This is a subcontract to develop methodologies for elastic and viscoelastic forward modeling and inversion, to estimate the stiffness of human carotid arteries.

This collaborative project is with Professor Vladimir Druskin or WPI and Elena Cherkaev of University of Utah. Following is the TENTATIVE combined abstract: Krylov subspace algorithms are well established tools for matrix function computations. The solution of fractional PDEs plays prominent role among numerous applications of the these algorithms thanks to their algebraic elegance and computational efficiency. They reduce the solution of fractional PDEs to the discretization of standard second order problems and consecutive application of well developed linear algebraic methods. However, the matrix function approach has two major drawbacks. It does not allow space dependence of fractional power and does not scale well for very large problems. If the former is rather specific for fractional derivative PDEs, the latter is generic for the most of large scale matrix function computations. The foundation of the proposed research program is recent multiscale reduced order (ROM) approach for massive wave propagation problems. Similarly to many multiscale methods the computational domain discretized on a fine grid is split into coarse cells. The novelty is to use sparse network ROM realizations to approximate the DtN maps of the coarse cells, resulting in sparse compressed graph-Laplacian type of approximation of the entire problem. The sparse realization is obtained with the help of matrix-valued Stieltjes continuous fractions, hence the name `Multiscale Stieltjes fraction reduced order model (MSSFROM). The sparse structure of the MSSFROM allows scalable implementation on modern high-performance platforms without significant limitations on the problem complexity that was in particular critical for elastic wave propagation problems in heterogeneous anisotropic media.

The Federal Highway Administration (FHWA) has developed mechanistically based performance comparison models to evaluate the cracking and rutting performance of asphalt pavement mixtures. These models form the basis of an asphalt performance comparison development effort and are being implemented into a FlexPAVETM software program for analyzing pavements and predicting distress. In this research study, NCSU will assess current asphalt pavement cracking models that can be applied to reflective cracking and further research, develop, calibrate, train, and validate a mechanistically based asphalt pavement reflective cracking model that is consistent with existing FlexPAVETM methodology and performance tests; incorporate it into the FlexPAVETM software and the FlexMATTM and FlexMIXTM data analysis tools, and assess and incorporate run time improvements to the model, software, and analysis tools.

North Carolina current allows two basic types of pavement design on NCDOT roadways; 1) those whose structural capacity comes primarily from asphalt concrete (flexible pavements) and 2) those whose structural capacity comes primarily from portland cement concrete (rigid pavements). These designs have been used successfully in many applications throughout the State; however, they utilize a large amount of relatively expensive and difficult to produce materials (asphalt concrete and portland cement concrete). A third technique, inverted pavement design that requires less of these materials and is purported to provide equivalent or superior performance is not currently allowed with the NCDOT specifications. Inverted pavements consist of a 2 - 3.5-inch asphalt concrete surface, supported by a 6 ������������������ 10-inch layer of unbound aggregate base and then by 8 - 12 inches of a cement treated subbase. Literature and experience have shown that these pavements can be designed and used in many applications at a substantial cost savings. However, there are many unknowns when directly adopting design specifications from elsewhere as local materials, practices, and experience may not be fully accounted for. Thus, there exists a need to gain state specific experience in the engineering and performance of these structure before their adoption can be considered.

The proposed five-year effort involves collaborating with Mayo Clinic and Duke University to develop new methodologies to estimate arterial stiffness using ultrasound measurements from acoustic radiation force (ARF) excitation of carotid artery. NCSU's portion of the effort would be to develop efficient forward algorithms to computationally simulate wave propagation in the artery and inverse modeling techniques to estimate the arterial properties from ultrasound measurements. In addition, NCSU would work closely with Mayo Clinic to optimize the data acquisition geometry and procedure.

The project is aimed at estimating material properties of layered media with the help of PI's recently developed techniques of guided wave simulations and inversion, combined with the extensive expertise of the co-PI in uncertainty quantification and Bayesian inversion. At the end, the project is expected to result in methodologies applicable for characterizing layered media ranging from geotechnical sites, composite laminates, thin films on substrates, immersed and buried pipelines as well as human arteries.

The dynamic modulus (|E*|) is the main parameter that is used in modeling pavement responses in the Pavement ME Design program. Therefore, the rehabilitation design feature of the Pavement ME program requires the determination of the |E*| values of existing asphalt layers. The Pavement ME guide recommends three different approaches to determine the |E*| values of existing asphalt layers. The Level 1 and Level 2 approaches require the use of the Witczak������������������s predictive equation, which could result in up to 100 percent error. The Level 3 approach also has a high probability of yielding erroneous results because it is based on pavement condition survey data.

NCDOT continues to face significant challenge to ensure that the foundations of bridges are strong enough for public safety. One of the primary issues is scour around the supporting pile foundations, potentially compromising the integrity of the foundation system. Given this, combined with the fact that many foundation records are missing, there is a critical need to estimate the embedded length of pile foundations. Estimating the embedded pile depth would also cater to the need to estimate the strength of existing foundations for reuse, which is also promoted by FHWA and actively pursued by NCDOT.

This is a proposal for a two-year project for the Alaska Department of Transportation and Public Facilities (AKDOT&PF), for the development and implementation of non-destructive testing techniques to determine the length of piles supporting bridge substructures. Fifty two bridges in AKDOT&PF������������������s inventory have undocumented foundation characteristics (U-bridges); the most common unknown variable is pile length. This complicates evaluation of substructure vulnerability to scour, which is a mandatory evaluation at all bridges, per the Federal Highway Administration (FHWA).

Asphalt mixtures used in pavement construction are required to meet the NCDOT moisture sensitivity specifications. The current lab procedure to test moisture sensitivity uses conditioning procedures as per modified AASHTO T283. This is a fairly lengthy procedure involving specimen preparation, sample saturation, conditioning the samples for 24 hours, and then indirect tension testing. The variability involved in TSR test results is also observed to be high. The current test method uses the ratio of indirect tensile strength of the conditioned and unconditioned specimens (TSR). The indirect tensile strength is a qualitative measure of the moisture sensitivity. There is a need for a quicker test method(s) that is quantitative and has less variability. The new test should also lend itself to measure intrinsic properties such as the dynamic modulus of asphalt concrete that will allow inferior mixtures to be eliminated even though they may pass the TSR test.