrager model. Data from the f-sAPT pavement at CAPTIF was used to evaluate the calculated stresses within the pavement. As backcalculation methods depend mostly on the measured deflection basin, the use of isotropic multilayer elastic solu- tion appeared to yield unsatisfactory results if the plastic behavior of the material is pronounced. Increasing both the axle load and tire pressure will have the most damaging effect by increasing rutting significantly, with the base layer contributing about 37% of the total rutting and the subgrade layer up to 63%. Erlingsson (2004, 2007) illustrated how f-sAPT results (obtained from two thin pavement structures) assist in increas- ing the understanding of thin pavement behavior, and how a bitumen stabilized base compares with an unbound base. Non- linear analyses provided better agreement with measured data for the unbound base course while rutting prediction using a power law function showed good agreement with actual mea- surements of rutting development. F-sAPT at the Virginia Smart Road allowed several hy- potheses related to flexible-pavement design to be verified by Loulizi and Al-Qadi (2004). The LET overestimated the vertical compressive stress in flexible pavement layers at low and intermediate temperatures and underestimated it at high temperatures. Onar et al. (2005) evaluated the utility of mixed-effects models in analyzing performance-type data resulting from f-sAPT experiments. Analysis of f-sAPT data indicated that both binder type and temperature are significant factors in rutting development. It was found that a sound experimental design requires the consideration of all potential interaction effects between various design parameters to prevent alter- ation of data inferences through unidentified interactions. By capturing the variability among test tracks separately, the mixed-effects model provided a more powerful approach to estimating the parameters of the model. Molenaar (2006) indicated that based on work done at the Delft University in the field of f-sAPT, linear elasticity can be used to provide accurate pavement life predictions pro- 0 2 4 6 8 10 Ba ck ca lcu lat ion De fle ctio n De for ma tio n Fa tigu e Lo ad eq uiv ale nc e Ste ss/ str ain 12 14 16 18 20 N um be r o f r es po nd en ts Elastic layer Elasto-plastic Finite element Iterative Statistical Visco-elastic layer FIGURE 48 Model types used for selection of f-sAPT analysis processes.
94 vided that ample attention is placed on the characterization of the traffic and climatic influences as well as on material characterization. Longitudinal and transverse strains mea- sured at the bottom of the HMA layer could be predicted by a linear visco-elastic analysis, and good agreement was found between the measured peak strain values and the calculated ones using a linear elastic multilayer program. The transfer functions in an M-E pavement design proce- dure are used to relate pavement structural responses (deflec- tions, stresses, and strains) to pavement performance (cracking, rutting, etc.). NAPTF performance test results (Gopalakrishnan and Thompson 2006b) were used to investigate the relative effects of four- and six-wheel aircraft gear loads and verify fail- ure criteria to be used for development of mechanistic-based airport pavement design procedures. It was observed that a deflection ratio (D1/D3) showed the strongest correlation with the number of load repetitions to reach functional fail- ure, indicating the potential for developing HWD deflection- based rutting failure transfer functions for airfields. Lee et al. (2006b) developed pavement response models for calculating the critical pavement responses in a long-life pavement. A synthetic database was developed using a FEM approach with a range of layer thicknesses and moduli. It was found that the HMA base layer should be thicker than 7 in. (175 mm) and have a modulus of at least 507 psi (3.5 GPa). F-sAPT sections were constructed for validation, and a com- parison study between the computed and measured strain values indicated that the proposed procedure can predict the actual pavement responses accurately. Bruce et al. (2007) developed a FEM approach to model thin-surfaced unbound granular pavements incorporating a nonlinear anisotropic material model for the granular material and a nonlinear material model for the subgrade. Coefficients for the material models were determined from laboratory- repeated load tri-axial tests, and the model was validated using data obtained from a test pavement at CAPTIF. Analysis results indicated the need to use a full nonlinear model to obtain realistic results when modeling FWD loading data on the f-sAPT pavement. A shift factor that depended on material properties was required to translate the results from the laboratory space to the field space. The granular stiffness values calculated in the model varied with load and depth below the surface, supporting the use of a nonlinear model. Al-Qadi et al. (2007) developed a 3-D finite element model to simulate pavement sections at the Virginia Smart Road. Results of the finite element model were compared with the layered theory and field-measured pavement responses. To improve the FEM accuracy, a laboratory-calibrated time- hardening model was successfully incorporated into the model to simulate time retardation of HMA in the transverse direc- tion and fast relaxation of HMA in the longitudinal direction. The finite element model was capable of predicting pavement surface damage and its partial recovery after load application. Analysis emphasized the requirement to incorporate aniso- tropic HMA characteristics to accurately simulate pavement responses in the lateral direction. The measured and calculated vertical stresses (FEM calculated) were in good agreement with the testing conditions, while the locations of the tensile and compressive fields were in agreement with field measure- ments, validating the contact conditions assumed in the modi- fied model. Discrepancies in the strain magnitude support the anisotropic behavior of the material at high temperatures with HMA that appears to be softer in the lateral directions than in the vertical direction, probably as a result of the compaction process. F-sAPT supplements laboratory testing and supports advances in practice and economic savings for the evalua- tion of new pavement configurations, stress level-related fac- tors, new materials, and design improvements by simulating field conditions. Guo and Prozzi (2008) described a method using a bias correction factor or function to account for all quantifiable differences between f-sAPT measured response and actual field response of a pavement. The bias correction factor typically includes factors to cater for the differences between the f-sAPT and the field for the loading frequency, rest periods and loading time, lateral distribution of traffic, temperature, and subgrade moisture content. The methodol- ogy is generic, independent of the f-sAPT facility, condi- tions, or environment. Currently the material aging proper- ties and actual traffic load spectrum are not addressed in the approach. Kim et al. (2008) compared the strain responses of a pave- ment model with those measured in an f-sAPT experiment. The predicted strains from the 3-D visco-elastic model agreed well with the strains measured in the field, indicating that the model simulated the response of the pavement in the field well. The material properties determined from the laboratory and field tests were accurate and reliable. The time-, rate-, and temperature-dependent behavior of the HMA layer are critical to ensure good modeling of the field response of the pavement. The energy ratio concept was evaluated as a predictor of top-down cracking performance in Florida based on f-sAPT at NCAT (Timm et al. 2009). Two f-sAPT sections were tested and both initially exhibited similar structural response as mea- sured by embedded strain sensors, confirming that differences in as-built properties did not contribute significantly to the resulting structural response under load until after cracking became evident. The primary difference between the two sec- tions was the binder used in the upper two lifts. The first sec- tion used PG 67-22, while the second section used PG 76-22, which resulted in approximately double the energy ratio. The section with the lower energy ratio value cracked first and more extensively, although both sections experienced top- down cracking. Field performance data were matched with the expected results, indicating that the energy ratio has the potential to reliably evaluate top-down cracking performance of HMA mixtures.
95 Data from an f-sAPT section were used to forecast resilient responses obtained from NCAT pavements generated under completely different loading and environmental conditions (Levenberg 2009a, b). The overall objective of the f-sAPT study was to develop an analysis approach by which pave- ment behavior in the f-sAPT could be used to reliably forecast the behavior of a similarly constructed pavement in the field serving different loading and environmental conditions. The f-sAPT experiment was modeled using isotropic LET using backcalculated material properties based on the entire time history of pavement response during one f-sAPT pass. This inverse analysis is vital as it minimizes systematic errors origi- nating from the application of a rudimentary pavement model. The f-sAPT model was enhanced by adjusting the HMA model to reflect differences in loading speed and temperature rela- tive to the calibration conditions through analysis of complex modulus data. Application of the enhanced f-sAPT model to forecast the responses generated by a moving truck in a simi- larly constructed pavement system at NCAT showed that the model performed relatively well. Romanoschi et al. (2010) used f-APT and laboratory data to validate the response and distress models in the MEPDG. The revised Witczak model was found to predict the dynamic modulus of HMA mixes at a range of loading frequencies (0.1 to 25 Hz) and temperatures [68°F to 95°F (20°C to 35°C)] adequately. The MEPDG structural response model under- predicted the longitudinal strains at the bottom of the HMA layers by two to three times, while the MEPDG model pre- dicted higher total rutting than the measured. Models were derived for HMA modulus (as function of reduced time), unbound layer moduli (as a function of the stiff- ness of the layers above and as a function of the load level), HMA modulus decrease caused by fatigue, and slip develop- ment between HMA layers using laboratory data for HMA used on 13 HVS test sections (Ullidtz et al. 2008b). These models, calibrated with f-sAPT response, resulted in a relatively good prediction of the resilient deflections of the pavements at all load levels and for the whole duration of the tests. empirical analysis Chen et al. (2001) conducted more than 60 Dynamic Cone Penetrometer (DCP) tests on two f-sAPT test pavements to assess the validity of empirical equations proposed in pre- vious literature to compute layer moduli from DCP data. Elastic moduli values for the pavement layers were obtained from the f-sAPT data. Both DCP and FWD results indicated minimal effects of f-sAPT (MLS) loading on the base and subgrade layers. About 85% of Australiaâs sealed arterial road network con- sists of unbound granular pavements and a thin bituminous surface treatment, normally a chip seal (Martin and Sharp 2009). The feasibility of using f-sAPT to predict the influence of various surface treatments on pavement deterioration was confirmed by a pilot test. In a follow-up trial, ten experiments and various types of surface treatment on separate test pave- ments were undertaken under controlled environmental con- ditions. The observed deterioration data were used to estimate relative performance factors for rutting and roughness for a range of surface treatments under surface conditions varying from dry to continuously wet. The data are supplemented by data being collected in various long-term pavement monitor- ing projects, including a project directed specifically at main- tenance treatments. Steyn (2009b) evaluated the application of f-sAPT for the analysis of pavement preservation actions. It was shown that these treatments can be evaluated successfully using f-sAPT devices, if aspects such as the preparation of the test section, monitoring of pavement response for all potential failure mechanisms, and analysis incorporating information obtained from in-service pavements and laboratory test outputs are incorporated into the process. F-sAPT provides the option of simulating different types of failure conditions to ensure that the preservation treatment can be exposed to similar condi- tions to those expected in the field. Mandapaka et al. (2011) described an attempt to evaluate and select an optimal maintenance and rehabilitation strategy for a flexible pavement integrating life-cycle cost analysis and M-E design procedures. Through application of CalME and life-cycle cost analysis principles, extended pavement pres- ervation with HMA was found to be the most cost-effective M&R strategy for the case study evaluated. This result is influ- enced by climate region and traffic conditions. design Methods The recent Danish pavement design guide includes three lev- els of design (Busch et al. 2005). The lower level consists of a pavement catalog, the intermediate level is a mechanistic design method, and the upper level is an incremental-recursive simulation tool allowing the long-term performance of a design to be simulated. This upper level tool is based on the Mathemat- ical Model of Pavement Performance that has been calibrated using data from the AASHO Road Test, f-sAPT, and general experience with pavements in Denmark. It is capable of pre- dicting longitudinal roughness, rutting, and fatigue cracking of a pavement consisting of an HMA or cement bound layer, a granular base, and subbase layer and subgrade, consider- ing the variations in pavement layer thickness, elastic stiff- ness, plastic parameters, and dynamic load along the length of the road. Tompkins et al. (2008) evaluated the effects of the MnROAD facility on pavement design methods and observed that although MnROAD was originally designed as a thick- ness, or structural, experiment, it was quickly observed that the environment plays a major role in pavement response
96 (especially in this relatively cold areas). Work on MnROAD influenced the CRREL M-E model for cold regions pave- ments, the MnDOT rigid pavement design guidelines, the 1993 AASHTO Guide for Design of Pavement Structures (AASHTO-93), the 1984 Portland Cement Association Thick- ness Design for Concrete Highway and Street Pavements (PCA-84), and the MEPDG (NCHRP Project 1-37A) design procedure. The MEPDG method incorporated a large amount of MnROAD data and expertise, specifically for calibrating the MEPDGâs ability to predict rutting in the lifts of an HMA pavement, and development of the MEPDG thermal crack- ing model. Ullidtz et al. (2007a, b) indicated that Incremental- Recursive models provide reasonable results when predict- ing the response and performance of pavement under f-sAPT loading. Ullidtz et al. (2008b) described the development of M-E models using data from 27 f-sAPT sections. Issues to address in the calibration process are the inclusion of an aging model, allowance for seasonal variation effects, traffic load rest peri- ods, and variability of materials, structure, loads and climate. Ullidtz et al. (2008a) described validation and calibration of CalME models using the FHWAâs WesTrack project data. All the results of the WesTrack experiment were imported to the CalME database after which the experiment was simulated on an hourly basis using the incremental-recur- sive method with the model parameters derived from labo- ratory tests. Very good agreement was obtained between the measured and calculated response during the duration of the WesTrack trafficking on each section in terms of the deflection under the load plate of the FWD. Factors such as the estimated HMA temperature during the FWD test, HMA modulus versus reduced time relationship, moduli of the unbound materials, hardening of the HMA and HMA fatigue damage were significant. CalME predicted less damage for the fine, coarse, and fine plus mixes than that estimated from the FWD. Resilient deflection responses were predicted well, while the CalME-predicted damage (based on laboratory fatigue tests) was somewhat lower than the damage estimated from FWD tests. CalBack was developed as a software tool with versatility by means of three deflection-matching search engines, three response models for flexible pavements, a Westergaard model for rigid pavements, and a large, self-contained, expandable material characterization library (Lu et al. 2008a). Caltrans adopted the M-E pavement design methodology to replace existing pavement design methods, and a number of M-E models have been developed, tested, and collected into a design system known as CalME (Lu et al. 2009), which employs an incremental-recursive approach using the time hardening procedure and WIM load distribution data. CalME is intended to be supported by the required databases, guide- lines, and test methods that will result in more cost-effective pavements (Harvey et al. 2010). CalME can be calibrated using f-sAPT data as well as test track and field section data. The incremental-recursive approach used in CalME means that the entire damage process measured by f-sAPT instru- ments can be used for calibration of response and damage models. This approach permits the use of pavement response data that track the damage and aging processes on sections for calibration of the damage process, even when failure has not yet manifested itself on the pavement surface. In contrast, the MEPDG and other M-E methods using Minerâs Law only use the initial undamaged responses of the pavement to tem- perature and load, and assume the entire damage process to the end failure state. CalME was used to simulate f-sAPT conducted at CEDEX by first verifying the mechanistic pavement response mod- els against the measured responses during the experiment, followed by calibration of the distress models (Ullidtz et al. 2010a). Master curves determined from frequency sweep testing in the laboratory and derived from FWD for the HMA, as well as resilient moduli obtained from triaxial testing and backcalculated moduli for the surfacing layer and the sub- grade were in good agreement. The empirical fatigue dam- age model determined from flexural beam testing gave a reasonably good prediction of the fatigue of the HMA layer, whereas the relationship between cracking and fatigue dam- age tended to overpredict the actual cracking. Rutting was shown to be dominated by the compression of the capping layer and the default empirical model for unbound materials in CalME would have predicted much less rutting than was observed. The rutting model determined from RSST-CH pro- vided acceptable predictions of HMA rutting. CalBack and CalME were successfully used to predict in situ pavement performance of selected MnROAD sections (Tsai et al. 2010). The applied shift factors for fatigue crack- ing and rutting were based on the Caltrans HVS/WesTrack project calibration study. M-E HMA pavement design systems consist of a mecha- nistic model for calculating the critical primary responses in the pavement and empirical models relating the calculated responses to the pavement distress or performance. Ullidtz et al. (2010b) demonstrated how CalME can be used to develop an effective flexible pavement design system based on the facility for importing the results of f-sAPT experi- ments in terms of hourly loads, temperatures, response mea- surements, backcalculated moduli, permanent deformations, and cracking. It is still recommended that the data be comple- mented by track testing to incorporate the effects of realistic loads and real climatic conditions. Ullidtz et al. (2010c) described the successful develop- ment of an overlay design procedure for reflection cracking and rutting for CalME based on the incorporation of f-sAPT data from overlay test sections.
97 One of the goals of the Caltrans transition to ME design is to calibrate and update the M-E methods as innovations sur- face using laboratory testing, modeling, f-sAPT, and PMS data (Basheer et al. 2010; Harvey et al. 2010). The materials mod- els include coefficients for a standard equation for stiffness, with different equations for HMA and unbound materials, as well as coefficients for performance equations for fatigue and rutting. These various coefficients for the equations are deter- mined through laboratory and field testing. Gibson et al. (2010) summarized the outcome of the Trans- portation Pooled Fund Study TPF-5(019) and SPR-2(174) Accelerated Pavement Testing of Crumb Rubber Modified Asphalt Pavements Projects. With relevance to MEPDG, it was found that additional mixture-specific characterization inputs are needed apart from the E*dynamic modulus, to enable improved discrimination and ranking of modified and unmodified HMA performance. Although the MEPDG models are largely calibrated using LTPP data, there are not significant amounts of polymer- modified HMA data available, while f-sAPT data (FHWA ALF) included several different polymer-modified HMA sections. The actual MEPDG software was found not to be able to be used for HMA performance predictions, as it was not developed to accommodate specialized f-sAPT condi- tions. It was further found that material modulus measured at small strains did not mobilize the material into regions that force rutting or fatigue crack resistance to be revealed. The NCHRP 9-30A project is currently pursuing this type of material characterization inputs, and recalibration of the MEPDG guide will be required to ensure improved rutting prediction. Two aspects of damage and fatigue cracking that the MEPDG does not provide were highlighted in this study. PSPA tests on ALF lanes indicated that HMA modulus decreases significantly before fatigue cracks are visible on the surface. The HMA modulus applied in the MEPDG is cur- rently not recursively updated to reflect this type of damage. Further, the pattern in which actual bottom-up fatigue crack- ing develops is not captured, while the surface remains crack free until surface cracking is initiated and propagates. The MEPDG was still deemed useful in analyzing the uniformity of the f-sAPT (FHWA ALF) section construction. The FAA Advisory Circular on Airport Pavement Design and Evaluation (AC150/5320-6E 2009) provides guidelines for the thickness design of airport pavements. It is typically used together with the FAARFIELD (FAA Rigid and Flexible Iterative Elastic Layer Design) software. The guideline is based on LET for flexible pavement design and three-dimensional finite element theory for rigid pavement design. The impact of new landing gear configurations and increased pavement load conditions can be evaluated using the guideline, and it was found to be robust and able to address novel gear config- urations. The International Civil Aviation Organization made intensive use of data obtained from the various FAA NAPTF f-sAPT projects for developing this guideline. MnDOT used data from the MnROAD experiment to develop an M-E flexible pavement design program (MnPAVE) for Minnesota. The approach is applicable to both low-volume and high-volume roads. The MnPAVE thickness design pro- cedure is a M-E computer software program that takes into account many variables that could not be considered previ- ously. The MnPAVE procedure is based on work done at the University of Minnesota using an elastic layered system WESLEA developed by the U.S. Army Corps of Engineers. MnPAVE is based on performance prediction equations for fatigue and subgrade rutting based on material properties and performance of test sections at MnROAD. Performance prediction equations verified using performance data from 40-year-old test sections that have been used to check the per- formance prediction equations used in MnPAVE. The appli- cation of an M-E design procedure allows for different local material properties to be incorporated into the design to enable performance prediction for specific roads (Skok et al. 2003; Tanquist and Roberson 2010). chapter suMMary The modeling and analysis chapter focused on the various modeling approaches followed and reported for f-sAPT programs. Although attempts are made to incorporate more advanced model formulations to closer predict material behav- ior, in some cases the use of linear elastic layered theory still provides reasonable results. However, researchers should be careful as it was shown that in many cases specific material properties prevent the use of simplified theories to accurately predict field performance. The development of advanced pavement design methods and the use of f-sAPT data for the calibration of these methods is becoming a frequent activ- ity. The synthesis incorporates sections on advanced model- ing and design methods. The application of f-sAPT data into advanced pavement response models and improved pave- ment design methods is evident from the body of papers on these topics. The focus period of the synthesis (2000 to 2011) is important in this part of the synthesis, as major develop- ments in prominent pavement design methods that incorpo- rated f-sAPT (such as in Australian, South African, and Min- nesota) have either been covered in the previous syntheses (Metcalf 1996; Hugo and Epps Martin 2004), or much of the work is only currently being completed and thus has not yet been reported in the literature. Readers are urged to consult with these documents as well as the 4th International Con- ference on Accelerated Pavement Testing (September 2012) proceedings to ensure that a complete picture of modeling and analysis aspects can be formed.
