Backcalculation Analysis Research Articles

Implementation of Reliability-Based Backcalculation Analysis

The reliability concept provides a means of incorporating some degree of certainty into the pavement design process to ensure that the outcomes of the process will provide acceptable levels of service until the end of the intended design life. Pavement structural performance and rehabilitation design are highly dependent on the in situ layer properties. Pavement layer thickness is an essential input in backcalculation analysis performed with measured surface deflections to evaluate the in situ structural capacity of a pavement. Inaccurate thickness information may lead to significant errors in the backcalculated layer moduli and, hence, in the rehabilitation design. Because pavement layer thickness has some degree of variability (normal variability), it is important to consider this variability in the backcalculation analysis and rehabilitation design. A procedure was developed to implement the reliability concept in backcalculation analysis to account for the normal variability in layer thickness within structurally homogeneous sections. This procedure was developed on the basis of in situ layer information obtained from a ground-penetrating radar study performed for the New Jersey Department of Transportation. This paper provides an overview of the procedure, along with the results of the pilot implementation of the procedure. This reliability procedure complements the reliability factor of the 1993 AASHTO pavement design guide, as the latter reliability factor does not account for the in situ layer thickness.

Implementation of Reliability-Based Backcalculation Analysis

The reliability concept provides a means of incorporating some degree of certainty into the pavement design process to ensure that the outcomes of the process will provide acceptable levels of service until the end of the intended design life. Pavement structural performance and rehabilitation design are highly dependent on the in situ layer properties. Pavement layer thickness is an essential input in backcalculation analysis performed with measured surface deflections to evaluate the in situ structural capacity of a pavement. Inaccurate thickness information may lead to significant errors in the backcalculated layer moduli and, hence, in the rehabilitation design. Because pavement layer thickness has some degree of variability (normal variability), it is important to consider this variability in the backcalculation analysis and rehabilitation design. A procedure was developed to implement the reliability concept in backcalculation analysis to account for the normal variability in layer thickness within structurally homogeneous sections. This procedure was developed on the basis of in situ layer information obtained from a ground-penetrating radar study performed for the New Jersey Department of Transportation. This paper provides an overview of the procedure, along with the results of the pilot implementation of the procedure. This reliability procedure complements the reliability factor of the 1993 AASHTO pavement design guide, as the latter reliability factor does not account for the in situ layer thickness.

Seed Modulus Generation Algorithm for Backcalculation of Flexible Pavement Moduli

The seed moduli chosen for backcalculation analysis of multilayer flexible pavements can have significant impacts on the performance of backcalculation software and, sometimes, the final solutions of the backcalculated moduli. Practically all backcalculation programs provide internally generated seed moduli for backcalculation analysis. However, as the internally generated seed moduli do not always produce satisfactory results, the use of user-input seed moduli is generally encouraged. With the aim of providing useful guidance in the choice of seed moduli, a seed modulus generation algorithm, 2L-BACK, for multilayer flexible pavements based on a closed-form modulus backcalculation solution for two-layer flexible pavement structures was developed. The proposed algorithm does not require any subjective judgment by the user. An evaluation analysis of the effectiveness of the proposed procedure is presented by the use of two types of backcalculation software, MICHBACK and EVERCALC, and is based on measured an...

Seed Modulus Generation Algorithm for Backcalculation of Flexible Pavement Moduli

The seed moduli chosen for backcalculation analysis of multilayer flexible pavements can have significant impacts on the performance of backcalculation software and, sometimes, the final solutions of the backcalculated moduli. Practically all backcalculation programs provide internally generated seed moduli for backcalculation analysis. However, as the internally generated seed moduli do not always produce satisfactory results, the use of user-input seed moduli is generally encouraged. With the aim of providing useful guidance in the choice of seed moduli, a seed modulus generation algorithm, 2L-BACK, for multilayer flexible pavements based on a closed-form modulus backcalculation solution for two-layer flexible pavement structures was developed. The proposed algorithm does not require any subjective judgment by the user. An evaluation analysis of the effectiveness of the proposed procedure is presented by the use of two types of backcalculation software, MICHBACK and EVERCALC, and is based on measured and computed data for flexible pavement segments from the Long-Term Pavement Performance project. A comparison was made of the backcalculation program performance and the computed moduli of solutions obtained from internally generated seed moduli and those obtained from seed moduli generated by the proposed algorithm. It was found that the proposed seed modulus generation algorithm led to enhanced program performance of MICHBACK with respect to convergence characteristics and the accuracies of the backcalculated solutions. In comparison, the corresponding improvements for the case of EVERCALC were less. The proposed seed modulus generation algorithm does not suffer from the location and pavement type transferability constraints of most regression-based seed modulus generation methods. The results of the study suggest that the algorithm can be effectively incorporated into backcalculation software for multilayer flexible pavements.

Paleoliquefaction features on Tenerife (Canary Islands) in Holocene sand deposits

On Tenerife, one of the Canary Islands, a series of clastic dikes and tubular vents is attributed to liquefaction of sediments during a high-intensity paleoearthquake. Geotechnical, geological, tectonic, and mineralogical investigations have been carried out to identify the soil composition and structure, as well as the geological processes operating in the area. Geochronological analysis has indicated an age ranging from 10,081±933 to 3490±473 years BP for the liquefaction features. The area in which these liquefaction features are found has undergone tectonic uplift and is affected by two faults. One of these faults was responsible for displacing the Holocene materials. The paleoearthquake responsible for this liquefaction has been analysed in terms of its peak ground acceleration (pga) and magnitude by back calculation analysis based on the cyclic stress and Ishihara methods. A range of 0.22–0.35 g was obtained for the pga, with the value of 0.30 g being selected as most representative. From this, an earthquake-modified Mercalli intensity of I MM=IX was estimated for the liquefaction site. The magnitude-bound method and energy-based approaches were used to determine the magnitude of the paleoearthquake, providing a moment magnitude M in the range of 6.4–7.2; M =6.8 is taken as the representative figure.

DYNAMIC STRUCTURAL EVALUATION OF PAVEMENT AND INFLUENCE OF SEED VALUES

Generally, backcalculation analysis based on FWD test data is an unstable procedure greatly influenced by several types of errors. These errors may be categorized by accuracy of forward analysis, measurement error, instability of backcalculation analysis, etc. Due to instability of the backcalculation algorithm, seed values of layer moduli highly influence backcalculation results, especially in case of thin asphalt concrete layer. In this paper, following verification of the accuracy of forward analysis, importance of dynamic backcalculation analysis will be explained and the use of Monte Carlo simulation for seed values of layer moduli to accurately backcalculate layer moduli will be presented.

Enhancing Backcalculation Procedures Through Consideration of Thickness Variability

Pavement structural performance and in situ structural capacity are evaluated by performing deflection testing and backcalculation analysis. Layer thickness information obtained from as-built data and core-bore logs is an essential input for this analysis and has significant impact on the backcalculated layer moduli. However, as-built records are not always available, and they provide general layer thickness information. Also, the number of cores and bores is limited because of their destructive nature. The current practice of backcalculation uses the common assumption that a pavement section has constant layer thickness, with allowable tolerance ignored, and that all variability in the measured deflection is related to variability in material stiffness. A pavement section is not expected to have identical thickness along its length. Also, pavement materials are undeniably nonhomogeneous and have variable stiffness along section length. However, this variability is expected to be within reasonable limits, especially for relatively new pavements constructed in accordance with stringent construction specifications and material properties and which exhibit similar distresses and deflections. A procedure was developed to account for the normal variability in layer thickness (allowable tolerance). This procedure is outlined and an implementation example is provided. The impact of ignoring the allowed variability in layer thickness on the backcalculation results, as well as on the design pavement moduli that are used in the rehabilitation analysis and design, is discussed.

The predictability of the epidemic of variant Creutzfeldt-Jakob disease by back-calculation methods.

We present a back-calculation analysis of the variant Creutzfeldt-Jakob (vCJD) epidemic in the UK to estimate the number of infected individuals and to explore the likely future incidence of the disease. The main features of the model are that the hazard of infection was assumed proportional to the incidence of BSE in the UK with allowance for precautionary control measures taken in 1988 and in 1996, and that the incubation period distribution of vCJD follows an offset generalized F distribution. Our results indicate that current the numbers of cases with onset up to 31 December 2000 data are broadly compatible with numbers of primary infections ranging from a few hundred to several million. However, if a very large number of persons were infected, the model suggests that the mean incubation period is likely to be well beyond the human lifespan, resulting in a disease epidemic of much smaller size (maximum several thousand). A sensitivity analysis indicates that our results are sensitive to the underreporting of vCJD cases before 1996. Finally, we show that, in the absence of a reliable test for asymptomatic infection, uncertainty in estimates of the total number of infections is likely to remain for at least several years, even if the number of clinical cases remains low.

Paleoearthquake evidence in Tenerife (Canary Islands) and possible seismotectonic sources

A series of clastic dikes and tubular vents were identified in southern Tenerife (Canary Islands). These features are the result of seismic liquefaction of a Holocene sand deposit, as the consequence of a high intensity paleoearthquake. The peak ground acceleration (pga) and magnitude of the paleoearthquake generating these liquefaction features were estimated by back calculation analysis. A representative value of 0.30 ± 0.05 g was obtained for the pga. From this, an earthquake intensity of IX was estimated for the liquefaction site. Magnitude bound methods and energy based approaches were used to determine the magnitude of the paleoearthquake, providing a moment magnitude M = 6.8. The zone in which the liquefaction structures are found has undergone tectonic uplift and is affected by two faults. One of these faults was responsible for displacing Holocene materials. Dating of the uplifted sand formation indicates an age of 10,081 ± 933 years, the liquefaction features ranging from this age to 3490 ± 473 years BP. This paleoearthquake was of much greater magnitude than those known historically. Faults with neotectonic activity are significant features that should be borne in mind when assessing the seismic hazards of the Canary Islands, presently considered as low and mainly of volcanic origin.

Predictability of the UK variant Creutzfeldt-Jakob disease epidemic.

Back-calculation analysis of the variant Creutzfeldt-Jakob disease epidemic in the United Kingdom is used to estimate the number of infected individuals and future disease incidence. The model assumes a hazard of infection proportional to the incidence of bovine spongiform encephalopathy in the United Kingdom and accounts for precautionary control measures and very wide ranges of incubation periods. The model indicates that current case data are compatible with numbers of infections ranging from a few hundred to several millions. In the latter case, the model suggests that the mean incubation period must be well beyond the human life-span, resulting in disease epidemics of at most several thousand cases.

INFLUENCE OF CORRELATION AMONG DEFLECTION DATA ON THE BACKCALCULATION RESULTS

A study on how correlation among FWD deflection data influences accuracy of the backcalculated pavement layer moduli is presented. FWD data were obtained from the Ministry of Construction, Road Test Section 609 and the data with stronger correlation were used in this study. Deflections without correlation and with similar correlation to the FWD data were generated using Monte Carlo simulation in order to investigate the effect of correlation on the backcalculation results. Furthermore, backcalculation analysis using theoretical deflection data with the same standard deviation but different correlations showed smaller variation in the backcalculation results for the deflection data with stronger correlation.

Falling-Weight Deflectometer Sensor Location in the Backcalculation of Concrete Pavement Moduli

Abstract This paper discusses the principles of two closed-form algorithms, ILLI-BACK and NUS-BACK, for backcalculating layer moduli of concrete pavements and their implications for selecting sensor locations in falling-weight deflectometer tests. It is found that sensor location has an effect on the results backcalculated using these two closed-form algorithms. Use of sensors at large radial distances may produce results with high variations since a small variation in the deflections recorded by these sensors will result in a significant change of layer modulus. Use of close sensor spacing will produce a ratio of deflections recorded by two consecutive sensors close to 1, leading to significant variations in backcalculation results in those cases where errors are involved in deflection measurements. The Strategic Highway Research Program (SHRP) FWD sensor configuration with sensors located at 0, 203, 305, 457, 610, 914, and 1524 mm is examined. Care should be taken in backcalculation analysis of concrete pavements using the SHRP sensor configuration in conjunction with the closed-form algorithms. Backcalculation results from deflections measured by SHRP and on Indiana US52 quantitatively confirm these findings.

Age and growth of the snipefish, Macrorhamphosus spp., in the Portuguese continental waters

Age and growth of the snipefish was studied based on samples collected in the Portuguese continental waters between 1996 and 1998. Analysis was conducted for two species, Macrorhamphosus scolopax and M. gracilis and for both species combined. Total length ranged from 5.5 to 18.2 cm for M. scolopax and from 5.4 to 17.3 cm for M. gracilis. Length–weight relationships were described for M. scolopax (a=0.00401; b=3.127), M. gracilis (a=0.00459; b=3.006) and both combined (a=0.00240; b=3.282). Age estimation, based on otolith observations, resulted in six and five years maximum age attributed to M. scolopax and M. gracilis, respectively. Back-calculation analysis based on a polynomial relation of the otolith radius on total length provided significantly smaller lengths-at-age compared with observed lengths. The von Bertalanffy growth curves fitted to observed lengths-at-age provided parameters of L∞=15.7 cm, K=0.654, t0=−1.066 for M. scolopax; L∞=14.2 cm, K=0.694, t0=−0.954 for M. gracilis and L∞=15.8 cm, K=0.470, t0=−1.408 for both species combined.

Parameters Back-Calculation for Concrete Pavement with Two Slab Layers

This paper presents a new procedure for back-calculating the properties of a concrete pavement with two slab layers using deflection measurements from nondestructive deflection testing. The two slab layers are first represented by an equivalent single slab layer based on the principle of equivalent flexural rigidity. In the back-calculation analysis, the pavement deflection response under load is evaluated using an analytical model for a slab supported on an elastic foundation. Employing a closed-form back-calculation algorithm, it is shown that the back-calculated equivalent radius of relative stiffness and subgrade modulus are unique and independent of the characteristics of the two slab layers. It follows that the equivalent flexural rigidity for the two slab layers is also unique. The next step employs a trial-and-error algorithm to back-derive the moduli of the two slab layers by matching the equivalent flexural rigidity. An upper bound and a lower bound to the modulus can be established for the slab layer with the higher modulus. Similarly, an upper bound to the modulus can be found for the slab layer with the lower modulus. Four numerical examples are presented to demonstrate the use of the proposed back-calculation method.

Back-Calculation of Parameters for Slab on Two-Layer Foundation System

Most highway and airport rigid pavements constructed today consist of a subbase layer, giving rise to a system of a concrete slab supported on a two-layer foundation. This paper makes use of the solution of a slab on a two-layer system to derive a closed-form procedure for back-calculation analysis of pavement parameters. A computer program called NUS-DEF3 to solve for surface deflections is developed as a subroutine in the back-calculation analysis. The algorithm for the closed-form back-calculation of this system is presented. This algorithm reduces a system of three equations with three unknowns to one single nonlinear equation. It differs from the conventional approach of searching for the best solution iteratively by means of the least-squares method, and gives unique closed-form solutions without the need to select an initial modulus to start with. Solutions to numerical examples of three typical slab-on-two-layer-foundation problems are presented.

Decreasing age at infection for homosexually acquired HIV in Italy: results of a back-calculation analysis.

The age-specific incidence of homosexually acquired HIV in Italy was examined, based on 3918 AIDS cases diagnosed by the end of 1994 and reported by the end of 1995 through the national surveillance system. Using a smoothed back-calculation analysis, the estimated median age at infection decreased over time, and HIV incidence among younger age groups peaked much later than among older age groups. These results support recent findings from other developed countries, and suggest that measures for preventing homosexual transmission of HIV are best targeted at younger age groups.

Closed-Form Back-Calculation of Rigid-Pavement Parameters

This paper describes the development of a solution of surface deflections for the problem of infinite-slab-on-elastic foundation and its use in back-calculation analysis. Numerical integration is employed to compute the surface deflections. The method adopted simplifies calculations and leads to easy application in back-calculation of rigid-pavement parameters. A microcomputer closed-form back-calculation program called NUS-BACK is developed for this purpose, using the surface deflections measured by nondestructive testing devices as input. A comparison is made between the proposed approach and a widely reported closed-form back-calculation algorithm called ILLI-BACK. The proposed closed-form back-calculation scheme presents a more general solution to the rigid-pavement-evaluation problem. NUS-BACK can be used with deflections measured by any type of nondestructive surface deflection measuring devices directly. A major advantage of NUS-BACK over ILLI-BACK is its superiority in handling deflection data with measurement errors. Numerical examples are presented to illustrate the differences between the two closed-form back-calculation solutions.

Use of FWD Data for Pavement Material Characterization and Performance

Conventionally used FWD backcalculation and pavement stress-strain computation procedures are based on linear static layered elastic theory. This paper presents a simple hypothetical case study in which the applicability of the assumptions made in the foregoing procedures is investigated using the finite-element method. The pavement displacements computed using static/dynamic falling-weight deflectometer (FWD) loading and constant and stress-dependent material properties were used as input for the backcalculation analysis. The assumed and backcalculated layer moduli were compared. The backcalculated asphalt concrete (AC) moduli values were within acceptable limits for all pavement sections studied except for the case of the thin AC pavement with a shallow rigid base. The subgrade moduli were consistently underpredicted; the base course moduli were both underpredicted and overpredicted. Widely used traffic-induced pavement strains that are related to pavement performance that were obtained under different loading and material property characterizations were also compared. Results indicate that the conventional procedures are not conservative, especially for thick AC pavement sections.