Bojan B. Guzina

Seismic soil-structure interaction analysis by direct boundary element methods

Abstract Upon establishing the mathematical framework necessary for a proper understanding of the analytical theory, a regularized form of the conventional direct boundary integral equation formulation for three-dimensional elastodynamics is presented for a general anisotropic medium. Founded on the basis of a full decomposition of the Greens functions into regular and singular parts, the alternative boundary integral equation format is compact and without demand ingmathematical and numerical complexities such as Cauchy principal values. Extended to deal with general seismic soil-structure interaction problems in semi-infinite media, the formulation is implemented computationally together with a rigorous treatment of singular dynamic multi-layered viscoelastic half-space Greens functions and interfacial boundary tractions arising in typical soil-structure-foundation configurations. A set of new benchmark numerical results are included.

Impediments to predicting site response: Seismic property estimation and modeling simplifications

Abstract We compare estimates of the empirical transfer function (ETF) to the plane SH -wave theoretical transfer function (TTF) within a laterally constant medium for invasive and noninvasive estimates of the seismic shear-wave slownesses at 13 Kiban-Kyoshin network stations throughout Japan. The difference between the ETF and either of the TTFs is substantially larger than the difference between the two TTFs computed from different estimates of the seismic properties. We show that the plane SH -wave TTF through a laterally homogeneous medium at vertical incidence inadequately models observed amplifications at most sites for both slowness estimates, obtained via downhole measurements and the spectral analysis of surface waves. Strategies to improve the predictions can be separated into two broad categories: improving the measurement of soil properties and improving the theory that maps the 1D soil profile onto spectral amplification. Using an example site where the 1D plane SH -wave formulation poorly predicts the ETF, we find a more satisfactory fit to the ETF by modeling the full wavefield and incorporating spatially correlated variability of the seismic properties. We conclude that our ability to model the observed site response transfer function is limited largely by the assumptions of the theoretical formulation rather than the uncertainty of the soil property estimates.

Impediments to predicting site response

Abstract We compare estimates of the empirical transfer function (ETF) to the plane SH -wave theoretical transfer function (TTF) within a laterally constant medium for invasive and noninvasive estimates of the seismic shear-wave slownesses at 13 Kiban-Kyoshin network stations throughout Japan. The difference between the ETF and either of the TTFs is substantially larger than the difference between the two TTFs computed from different estimates of the seismic properties. We show that the plane SH -wave TTF through a laterally homogeneous medium at vertical incidence inadequately models observed amplifications at most sites for both slowness estimates, obtained via downhole measurements and the spectral analysis of surface waves. Strategies to improve the predictions can be separated into two broad categories: improving the measurement of soil properties and improving the theory that maps the 1D soil profile onto spectral amplification. Using an example site where the 1D plane SH -wave formulation poorly predicts the ETF, we find a more satisfactory fit to the ETF by modeling the full wavefield and incorporating spatially correlated variability of the seismic properties. We conclude that our ability to model the observed site response transfer function is limited largely by the assumptions of the theoretical formulation rather than the uncertainty of the soil property estimates.

Static fundamental solutions for a bi-material full-space

In this paper, the complete static response of two joined dissimilar half-spaces due to an arbitrary interior point load is derived. By means of a method of displacement potentials and integral transforms, a dual format of the solution in the form of a Hankel integral representation and algebraic closed-form expressions is presented. As illustrations, its analytical degeneration to benchmark solutions for a homogeneous medium as well as its variation under general geometric and material conditions are shown. The importance of the dual format of the bi-material solution in connection with the method of asymptotic decomposition to the development of a rigorous treatment of its dynamic counterpart is also demonstrated.

A linear sampling method for the inverse transmission problem in near-field elastodynamics

Elastic-wave shape reconstruction of buried penetrable scatterers from near-field surface measurements is examined within the framework of the linear sampling method. The proposed inversion scheme is based on a linear integral equation of the first kind whose solution becomes unbounded as the (trial) source point of the reference Greens function approaches the boundary of an elastic scatterer from its interior. We provide a comprehensive theoretical setting to establish (i) the necessary transmission problems for near-field elastodynamics and (ii) solvability properties of the postulated linear equation in the context of penetrable obstacles. A set of numerical results with simply and multiply connected elastic scatterers is included to illustrate the performance of the reconstruction technique.

A linear sampling approach to inverse elastic scattering in piecewise-homogeneous domains

The focus of this study is a 3D inverse scattering problem underlying non-invasive reconstruction of piecewise-homogeneous (PH) defects in a layered semi-infinite solid from near-field, surface elastic waveforms. The solution approach revolves around the use of Greens function for the layered reference domain and a generalization of the linear sampling method to deal with the featured class of PH configurations. For a rigorous treatment of the full-waveform integral equation that is used as a basis for obstacle reconstruction, the developments include an extension of the Holmgrens uniqueness theorem to piecewise-homogeneous domains and an in-depth analysis of the situation when the sampling point is outside the support of the obstacle that employs the method of topological sensitivity. Owing to the ill-posed nature of the featured integral equation, a stable approximate solution is sought via Tikhonov regularization. A set of numerical examples is included to demonstrate the feasibility of 3D obstacle reconstruction when the defects are buried in a multi-layered elastic solid.

Experimental validation of the Topological Sensitivity approach to elastic-wave imaging

In this study the method of topological sensitivity (TS) for solving inverse scattering problems, previously supported by a broad set of numerical simulations, is put to test experimentally with the focus on 2D obstacle reconstruction in a thin aluminum plate via elastic waves. To this end, the in-plane measurements of transient elastodynamic waveforms along the edges of the plate are effected in a non-contact fashion by a 3D laser Doppler vibrometer. Using an elastodynamic (time-domain) finite element model as a computational platform, the TS reconstruction maps are obtained and analyzed under varying experimental conditions. The results show significant agreement between the defect geometry and its reconstruction, thus demonstrating the utility of the TS approach as an efficient and robust solution tool for this class of inverse problems. For completeness, the experimental investigation includes a set of parametric studies geared toward exposing the effect of key problem parameters on the quality of obstacle reconstruction such as the (dominant) excitation frequency, the source aperture, and the duration of the temporal record. On the analytical front, it is shown that the use of a suitable temporal windowing function in specifying the L2 cost functional (that underpins the TS formulation) is essential from both theoretical and computational points of view.

ELASTIC SCATTERER RECONSTRUCTION VIA THE ADJOINT SAMPLING METHOD

An inverse problem dealing with the reconstruction of voids in a uniform semi-infinite solid from near-field elastodynamic waveforms is investigated via the linear sampling method. To cater to active imaging applications that are characterized by a limited density of illuminating sources, existing formulation of the linear sampling method is advanced in terms of its adjoint statement that features integration over the receiver surface rather than its source counterpart. To deal with an ill-posedness of the integral equation that is used to reconstruct the obstacle, the problem is solved by alternative means of Tikhonov regularization and a preconditioned conjugate gradient method. Through a set of numerical examples, it is shown (i) that the adjoint statement elevates the performance of the linear sampling method when dealing with scarce illuminating sources, and (ii) that a combined use of the existing formulation together with its adjoint counterpart represents an effective tool for exposing an undersam...

Effective Tool for Enhancing Elastostatic Pavement Diagnosis

The falling weight deflectometer (FWD) test is one of the most commonly used tools for nondestructive evaluation of flexible pavements. Although the test is intrinsically dynamic, the state-of-practice back-calculation techniques used to interpret the FWD records are primarily elastostatic based, partly because of the high computational cost of dynamic multilayered solutions. It has long been known that the foregoing discrepancy may lead to systematic errors in the estimation of pavement moduli in situations of pronounced inertial and resonance phenomena due to the presence of bedrock or seasonal stiff layer. In this investigation, a simple, yet effective algorithm is proposed that allows the static backcalculation analyses to perform well even when dynamic effects are significant. The technique is based on the use of the discrete Fourier transform as a preprocessing tool to filter the dynamic effects and extract the static pavement response from transient FWD records. With the filtered (i.e., zero-frequency) force and deflection values in lieu of their peak counterparts, the static backcalculation can be further performed in a conventional manner, but free of inconsistencies associated with the neglect of dynamic effects. Results based on synthetic deflection records demonstrate a marked improvement in the elastostatic prediction of pavement moduli when the proposed modification is used. The filtering algorithm can be implemented on a personal computer as a preprocessor for the conventional FWD data interpretation, requiring only a minimal increase in the computational effort to backcalculate the pavement moduli.

Three-dimensional wave propagation analysis of a smoothly heterogeneous solid

Abstract A method of analysis is presented for three-dimensional wave propagation problems of a vertically-heterogeneous half-space with a linear shear wave velocity profile. With the aid of a displacement-potential representation, Hankel transforms and Fourier decompositions, the dynamic response of the semi-infinite solid to an arbitrarily distributed buried source is shown to admit integral representation in terms of modified Bessel functions. Specific aspects of the problem such as the multiple poles along the inversion path on the complex plane and the characteristics of the wave propagation in the vertical direction are elucidated. Apart from its intrinsic interest, the solution can be degenerated to ring-load and point-load Greens functions which are fundamental to boundary integral equation formulations.