Kunihito Matsui

An efficient backcalculation algorithm of time domain for large-scale pavement structures using Ritz vectors

This paper describes a backcalculation algorithm to determine the layer moduli and damping coefficients in the time domain for large-scale pavement structures. Pavement is modeled by three-dimensional finite element (3D FE). The parameter identification procedure makes use of Ritz vectors to reduce the size of matrices involved in the forward dynamic response analysis and the deflection sensitivity analysis. An exact complex mode superposition technique is used to obtain the dynamic response of the reduced equation system in the time domain. This method is more efficient, accurate and stable. The parameter estimates are improved iteratively by means of an algorithm that calls the finite element program of dynamic response analysis as a subroutine combining truncated singular value decomposition (TSVD) method. Simulation of a numerical solution validates the efficiency of the proposed method. Finally, the method is implemented for two experimentally tested sections of semiflexible pavement. All parameters are determined using the surface deflections of pavement experimentally recorded at the sensor locations of falling weight deflectometer (FWD).

Linear elastic analysis of pavement structure under non-circular loading

Conventional methods for road and airport pavement analyses, such as BISAR and GAMES, were developed based on a cylindrical coordinate system. Because of the loading symmetry due to the assumption that a circular uniformly distributed load is acting on the pavement surface, it was useful to use a cylindrical coordinate system. However, depending on the magnitude of the tire load, several research reports on tire–pavement contact stresses have shown that the contact patch is predominantly rectangular and not circular in shape. Based on this observation and the fact that it may be difficult for most multi-layer linear elastic software packages to make use of the field measured tire–pavement contact stresses, which are rectangular in shape, this paper presents the development of a method for pavement structural analysis considering both uniform and non-uniform loads acting over a rectangular area. In this approach, three components of displacements, which satisfy Naviers equations, are expressed using Neuber-Papkovich functions. Worked examples for vertical and horizontal loads acting over rectangular area are presented in this paper. In order to verify the validity of the solutions obtained, the results are compared with those obtained from freeware GAMES software, which analyses loads acting over a circular area and is widely used in Japan and South Africa and a number of institutions in Australia, Europe and US.

Sensitivity analysis on measurement noise in the identification of soil properties from vertical array observation data

This study clarified the effects of measurement noise on identification of soil properties from vertical array observation of seismic waves. In order to evaluate the sensitivity of the unknown parameter with respect to error caused by noise, the amplitude of a transfer function was used to formulate the evaluation function in the frequency domain. Also the logarithmic amplitude was used to formulate the evaluation function and compare the sensitivity between the two types of amplitude expressions. A numerical experiment, based on a simple-structured ground model, showed that these evaluation functions produced satisfactory results which were in good agreement with identified results obtained by the measurement data contaminated by artificially generated errors. The present theory, when applied to actual earthquake records, proved useful in evaluating the influence of the non-linearity of soil characteristics.

Finite Element Model Analysis of Thermal Stresses of Thick Airport Concrete Pavement Slabs

Thermal stress caused by temperature distribution in pavement slab is important in the structural design of airport concrete pavements. Airport concrete pavement slab is thick; therefore, temperature in the slab varies nonlinearly throughout its depth. Thermal stress caused by nonlinear temperature distribution differs from that of linear temperature distribution. In this study, thermal stress caused by nonlinear temperature distribution was calculated by using temperatures and restraint strains measured in an experimental concrete pavement with 460-mm-thick slabs. The calculated thermal stress differed from curling stress because of the linear temperature distribution. Temperature distributions in concrete slabs of various thicknesses were computed by solving the heat transfer equation with the control volume method. This calculation revealed that temperature distributions in thick concrete slabs were highly nonlinear. Thermal stress was analyzed to compute the nonlinear thermal stress distributions in concrete slabs from the computed temperature distributions by using a three-dimensional finite element model. On the basis of the analysis, effects of slab thickness and nonlinear temperature distribution on thermal stress were discussed. The effect of nonlinearity was found to be pronounced at a slab thickness greater than 300 mm. In this range, the reduction factor for taking into account the effect of nonlinear distribution was larger than 0.7. It was also found that thermal stresses in summer and spring were relatively large.

Time domain backcalculation of pavement

Falling weight deflectometor (FWD) has been frequently used to evaluate structural integrity of pavement. The device applies an impulsive force on the surface of pavement and measure surface deflections at several locations including the place of loading. Although the test is dynamic, the data is regarded as pseudo-static data. According to common practice, using the peak load and the corresponding peak deflections, layer moduli are estimated in a static domain such that the measured peak deflections coincide with the corresponding calculated deflections based on the assumption of the theory of linear elasticity. This paper presents a method to back calculate layer moduli in dynamic domain such that the histories of both measured and calculated responses corresponding to the impulsive force coincide. Pavement is modeled by an axisymmetric linear elastic system. FEM is utilized coupled with Ritz vector to reduce a matrix and thus to improve computational efficiency. The backcalculation algorithm used is the Gauss-Newton method coupled with a truncated singular value decomposition.

COMPARATIVE STUDIES OF BACKCALCULATED RESULTS FROM FWDS WITH DIFFERENT LOADING DURATION

The falling weight deflectometer (FWD) test applies an impulsive force on the surface of pavement and measures surface deflections at several locations. FWDs produced at different manufacturers often differ in loading duration. The difference may affect backcalculation results because the FWD test is dynamic in nature, This paper investigates the effect of the difference on backcalculated layer moduli.

Back-calculation of temperature parameters for determination of asphalt layer modulus

The pavement elastic modulus of each layer was usually assumed not to be dependent on the environmental factors when the backcalculation of asphalt pavement was conducted from the measured surface deflections of FWD. However, it is well known that the elastic modulus of asphalt layer changes with the variation of temperature. Considering the influence of atmospheric temperature and radiant heat, the temperature distribution is nonlinear along the asphalt layer thickness, and has always been changed. Therefore, the distribution of elastic modulus in the asphalt layer has been considered to change as well. In this paper, we assume the elastic modulus distribution of the asphalt layer to vary with its temperature in terms of the exponential form. Based on the finite element method forward analysis, we propose a method to estimate a standard elastic modulus and temperature coefficient at 20 degrees Celsius for the asphalt layer from the backcalculation analysis. The corresponding FEM backcalculation program using Gauss-Newton method was developed to determine the pavement layer moduli and temperature dependent coefficient, in which the singular value decomposition (SVD) was used for the inverse analysis with scaling of unknown parameters. This method results in a smaller condition number that contributes to improvement of numerical stability. Both numerical simulation and measured data from FWD testing are used to demonstrate the potential applications of this method. As a result, the backcalculation procedure is less dependent on the users initial values, fast in convergence rate and effective in the pavement engineering.

Influence of Seed Layer Moduli on Finite Element Method-Based Modulus Backcalculation Results

The determination of pavement layer moduli from falling weight deflec-tometer test data is known as backcalculation analysis. Generally, back-calculation analysis is unstable—greatly influenced by several causes of error. They may be categorized as modeling error in the forward analysis, deflection measurement error, or numerical computation error due to instability in the backcalculation procedure, for example. Because of these problems, the seed values selected for layer moduli greatly influence backcalculation results. To reduce the effects of measurement error, truncated singular-value decomposition is used for regularization. Variable scaling, often used in optimization algorithms, is implemented to improve numerical accuracy. A Ritz vector reduction method is used to solve a large system of dynamic equations in dynamic backcalculation efficiently, and various other means are introduced to decrease computational time. Recent updates of Dynamic Back Analysis for Layer Moduli software, first developed ...

Structural evaluation of pavement using surface wave and portable FWD tests

SASW has been well known as one of nondestructive testing methods for pavements. This method makes use of the dispersion characteristics to estimate the thickness and modulus of pavement layers. It is difficult to obtain accurate dispersion curves even if the analytical surface wave fields are used, where only the stiffness proportional damping is considered. However, the good agreement of dispersion curves has been found for the analytical surface wave fields if Rayleigh damping is adopted in the numerical simulation. In this paper, a dynamic general FEM software was developed to inverse the layer moduli and Rayleigh damping coefficient of the tested pavement structure using the portable FWD data. It shows that the predicted dispersion curves are well approximately to ones obtained from experimental SASW.

Airport pavement roughness evaluation based on aircraft response

Runway roughness affects primarily ride quality and dynamic wheel loads. The forces applied onto the airport pavement by aircraft vary instantaneously above and blow the static weight, which in turn increase the runway roughness. One method to effectively assess the ride quality of the airport runway is to measure its longitudinal profile and numerical simulate aircraft response performing a takeoff, landing or taxiing on that profile data. In this study the aircraft responses excited as the aircraft accelerates or moves at a constant speed on the runway during takeoff and taxi are computed by using the improved computer program TAXI. This procedure is capable of taking into account both the effects of discrete runway bumps and runway roughness. Thus, sections of significant dynamic response can be determined, and the maintenance and rehabilitation works for airport runways will be conducted.