Backcalculation of viscoelastic and nonlinear flexible pavement layer properties from falling weight deflections

Appropriate characterisation of individual layer properties is crucial for mechanistic analysis of flexible pavements. Typically in inverse analyses, pavements are modelled as elastic or nonlinear elastic to obtain layer material properties through non-destructive falling weight deflectometer (FWD) testing. In this study, a layered viscoelastic–nonlinear forward model (called LAVAN) was used to develop a genetic algorithm-based backcalculation scheme (called BACKLAVAN). The LAVAN can consider both the viscoelastic behaviour of asphalt concrete (AC) layer and nonlinear elastic behaviour of unbound layers. The BACKLAVAN algorithm uses FWD load-response history at different test temperatures to backcalculate both the (damaged) E(t) and |E^*| master curve of AC layers and the linear and nonlinear elastic moduli of unbound layers of in-service pavements. The BACKLAVAN algorithm was validated using two FWD tests run on a long-term pavement performance section. Comparison between the backcalculated and measured results indicates that it should be possible to infer linear viscoelastic properties of AC layer as well as nonlinear elastic properties of unbound layers from FWD tests.     

Network-level flexible pavement structural evaluation

The Kansas Department of Transportation has a comprehensive pavement management system known as network optimisation system (NOS). Annual condition surveys are conducted for NOS. Currently, the structural number (SN) of flexible pavements is computed using the American association of state highway and transportation officials equation based on the centre and fifth sensor deflections of a falling weight deflectometer (FWD). However, a rolling wheel deflectometer (RWD) can be used to collect deflection data at the network-level. This study was conducted to see whether the SN of flexible pavements can be obtained from this RWD deflection and NOS condition survey results. In this study, FWD deflection data, collected from 1998 to 2006, were analysed. Multiple regression analysis was done. The results showed that there is a negative relationship between SN and centre deflection. Equations can be used to calculate SN based on FWD (or RWD) centre deflections and network-level condition survey results. The SN is more sensitive to centre deflection than the total pavement thickness.     

Limits of agreement method for comparing TSD and FWD measurements

This article uses the limits of agreement (LOA) method to compare the falling weight deflectometer (FWD) and the traffic speed deflectometer (TSD), two pavement structural evaluation devices. The TSD measures deflection slope, whereas the FWD measures deflection. For this reason, measurements were converted to the surface curvature index (SCI) and the base damage index (BDI), which can be obtained from each device. The SCI and BDI agreement between the two devices was then evaluated. Although the relationship between the calculated SCI and BDI using both equipments is reasonably close to the line of equality, there is a significant variation and a bias in this relationship. For example, for an average SCI or BDI value of 300 μm, the bias was 30 μm (FWD values lower than TSD values), and the LOA was 380 μm.     

Simulation of unbound material resilient modulus effects on mechanistic-empirical pavement designs

The variability of resilient modulus (M _R) of unbound materials and subgrade due to laboratory test conditions affect pavement performance and designs. The performance-based mechanistic-empirical pavement design guide (MEPDG) is gaining more popularity in recent years for pavement design use. However, limited research efforts have quantitatively studied M _R effects based on ME models. This research targets to evaluate the influences of M _R variability on pavement performance and designs based on the MEPDG performance models. With a normal-distribution of M _R seed values, pavement responses were computed with a layer-elastic analysis model, pavement performance was then predicted using MEPDG models, and design variability was studied via Monte Carlo simulation. Results indicate that the relationship between layer design thickness and M _R varies from almost linear to nonlinear, which is highly dependent on the pavement structure and material properties. For the evaluated specific pavement structure and range of M _R values, the least susceptible is the HMA design thickness as a function of M _R under fatigue with a design Coefficient of Variance (CV) of 7.51 %, while the most susceptible is the base design thickness as a function of M _R also under fatigue with a CV of 54.32 %. The combined effect of both rut depth and fatigue life considering the variability of both base and subgrade results in a design CV of 22.58 % for asphalt layer and 26.08 % for base layer. When using a weaker base layer or a thinner HMA layer, the modeled thickness design CV has changed ?4.19 to 1.14 %.     

Limitations and potential improvement of the aircraft pavement strength rating system to protect airport asphalt surfaces

A pavement strength rating system is internationally adopted in order to protect aircraft pavements from inadvertent overload. The system has two elements. The primary element is designed to protect the pavement against subgrade rutting and the second is intended to protect asphalt pavement surfaces. The surface-protection element is arbitrary and empirical, placing category-based limits on aircraft tyre pressures. In 2008, increases in the tyre pressure limits were proposed by aircraft manufacturers and these were approved in 2013. The research reported in this paper assesses the impact of tyre pressure and individual wheel load increases on calculated flexible pavement stress indicators, as well as identifying an improved surface layer protection element. Stresses were calculated near the surface, at the surface layer interface and at the subgrade. Tyre pressure and wheel load combinations included current (18 t and 1.35 MPa), imminent (33 t and 1.75 MPa) and future (40 t and 2.15 MPa) aircraft. Surface layer stress increased significantly (20–30%) with increases in both tyre pressure and wheel load. The subgrade stress increased near-equally (97%) with wheel load but was insensitive (<1%) to tyre pressure changes. The ability of the current aircraft pavement strength rating system to protect pavements from the increasing demands of aircraft was demonstrated to be limited to the subgrade. It is recommended that the tyre pressure rating be amended to reflect the combined impact of both tyre pressure rating and individual wheel load. It is also recommended that ongoing efforts to incorporate additional asphalt surface failure modes into routine pavement design be given high priority. The importance of these issues is reinforced by the limited availability of remedies to counter any negative impacts of increased surface layer stresses, especially in hot climates.     

Large third-order nonlinearity of nonpolar A-plane GaN film at 800 nm determined by Z-scan technology

We report an investigation on the optical third-order nonlinear property of the nonpolar A-plane GaN film. The film sample with a thickness of ~2?μm was grown on an r-plane sapphire substrate by metal-organic chemical vapor deposition system. By performing the Z-scan method combined with a mode-locked femtosecond Ti:sapphire laser (800?nm, 50?fs), the optical nonlinearity of the nonpolar A-plane GaN film was measured with the electric vector E of the laser beam being polarized parallel (//) and perpendicular (⊥) to the c axis of the film. The results show that both the third-order nonlinear absorption coefficient β and the nonlinear refractive index n₂ of the sample film possess negative and large values, i.e. β_//?=??135?±?29?cm/GW, n_2//?=??(4.0?±?0.3)?×?10^?3?cm²/GW and β_⊥?=??234?±?29?cm/GW, n_2⊥?=??(4.9?±?0.4)?×?10^?3?cm²/GW, which are much larger than those of conventional C-plane GaN film, GaN bulk, and even the other oxide semiconductors.     

Development of serviceability prediction model for county paved roads

This paper developed a pavement serviceability prediction model for county paved roads. Most county paved roads were built decades ago without following minimum design standards. The recent increase in industrial/mineral activities in the State of Wyoming required developing a pavement management system (PMS) for local paved roads. The developed PMS used the pavement serviceability index (PSI) as a pavement performance parameter. The proposed PSI model for local roads is based on: international roughness index, pavement condition index (PCI) and rut depth for flexible pavements only. Ten panellists from Wyoming rated 30 pavement sections that were randomly selected at different distresses’ levels; using two vehicles (SUV and Sedan). The statistical analysis indicated that the seating position, age and gender are not significant to the rating process. However, the vehicle’s type found to be significant. The newly developed model from this study explains 80% of the variations in the PSI values of county roads (adjusted R² = 0.80). In addition, the new model seems to provide more realistic representation of the conditions of county roads than the statewide model used on the state’s highway system.     

Estimating fatigue endurance limits of flexible airfield pavements

In perpetual pavements, damage from bottom-up cracking can be limited to the top surface lift through using a very thick surface layer or a binder-rich intermediate layer. This can be attained by maintaining tensile strains at the bottom of the hot-mix asphalt (HMA) layer below a certain value known as the fatigue endurance limit (FEL). This paper presents a method for estimating a strain-based FEL for flexible airfield pavements. The proposed method is based on the concept that a 50% reduction in HMA layer modulus would indicate initiation of fatigue cracking. Falling weight deflectometer (FWD) testing results, collected from National Airport Pavement Test Facility (NAPTF) flexible pavement sections, were analyzed to determine at which loading pass each section had a 50% reduction in HMA layer modulus (N_f50). NAPTF tensile strain data were also used to determine the tensile strain at N_f50 for each pavement section by averaging the peak tensile strains. The proposed approach was validated by comparing its results to those obtained using a common FEL estimation model known as the rate of dissipated energy change (RDEC) model. To further verify the results of the proposed approach, peak tensile strain was plotted vs. number of loading cycles for all sensors. Using these plots, the peak tensile strain at which the variability in the strain gauge data increased was used as an estimate of a possible FEL. The N_f50 tensile strains estimated using the proposed method were comparable to the values determined from RDEC and variability approaches.     

Backcalculation of pavement layer elastic modulus and thickness with measurement errors

This paper presents a backcalculation method for pavement layer elastic modulus and thickness. The effect of deflection measurement errors on the backcalculated results is also considered. The falling weight deflectometer (FWD) data are generated by applying a load to the pavement while calculating deflection at various fixed distances from the load centre. The measurement errors in FWD data are simulated by perturbing the theoretical deflections. Using these data, a backcalculation technique based on the improved genetic algorithm is proposed. In order to deal with the measurement errors, besides the common root mean square, a new objective function called area value with correction factor is introduced to the backcalculation algorithm. Numerical examples for two- and four-layer pavement structures are presented, which show the capability of the proposed method in backcalculation of pavement layer modulus and thickness.     

Systematic back-calculation protocol and prediction of resilient modulus for MEPDG

A research focusing on the characterisation of representative local material properties was conducted to facilitate the full implementation of the Mechanistic-Empirical Pavement Design Guide for roadway designs in Wyoming. As part of the test program, falling weight deflectometer deflection data were collected from 25 test sites in Wyoming for back-calculation of subgrade resilient modulus. Also, subgrade materials from these test sites were sampled for laboratory resilient modulus measurement in accordance with the AASHTO T 307. The back-calculation is a user-dependent procedure and produces a non-unique resilient modulus estimation. To alleviate this limitation, this paper focuses on the recent development of a systematic back-calculation protocol for subgrade resilient modulus using MODCOMP6 software. The protocol is intended for use on a flexible pavement with a crushed base. The proposed procedure discusses pre-analysis checks, seed modulus adjustment, pavement structure adjustment and program termination criteria. A correlation study was conducted to correct back-calculated resilient modulus to laboratory-equivalent values. The results conclude that a non-zero intercept linear regression model provides a better correlation than the widely used zero intercept linear regression model. Furthermore, better correlations are achieved when the back-calculated resilient modulus of a lower subgrade layer and resilient modulus measured at higher laboratory test sequences Nos. 11 to 15 are considered. The non-zero model based on M_r test sequence No. 14 and lower subgrade layer yields the best correlation. For the zero model, a C-factor of 0.645 based on M_r test sequence No. 15 and lower subgrade layer yields the best correlation.     

Resilient modulus–moisture content relationships for pavement engineering applications

In recent years, there has been an increased interest in determining the influence of moisture changes on the resilient modulus (M_R) of subgrade soils beneath pavement structures. Efforts have also been made to develop mathematical models that predict the change in M_R values with moisture. These models are expected to account for seasonal variations in subgrade moisture content. This study evaluates the variation of resilient modulus with post-compaction moisture content of soils in the State of Oklahoma and the State of Pennsylvania. A series of specimens was compacted at optimum moisture content and then tested for resilient modulus; other series of specimens were prepared at optimum moisture content and then either wetted or dried prior to M_R testing. Employed wetting and drying procedures are time-efficient in developing the M_R–moisture relationships. Results showed that M_R–moisture content relationships varied with soil types and M_R values varied inversely with changes of moisture content. In addition, an M_R–moisture model predicting the variation of resilient modulus with moisture contents is proposed. This model can be used to predict changes in the bearing capacity of pavements due to seasonal variations of moisture content.     

Evaluation of performance and design of GFRP dowels in jointed plain concrete pavement – part 1: experimental investigation

Dowel bars are provided at the transverse joints of the jointed plain concrete pavement to allow for expansion and contraction of the pavement due to moisture and temperature changes. This paper presents experimental and analytical investigations for the deflection response of glass fibre-reinforced polymer (GFRP) dowels for different joint widths and concrete grades. The results were compared with those obtained from investigations into the conventional epoxy-coated steel dowel bars of similar rigidity. The experimental results showed that the 38 mm (1.5 in.) GFRP dowels perform better in terms of joint face deflection compared with 25 mm (1 in.) epoxy-coated steel dowel bars. In addition, these results showed that the deflection of the GFRP dowel was significantly affected by changing the concrete compressive strength and the joint widths.     

Dual boundary method for assembled plate structures undergoing large deflection

In this paper, the dual boundary element method is combined with a multiregion formulation to simulate plate assembly undergoing large deflection. The incremental load approach is used to treat the geometrical nonlinearity, and radial basis functions are used to approximate the derivatives of the large deflection terms. The dual reciprocity method is used to transfer all the domain integrals to the boundary. Once the solution at the boundary is obtained for the assembly, a J ?integral for large deflection is implemented to extract the fracture parameters. Copyright © 2011 John Wiley & Sons, Ltd.     

Analysis of inverted base pavements with thin-asphalt layers

Inverted base pavements are flexible pavement structures built by placing a top quality compacted granular aggregate base between a rigid cement-treated base and a thin-asphalt surface layer. The proximity of the granular base to the load makes its behaviour critical to the pavement response. Three-dimensional finite-element simulations are conducted to assess the mechanical performance of different inverted base pavement structures, with emphasis placed on pavements that feature thin-asphalt surface layers. A nonlinear constitutive model captures the anisotropic stress-dependent stiffness of the granular base. Results show that the stress distribution within inverted base pavements is markedly different from that of conventional pavements due to the stiffness contrast between successive layers. Thin-asphalt layers deform more uniformly and experience lower tension than thick layers. However, in the presence of combined shear and vertical contact loads, the benefits of a membrane response in thin asphalt concrete layers may be overwhelmed by the increased tensile strain at the load edge. The transition from beam to membrane asphalt response depends on the relative stiffness between the asphalt layer and the aggregate base. In most cases, the transition takes place at an asphalt layer thickness between 25 mm and 50 mm.     

Implementation of stress-dependent resilient modulus of asphalt-treated base for flexible pavement design

Abstract

Asphalt-treated base (ATB) is a widely used base course material in flexible pavements. Due to its lower binder content and lower quality granular material, resilient modulus (M_R) of ATB exhibits a stress dependent property. While most of the pavement analysis software used in the current routine design tasks is based on Burmister’s multi-layer elastic theory, in which the M_R is the primary fundamental material property, the software cannot truly deal with the stress-dependent M_R of paving material. In this study, M_R model in the Mechanistic Empirical Pavement Design Guide was adopted to accommodate the stress-dependent M_R of ATBs and the model was implemented in pavement mechanistic analyses through Abaqus finite element software and its user programmed subroutine. The comparison of critical pavement responses was made among pavements with three types of ATBs. Pavement responses obtained using the multi-layered elastic theory and based on resilient moduli recommended by Alaska Department of Transportation & Public Facilities, were also included for comparison.     

Improvements to the structural condition index (SCI) for pavement structural evaluation at network level

Structural evaluation provides valuable information about the expected behaviour and response of pavements and can be used at the network level of pavement management to prioritise projects. The falling weight deflectometer (FWD) can be used to identify the beginning and end of management sections and group pavement sections with similar structural capacities. The structural condition index (SCI) was developed as a screening tool for the pavement network-level evaluation, and the FWD data are used to determine the SCI. For the successful implementation of the SCI concept at the network level, one of the critical issues is the accuracy of the index. This article evaluates the accuracy of the SCI and also discusses a concept and procedure how to improve the SCI and its algorithm for low-volume flexible pavements. A case study (Texas) illustrates that the original SCI algorithm underestimates the existing structural condition, resulting in overestimated treatments in the pavement maintenance and rehabilitation.     

Simplified approach for structural capacity evaluation of flexible pavements at the network level

Pavement surface deflection has been used by several highway agencies to assess the structural condition of the pavement structure. Falling weight deflectometer, deflectograph and other devices are commonly used to measure the deflected shape of the pavement surface under loading. Several parameters have been derived from the measured deflection bowl to evaluate pavement structural condition; however, there is no universally agreed parameter that can reliably rank the structural condition of the highway network. In addition, each pavement type deflects differently under traffic loads. Therefore, it is not possible to have one single scale to evaluate and rank pavement structural capacity for all different types. In this research paper, four different scales were developed to evaluate structural capacity of different flexible pavement structures. The area ratio, deflection ratio and their normalised values were derived from the deflection bowls of both field measured deflections and computer simulated data.     

Stresses at joints and cracks in highway and airport pavements

The weight function method is used to determine the stress intensity factors for cracks and joints in highway and airport pavements. The relationship between the stress intensity factors and the deflection caused by a wheel load are then used to obtain the stresses in the pavement. The new method that combines the theory of elasticity and fracture mechanics is called EFM. The results from EFM for the deflection and bending stress at the midslab position along the longitudinal edge are compared with the theoretical solution of Westergaard, solutions using the finite element method, and with the experimental data from the AASHO road test. The deflection caused by an axle load at the corner of a transverse joint for a rigid pavement determined by EFM is also compared with the test data from the AASHO road test. There is good agreement in all cases.     

Dielectric nonlinearity and electrical properties of K0.5Na0.5NbO3–SrTiO3 relaxor ferroelectrics

K_0.5Na_0.5NbO₃–xSrTiO₃(x = 0, 0.1 and 0.2) ceramics were prepared using the solid-state method. The phase transition behaviors, electrical properties, and electric field-induced dielectric nonlinearity behaviors were investigated as a function of the SrTiO₃ content. The electrical properties of the investigated compositions exhibited a significant dependence on the content of SrTiO₃. Doped content more than x = 0.1 induced a relaxor transformation, while the dielectric loss decreased quickly. In addition, an “extrinsic” polarization contributed to the dielectric nonlinearity behavior of the composition x = 0.1 with the polar nanoregions and domain-wall motions, by means of the multipolarization-mechanism model fittings of the electric field dependence of the dielectric permittivity. The dielectric tunability and loss angle tangent of the composition x = 0.1 were 32.6 % and 0.028, respectively.     

Coupled thermo-hydraulic modelling of pavement under frost

Frost action is a major factor causing deteriorations of pavements in cold regions. The resultant temperature and moisture redistributions play an important role in determining the mechanical responses of pavement. This paper develops a multi-physical model to analyse the coupled thermo-hydraulic field under pavements, especially those in the unsaturated base and subgrade. This model integrates the Fourier's laws for heat transfer, Richards' equation for fluid transfer and poroelastic constitutive relationships. Various coupled parameters were utilised to transfer information between field variables. Additional relationships, such as the similarity between drying and freezing processes and the Clapeyron equation for ice–water balance, were incorporated to allow for the effects of frost action. The coupled nonlinear partial differential equation system was solved on a multi-physical platform. Two instrumented pavement sections (one asphalt pavement and one concrete pavement) were used to validate the results of the model simulations. The simulation results match reasonably well with the field-monitored data.