Scattered Wave Field Research Articles

Novel method to evaluate 3-D printed concrete quality using ultrasonic scatter energy techniques

ABSTRACT This study investigates the feasibility and effectiveness of a non-destructive ultrasonic testing method to evaluate the quality of 3-D printed concrete (3DPC) under varying printing conditions. To simulate different types of layer completions of 3DPC under real-world conditions, three printing schemes with different open times were adopted: no time gap, a 2-minute time gap, and a 5-minute time gap between printing subsequent layers. An air-coupled ultrasonic scanning system was used to measure multiple ultrasonic signals collected from three different 3DPC specimens. The signals were analysed in the frequency-wavenumber (f-k) domain to decompose forward propagating and scattered wave fields. The experimental results demonstrate that ultrasonic scatter energy increases with longer time gaps between subsequent layers in 3DPC. Additionally, the scatter energy was found to correlate well with defect density of 3DPC, assessed by digital image processing using image binarization methods. The findings of this study suggest that the ultrasonic scatter energy approach shows potential more thoroughly assess the quality of 3DPC structures because it interrogates the full volume of the materials and it provides superior damage sensitivity than ultrasonic velocity measurements do.

Surface wave manipulation by metasurfaces in unsaturated soil: theoretical study

Metasurfaces provide a promising solution for modulating low-frequency surface waves (SW) in sub-wavelength size. However, they were coupled with single-phase soil or saturated soil in previous investigations, rather than the more common unsaturated soil whose properties cannot be simply evaluated from single-phase and saturated soils. Otherwise, they would not be operational in the intended frequency range. In addition, the screening performance of metasurfaces in unsaturated soils is unknown to us due to the complex physical fields and constitutive relationships of unsaturated soils. In this work, an analytical formulation is proposed to investigate interactions between SW and an array of resonators located atop the free surface of unsaturated soil semi-space and to evaluate the vibration damping performance of the metasurface in single-phase, saturated and unsaturated soils. The incident and scattered wave fields are clearly captured by using the Green's functions of an unsaturated semi-space subjected to a harmonic excitation source. Based on the multiple scattering theory, the displacement of the total wave field as well as some complex phenomena (surface-to-bulk wave conversion) are obtained and also validated in a 2D finite element model. It is notable that incorporating a resonator with different natural frequency create a new bandgap, implying that we can broaden the bandgap by installing more resonators with different natural frequencies. We expect this analytical formulation could solve SW scattering problems in geotechnical engineering, and the system with a broad bandgap could provide a conceptual design for weakening SWs.

An experimental study of a quasi-impulsive backwards wave force associated with the secondary load cycle on a vertical cylinder

Steep wave breaking on a vertical cylinder (a typical foundation supporting offshore wind turbines) will induce slam loads. Many questions on the important violent wave loading and the associated secondary load cycle remain unanswered. We use laboratory experiments with unidirectional waves to investigate the fluid loading on vertical cylinders. We use a novel three-phase decomposition approach that allows us to separate different types of nonlinearity. Our findings reveal the existence of an additional quasi-impulsive loading component that is associated with the secondary load cycle and occurs in the backwards direction against that of the incoming waves. This quasi-impulsive force occurs at the end of the secondary load cycle and close to the passage of the downward zero-crossing point of the undisturbed wave. Wavelet analysis showed that the impulsive force exhibits superficially similar behaviour to a typical wave-slamming event but in the reverse direction. To monitor the scattered wave field and extract run-up on the cylinder, we installed a four-camera synchronised video system and found a strong temporal correlation between the arrival time of the Type-II scattered wave onto the cylinder and the occurrence of this quasi-impulsive force. The temporal characteristics of this quasi-impulsive force can be approximated by the Goda wave impact model, taking the collision of the Type-II scattered waves at the rear stagnation point as the impact source.

Numerical simulation of scattering of TWIPS by underwater air bubble

Abstract The interaction of water with the subsurface of sea-ice leads to the generation of air bubbles. This heterogeneity results in additional challenges for unmanned underwater vehicles (UUV) conducting active detection in the upper water column of the Arctic Ocean. Under excitation by a high-amplitude acoustic source, asymmetric oscillations of the bubble are generated due to the high compressibility of gas, which further leads to acoustic scattering showing nonlinear characteristics. The corresponding signals may interfere with or even mask the echoes from potential targets, which are often linear scatterers, ultimately impairing the UUV’s active sensing capabilities under the sea-ice. Twin Inverted Pulse Sonar (TWIPS) is an underwater detection technique consisting of sending two pulse signals of equal amplitude but with opposing phases, benefiting from the difference in the responses of the bubble and target and the resulting echo signals for the eventual distinguishing. In this study, a numerical modeling of underwater bubbles for the acoustic study is developed by making use of both multiphysics and moving mesh features of Comsol. Numerical simulations were conducted to investigate the nonlinear feature of acoustic scattering from air bubbles. These results are then compared with analytical results for verification. Monochromatic signals and TWIPS at different frequencies are used as excitation signals, and the response of spherical air bubbles and the resulting scattered wave field are calculated, compared, and analyzed.

Analytical seismic model for a tunnel with segmental liner buried in the half-space soil

In this paper, by using the wave function expansion (WFE) and the expansion of the cylindrical wave into plane wave (ECPW) methods, an analytical method for the dynamic response of a circular tunnel with segmental liner buried in the half-space soil to harmonic elastic waves is developed. The liner of the tunnel is supposed to consist of several segments and joints. Both the segments and joints are treated as open cylindrical shells, and the segment and joint shells together thus form an equivalent continuous shell (ECS) liner, and the thin shell theory is utilized to describe its vibration. The scattered wave field due to the presence of the tunnel and boundary of the half-space soil is divided into two parts, namely, the direct scattered wave field and secondary scattered wave field. The expressions for the direct scattered cylindrical waves in the soil is determined via the WFE method, while the secondary scattered waves form the boundary of the half-space soil are obtained by the ECPW method together with the application of the boundary condition along the soil surface. Applying the cylindrical shell theory on the ECS liner and using the Fourier series expansions for the variables and parameters of the ECS liner along the azimuthal direction together with introducing the Fourier component constitutive relation for the ECS liner, a system of equations for the Fourier component ECS displacements are derived with the differential equations for the ECS liner displacements. By using the system of equations, the expressions for the free and scattered wave fields and the continuity conditions at the interface between the liner and soil, the system of equations for the ECS liner coupled with the soil are derived. By using the developed analytical method for the tunnel, some results of the ECS tunnel under different incident waves are given.

A semi-analytical approach for site-city interaction under oblique incident SH waves

In this paper, a semi-analytical approach was proposed for investigating the site-city interactions (SCI). The site was modelled as a horizontal layered half-space, while the building was represented as a collection of shear wall structures fixed on the surface of half-space. The total wave field was considered as a combination of free field and scattering wave field generated by buildings, simulated by direct stiffness method and Green's function, respectively. The coupling between the site and the city is achieved through the displacement continuity conditions at the bottom of the building. Finally, the impact and some influencing factors of SCI effect on site and buildings were studied. It is found that the SCI effect has a significant impact on surface displacement and building response. The SCI effect typically reduces surface displacement near cities and the amplitude of relative displacement of buildings, while increases the seismic duration of buildings. However, this influence will be affected by the incident angle, building layout, building height, and building spacing, so these factors should be comprehensively considered when analyzing the SCI effect. Through the case studies, it is demonstrated that this method can quickly calculate SCI models with complex factors without being limited by the number and thickness of soil layers, incidence angles, and different sizes and spacing of buildings.

Response of semicircular canyons and movable cylindrical cavities to SH waves in anisotropic half-space geology

The development of tunnels or the laying of underground pipelines are essential engineering projects in modern society, and in canyon tunnels and underground pipeline projects, the surface motion and cavity edge motion have been topics of concern in ground vibration problems. We investigate the wave scattering problem in an elastic half-space anisotropic medium containing a semicircular canyon and a subsurface movable cylindrical cavity by using the wave function expansion method, the complex function method, and the mirror method. By deriving the governing equation and transforming it into the standard form of the Helmholtz equation satisfying the zero-stress boundary condition, we solve the corresponding displacement functions. Introducing a position correction coefficient, the scattered wavefield in a half-space anisotropic medium is constructed by the mirror method, which improves the problem of scattered wave source singularity in anisotropic half-space media. Then, combining the free boundary conditions with a Fourier series expansion method, we solve the unknown coefficients in the equations. The correctness of the method is verified by degenerating it to a classical analytic solution. Finally, using frequency- and time-domain analysis, we investigate the effects of the relevant parameters on the surface motion [Formula: see text], the dynamic stress concentration factor, and the displacement amplitude [Formula: see text]. The results indicate that rock anisotropy and the presence of semicircular canyons have a significant effect on the dynamic response of subsurface structures. This not only provides a theoretical basis for practical unlined tunnels or pipeline projects but also can provide a basis for seismic design of underground structures.

Propagation attenuation of elastic waves in multi-row infinitely periodic pile barriers: A closed-form analytical solution

Periodically arranged media exhibit attenuation zones for elastic waves, and the related periodic structures play a crucial role in the design of seismic isolation and vibration mitigation. From the perspective of wave theory, this paper presents a closed-form analytical solution for the propagation attenuation of elastic waves through infinitely periodic, multi-row pile barriers. The innovative approach begins by deriving the extended Graf’s addition theorem to transform wave potentials across arbitrary coordinate systems, overcoming the constraints of traditional formulas that limit pile centers to linear configurations. Subsequently, it completes the wave function expansion by utilizing the phase differences in the frequency domain of wave fields around different periodic elements, thus skillfully integrating the effects of incident and scattered wave fields. For the first time, this study delivers exact expressions for the scattering of various types of plane waves (SH, SV, and P) by multi-row pile barriers with an infinite periodic array, addressing the complexities of large pile numbers in previous theoretical studies. The proposed solution increases computational efficiency by tens of times and markedly reduces the majority of resource usage, improving the analysis of complex vibration isolation systems involving numerous piles. Building on the accuracy verification and convergence analysis, several numerical examples are conducted to explore the effects of pile row, pile spacing, and pile arrangement on the propagation attenuation. The findings elucidate the mechanisms driving vibration reduction design using periodic wave barrier, furthering its application in engineering structures.

Reconstruction of rough surfaces from a single receiver at grazing angle

AbstractThis article develops a method for recovering a one‐dimensional rough surface profile from scattered wave field, using a single receiver and repeated measurements when the surface is moving with respect to source and receiver. This extends a previously introduced marching method utilizing low grazing angles, and addresses the key issue of the requirement for many simultaneous receivers. The algorithm recovers the surface height below the receiver point step‐by‐step as the surface is moved, using the parabolic wave integral equations. Numerical examples of reconstructed surfaces demonstrate that the method is robust in both Dirichlet and Neumann boundary conditions, and with respect to different roughness characteristics and measurement noise.

Scattering of SH waves by elliptical cavity and type-III crack in deep anisotropic geology

Most of the underground rock formations are anisotropic, and the study of the dynamic response of anisotropic geology containing internal defects is necessary for the development of underground tunnels or caverns. In this paper, the wave function expansion method, the complex function method, and the Green's function method are used to solve the problem of scattering of SH waves in anisotropic rock in the presence of elliptical cavity and type-III crack. Boundary conditions for solving the problem are given using the conformal transformation method, and crack in the medium is constructed using the "crack cutting" technique. The scattered wave field generated by the crack is constructed based on the Green function method, and the displacement and stress fields in the model are obtained by the wave field superposition principle in the case of SH wave incidence. The dynamic stress concentration factor (DSCF) on the boundary of the elliptical cavity and the dynamic stress intensity factor (DSIF) at the crack tip are derived. The correctness of the method is verified by degenerating it to a classical analytic solution. Finally, the effects of the anisotropic strength of the rock mass, the dimensions of the cavern, and the incidence angle and wave number of the SH wave on the DSCF and DSIF are analyzed by numerical calculations in both the frequency and time domains. The results show that the anisotropy of the rock mass, the shape of the cavern and the defects of the surrounding medium have a great influence on the dynamic response of the underground structures, which should be given enough attention in the development and design of deep underground caverns or tunnels.

Acoustic wave propagation and scattering in visco-acoustic medium: Integral equation representation and De Wolf approximation

A visco-acoustic medium is an approximate representation of the absorption and attenuation characteristics of the actual earth medium, which will cause energy attenuation and velocity dispersion of seismic waves. The propagation law of scattered waves in viscoelastic media can be revealed through seismic wave forward simulation. However, the numerical simulation of scattered waves in a visco-acoustic medium using the De Wolf approximation method based on the Lippmann-Schwingr (L-S) equation has not been studied. Therefore, based on the Futterman dispersion relation, the mathematical expression of the integral equation of acoustic wave propagation and scattering in the visco-acoustic medium is derived. We combine the De Wolf approximation with the quality factor Q. The thin slab approximation and screen approximation methods are two realizations of the De Wolf approximation. The thin slab approximation and the screen approximation continuation operator in the viscous-acoustic medium are constructed and applied to the numerical simulation of the scattered wave field. The research results of the concave model and complex model indicate that due to the influence of medium viscosity, the energy of the deep reflected waves is weaker in the forward modeling records of the thin slab approximation method and screen approximation method, and the dominant frequency of seismic waves moves towards the low-frequency direction; Compared with the finite difference results, they only calculate one reflection, and there are no multiple wave signals in the seismic records. Finally, We discuss the thin slab approximation and the screen approximation method for detail around the division of the thickness of the thin slab, the selection of the reference frequency, and the non-uniformity of the medium.

Scattering from time-modulated subwavelength resonators

We consider wave scattering from a system of highly contrasting resonators with time-modulated material parameters. In this setting, the wave equation reduces to a system of coupled Helmholtz equations that models the scattering problem. We consider the one-dimensional setting. In order to understand the energy of the system, we prove a novel higher-order discrete, capacitance matrix approximation of the subwavelength resonant quasi-frequencies. Further, we perform numerical experiments to support and illustrate our analytical results and show how periodically time-dependent material parameters affect the scattered wave field.

GEOCHEMICAL CHARACTERISTICS OF MAFIC ROCKS IN THE STRUCTURE OF THE YENISEI-KHATANGA TROUGH AND THEIR BELONGING TO THE SIBERIAN TRAP PROVINCE

Consideration is being given to the geochemical composition of the rocks, representing the hidden part of the volcanic and intrusive material in the structure of the Yenisei-Khatanga Trough (YKT), in relation to its belonging to a large igneous province (LIP) of Siberia. The geochemical characteristics of mafic rocks, presenting in the sedimentary complexes of the YKT, correspond to three types of mafic rocks allocated to the Siberian LIP: Nadezhdinsky (low Ti), Morongovsky (low Ti), and, in limited quantities, Ivakinsky (rift-related high Ti). Based on the seismic data, there was constructed a deep structural-tectonic cross-sectional model, and there was considered the position of mafic intrusions in the sedimentary section in the western junction zone of the Siberian Platform and the Kara (Taimyr-Severozemelsky) orogen. The seismic data show an anomalous area in the lower crust and at the crust–mantle boundary immediately below the YKT depocenter, whose seismic section is characterized by a chaotic scattered wave field with no reflective boundaries.

Dynamic response of semi-cylindrical depression, cylindrical cavity and type-III crack to SH wave in half-space anisotropic media

In this study, the anti-plane dynamic response of an elastic half-space anisotropic medium containing surface semi-cylindrical depressions and internal cylindrical cavity and type-III crack is solved analytically. The wave function expansion method, the complex function method and the Green's function method can be used to effectively construct the free wave field equation and the scattered wave field equation in the case of SH wave incidence, in which the scattered wave field generated by the crack is constructed by the Green's function method and the "crack cut" method. For the scattered wave field generated by a circular cavity is constructed using the mirror method, where the positional offset coefficient in the mirror method of a half-space anisotropic medium is introduced, which well solves the problem of the asymmetry of the scattered wave field. Finally, the effects of anisotropic strength of the medium, SH wave incidence angle and dimensionless incident wave number on the surface displacement amplitude (|W|), dynamic stress concentration factor (DSCF) at the boundary of the circular cavity and dynamic stress intensity factor (DSIF) at the crack tip are investigated in both frequency and time domains under different working conditions, and conclusions different from those of isotropic medium are obtained, which provide some theoretical references for the earthquake-resistant design of the underground structure with canyon topography and the surface building.

Dynamic anti-planar characteristics of circular holes in laminated structures under the action of line source

Based on the complex variable function method and the wave function expansion method, the dynamic anti-plane characteristics of the circular hole in the laminated structure under line source excitation were studied. To deal with the interface problem within the laminated structure, the idea of “fit” is adopted to construct continuity conditions that satisfy displacement and stress. The circular hole boundary stress-free condition is used, the wave field is constructed using the mirror method, and the unknown coefficients of the scattered wave field are solved through Fourier series expansion, and finally the total wave field in the laminated structure is obtained. Taking the dynamic stress distribution of a circular hole in a laminated structure as a specific calculation example, the effects of changes in line source position, layer thickness, and medium hard-soft ratio on the dynamic stress concentration coefficient around the circular hole are discussed. The results show that when the line source load is applied directly above the circular hole and the lower layer is narrow, the dynamic stress concentration coefficient will have a sudden change compared with other situations. When other conditions are the same, under low, medium, and high-frequency wave fields, the dynamic stress concentration caused by different soft-to-hard ratios shows completely different rules. These rules can be used to better detect defects in laminated structures.

Research on the hydroelastic response of ice floes and wave scattering field

Abstract The marginal ice zone (MIZ) is the area between sea ice and open water, the structure of which is mainly determined by wave and ice interactions. Thus mastering the characteristics of MIZ is of great significance to the Arctic routes opening and the natural resources development. In this paper, the hydroelastic response of ice floes in waves is studied, a three-dimensional numerical wave tank is established based on the computational fluid dynamics (CFD) technology. The finite volume method (FVM) and finite element method (FEM) are respectively utilized for discrete fluid domain and ice domain. A mapping interface at the junction of the fluid and ice floes domains is created to perform data mapping by the shape function interpolation method and the least square method. This work presents a series of numerical simulations to study the fluid-solid interaction (FSI) of waves and ice floes. Under the given incident wave parameters, the vertical bending deformation of ice floes with different shapes under the excitation of waves, the effect of ice floes' deformation on the wave field are studied, and the effect of wave overwash on the transmitted wave field is emphasized. Results show that the shape of the ice floes significantly affects its elastic deformation and scattered wave field, and the wave overwash phenomenon attenuates the scattering wave.

Scattering kernel of an array of floating ice floes: application to water wave transport in the marginal ice zone

A radiative transfer model of water wave scattering in the marginal ice zone is considered. In this context, wave energy redistribution across the directional components of the spectrum as a result of scattering by the constituent ice floes is typically modelled via a scattering kernel describing the far-field directionality of the scattered wave field produced by a single floe in isolation. Recognizing the potential importance of the floe size distribution (FSD) on wave scattering, we propose an enhanced scattering kernel constructed from the far-field scattering pattern of a circular array of floes. This is achieved by solving the self-consistent multiple scattering of a time-harmonic plane wave by a large array of floating circular floes with radii sampled from a prescribed FSD. A fast multipole method is implemented to accelerate the numerical estimation of the solution. Simulations are then conducted to characterize the properties of the scattering kernel for a range of configurations. It is found that the scattering kernel obtained for a wide array has a large, narrow transmission peak in the forward direction, while it uniformizes low-amplitude scattered waves in other directions. An idealized application to radiative transfer theory is also considered.

An ultrasonic approach for characterising subsurface fractures in concrete

ABSTRACT An ultrasonic Rayleigh wave detection method is proposed to determine the geometrical characteristics of subsurface small-scale fractures in concrete. A three-dimensional observation system, including an inclined wedge ultrasonic device, is used to obtain the Rayleigh wave wide-angle data to exhibit the azimuth-dependent scattered wave field. The anisotropic characteristics of Rayleigh wave transmission coefficient are used to determine the distribution range and dip angle of fractures. Fracture models in concrete with different dip angles are designed, and the dip angle is correlated with the degree of attenuation (transmission coefficient) anisotropy. The transmission coefficient characteristics are presented in a random observing system. A focusing approach can be adopted to distinguish the subsurface fracture and to verify the reliability and flexibility of the surface wave approach in practice. The tendencies of experimental results are consistent with patterns obtained from numerical simulation. The proposed method has important application prospects for the non-destructive testing of complex invisible fractures in concrete.

Geodesic equations for guided wave helical path separation for a pipe bend

The sections of pipe bends are susceptible to wall thinning by flow-accelerated corrosion due to the sudden change in the fluid flow direction and velocity. Compared to existing screening approaches, Guided Wave Tomography (GWT) has been demonstrated to provide more accurate information about the defect. In GWT an inversion problem is solved, in which a forward model is used to predict a synthetic dataset for a given physical model. Two-dimensional (2D) forward models are preferred for the inversion scheme due to the feasibility of combining these with tomographic algorithms. Since 2D models resemble the GW propagation of a plate, they do not consider the cyclic nature of the pipe. To overcome this limitation, a robust helical path separation was introduced in Huthwaite and Seher (2015) for a straight pipe. However, it relies on time-reversing the measured wave field ϕ(t) as a function of the propagation distance xs,r from the source to the receiver. Although ray-tracing and grid-based methods are capable of computing the distance xs,r for complex geometries such as the pipe bend, they are complex and time-consuming. Hence, in this paper a straight forward approach is proposed to compute xs,r based on the pipe geometry and the geodesic equations of a torus. Then the computed distance xs,r is used for removing the helical path trajectories. Compared to the distance obtained by using the Hilbert envelope, the results show that the geodesic distances preserve the information of the wavefront of interest, including the focusing effect and the scattered wave field from a Hann-shaped defect. The technique is applied to experimental data and demonstrated to separate the wavefront of interest.

Farklı malzeme özelliklerine sahip gömülü nesnelerin yer radarı (GPR) yöntemiyle tespit edilmesi

GPR, which permits the capture of high-resolution subterranean data, has developed into a key geophysical technique for determining the depth, geometry, boundaries, and volumes of buried shallow objects. In this study, the detectability of the location, size, and physical property parameters of buried objects with the ground radar method was revealed by creating a laboratory environment in real field conditions. For this purpose, a realistic laboratory environment with a depth and length of 5 m was created on the filled soil material at the test site, and buried objects with different material properties were placed. In addition, by adding sand material to the middle part of the soil fill material in the test area, its situation in different layers was tried to be examined. GPR data were collected on the models using the RAMAC CU II system and a 500 MHz center frequency shield antenna. After processing the data, reflected/scattered electromagnetic (EM) wave fields on the radargram of a profile perpendicular to the buried objects were examined. In this way, the positions, sizes, physical properties (types) of buried objects along with their depths and their situations in different layer environments have been revealed. According to the results, the peak width of hyperbolas and the sizes of buried objects were determined on the processed radargrams. The types of buried objects and their situations in different layer environments are clearly revealed. The scattered wave field amplitudes of the plastic pipe (A and C regions) from the reflection coefficients are substantially lower than the scattered wave field amplitudes of the iron pipe (B region) from the buried objects. It is thought that the strong reflections extending from the C region to the deep on the radar are caused by the lead blocks in the plastic pipe.