Rayleigh Wave Velocity Research Articles

Nonlinear Ultrasonic Second Harmonic Assessment of Concrete Defects Based on Embedded Piezoelectric Sensors

ABSTRACT In this work, the second harmonic generation (SHG) technique based on embedded piezoelectric (PZT) sensors is developed for the defect assessment of concrete samples. Three different imperfection forms of concrete including internal capillary void during the curing process, cracking damage due to compression, and bending loads are examined and analyzed. Clear second harmonics are observed by Fourier transform of time domain signal, and the square of fundamental signal amplitude shows a linear relation with the second harmonic amplitude as theoretically expected. The nonlinear parameter presents a good distinction for samples in different states of three cases, indicating the well-round feasibility of SHG technique based on embedded sensors. In addition, the nonlinear parameter presents an excellent correlation with the variation of internal capillary void and cracks in concrete. The high sensitivity of the developed SHG technique is further validated through a comparison between the nonlinear parameter and two traditional linear parameters, namely the phase velocity of Rayleigh wave and the resonance frequency of vibrations. Experimental results in this study demonstrate that the embedded sensors are promising for the nonlinear ultrasonic nondestructive evaluation of concrete structures, particularly as a low-cost alternative of commercial ultrasonic transducers.

SCoda and Rayleigh Waves From a Decade of Repeating Earthquakes Reveal Discordant Temporal Velocity Changes Since the 2004 Sumatra Earthquake

AbstractTemporal changes in the subsurface seismic velocity structure reflect the physical processes that modulate the properties of the media through which seismic waves propagate. These processes, such as healing of the surface damage zone and deep crustal deformation, are described by similar functional forms and operate on similar timescales, making it difficult to determine which process drives the observed changes. We examine earthquake‐induced velocity changes using the measured lag‐time time seriesτ(t) of the repeating earthquake sequences since the 2004Mw9.2 Sumatra and 2005Mw8.6 Nias earthquakes. TheScoda velocity changes (δVS, equivalent to−τS) recover steadily during the 2005–2015 period. The Rayleigh wave velocity changes (δVLR, or−τLR) undergo transient recovery, followed by a strongδVLRreduction in late 2007.δVSrecovery is most likely driven by deep processes, whereas the temporal breaks inδVLRrecovery in 2007 mostly reflect surface damage and healing induced by the strong ground motions of the 2004Mw9.2, 2005Mw8.6, 2007Mw8.4, andMw7.9 Bengkulu and 2008Mw7.3 Simeulue earthquakes. The observed differences between the temporal variations inδVSandδVLRcan distinguish deep processes from healing of the surface damage zone.

Subsonic to Intersonic Transition in Sliding Friction for Soft Solids.

We perform friction experiments between a compliant gel and a rigid cylinder at sliding velocities comparable to the Rayleigh wave or secondary wave velocity of the gel. We find that, when the sliding velocity exceeds the wave velocities, the contact state transitions from Hertzian like to flat punch like, resulting in the breakdown of the lubricating oil film and the abrupt increase in the friction coefficient. We succeed in deriving theoretical solutions for the contact pressure distributions and the deformation profiles in the presence of friction, which are consistent with our experimental observations.

The characteristics of high speed crack propagation at ultra high loading rate

It is important to understand the characteristics of high speed crack in brittle materials under ultra high loading rate forming through impact loading condition, which is important for understanding the impact damage evolution of ceramics and solid explosives. In this paper, a lattice spring model, which can accurately show the mechanical properties of brittle materials, is used to study the evolution law and mechanism of crack path and crack velocity in brittle materials under ultra high loading rate. This model uses the quantitative parameter mapping method proposed by Gusev to solve the spring stiffness coefficient of the model accurately, and the fracture criterion of the model based on the energy balance principle of Griffith is set up. Simulations show that the path of high speed crack behave the evolution process of a single crack and then micro-branching crack and bifurcation crack finally under the influence of ultra high loading rate. The crack propagation distance between the beginning and the bifurcation decreases with the increase of the loading rate; the crack bifurcation is not immediately after the crack initiation, but as the crack propagation speed reaches the critical value, the expansion path produces more secondary cracks, and then the crack is bifurcated. With the increase of loading rate, the average velocity of cracks gradually increases in three stages, but it shows a different variation after reaching the stable value. In the single crack stage, the steady average velocity is 0.584 times the Rayleigh wave velocity (CR), and there exists only a very small velocity oscillation; the steady value of the average crack velocity corresponding to the differential fork phase is 0.5 times the Rayleigh wave velocity, accompanied by a certain oscillation; The average speed of the stable crack corresponding to the bifurcation stage is much higher than the value of the first two stages, and it can reach 0.638 times the Rayleigh wave speed. It is also accompanied by obvious speed oscillation. The study of the propagation of cracks under different loading rates can predict the internal crack growth rate, propagation direction, and extension distance of brittle materials such as ceramics and rocks.

Propagation of Rayleigh waves in unsaturated porothermoelastic media

SummaryBased on the frame of elastic theory for unsaturated porous medium, considering the influence of thermal effect, the propagation characteristics of Rayleigh wave in unsaturated porous media are studied. Firstly, the thermoelastic wave equations for three‐phase porous media are established, in which the mass balance equations, generalized Darcy law, momentum balance equations, and generalized non‐Fourier heat conduction law are taken into account. Secondly, through theoretical derivation, the dispersion equation of Rayleigh wave for unsaturated porothermoelastic media is given by introducing the potential functions. Finally, the variations of the phase velocity of Rayleigh wave are analyzed with numerical examples. The results show that the thermal conductivity has little effect on the phase velocity of Rayleigh wave. The phase velocity of Rayleigh wave increase with increasing of the thermal expansion coefficient and media temperature.

The effect of the tortuosity of fluid phases on the phase velocity of Rayleigh wave in unsaturated porothermoelastic media

Based on the frame of elastic theory for unsaturated porous medium, considering the influence of the thermal effect, the effects of the tortuosity of fluid phases on the phase velocity of Rayleigh wave in unsaturated porous media are studied. Firstly, the thermoelastic wave equations for three-phase porous media are established by taking into account the effect of the tortuosity of fluid phases. Secondly, through a theoretical derivation, the dispersion equation of Rayleigh wave for unsaturated porothermoelastic media is given by introducing the potential functions. Finally, the variations of the phase velocity of Rayleigh wave are analyzed with numerical examples. The results demonstrate that the phase velocity of Rayleigh wave is not just related to the frequency but also affected by the tortuosity of pore-fluid. The effect of the tortuosity of pore-liquid on the phase velocity of Rayleigh wave is more significant than that of the tortuosity of pore-gas on the phase velocity of Rayleigh wave.

May Rayleigh waves propagate with group- and phase-velocities of opposite sign in the valley of Mexico City?

Con base a la fórmula que determina la velocidad de grupo de las ondas sísmicas y utilizando resultados previamente publicados por los autores, se discute en forma teórica la ocurrencia de velocidades de grupo negativas de ondas de Rayleigh en modelos simplificados de la cuenca del Valle de México.

Пространственное распределение коэффициента анизотропии в верхней мантии Европы

The radial (transversal) anisotropy of the Earth’s upper mantle was found by comparing the velocity sections of transverse waves obtained by inverse of the dispersion curves of Rayleigh and Love waves. Information on variations in anisotropy with depth was obtained from dispersion curves on fairly uniform oceanic paths. In the oceanic mantle the SH wave velocities obtained from the Love wave data are greater than the SV wave velocities determined from Rayleigh waves, so that the anisotropy coefficient is positive and is about 4% under the Moho boundary and decreases to zero at a depth of about 200 km. The information about the anisotropy of the continents is much more scarce and often contradictory due to a strong lateral inhomogeneity of the crust and upper mantle of the continents. In the European region, some authors reveal the zones where VSV>VSH in the upper mantle, whereas some others confirm VSH>VSV to be everywhere. The uncertainty in the observed values of the anisotropy coefficient is explained by the fact that it was always determined from the results of the Rayleigh and Love wave velocity tomography carried out on the basis of different samples of paths. Accordingly, the values of the SH and SV wave velocities turned out to be averaged over different regions, which led to errors in the estimates of the anisotropy coefficient. To reduce these errors, we proposed an alternative method for estimating the spatial distribution of the anisotropy coefficient: to estimate the anisotropy co-efficient in the beginning at each path and then to fulfill the tomographic inversion for this coefficient. Preliminary results on the distribution of the anisotropy coefficient in the upper mantle of Europe were presented according to an earthquake and seismic noise. However, analysis of the anisotropy coefficient values obtained from the earthquake data and seismic noise has shown that those obtained from noise are usually underestimated. Therefore, in the present study, we used only the data obtained from earthquakes. It was shown that the anisotropy coefficient under the continental part of the European region is close to zero but two areas where VSV>VSH are detected – in the central part of EEP and in southern Italy. In both cases, the negative values of the anisotropy coefficient are observed within the interval of ~60–100 km depth.

A single Rayleigh mode may exist with multiple values of phase-velocity at one frequency

SUMMARYOther than commonly assumed in seismology, the phase velocity of Rayleigh waves is not necessarily a single-valued function of frequency. In fact, a single Rayleigh mode can exist with three different values of phase velocity at one frequency. We demonstrate this for the first higher mode on a realistic shallow seismic structure of a homogeneous layer of unconsolidated sediments on top of a half-space of solid rock (LOH). In the case of LOH a significant contrast to the half-space is required to produce the phenomenon. In a simpler structure of a homogeneous layer with fixed (rigid) bottom (LFB) the phenomenon exists for values of Poisson’s ratio between 0.19 and 0.5 and is most pronounced for P-wave velocity being three times S-wave velocity (Poisson’s ratio of 0.4375). A pavement-like structure (PAV) of two layers on top of a half-space produces the multivaluedness for the fundamental mode. Programs for the computation of synthetic dispersion curves are prone to trouble in such cases. Many of them use mode-follower algorithms which loose track of the dispersion curve and miss the multivalued section. We show results for well established programs. Their inability to properly handle these cases might be one reason why the phenomenon of multivaluedness went unnoticed in seismological Rayleigh wave research for so long. For the very same reason methods of dispersion analysis must fail if they imply wave number kl(ω) for the lth Rayleigh mode to be a single-valued function of frequency ω. This applies in particular to deconvolution methods like phase-matched filters. We demonstrate that a slant-stack analysis fails in the multivalued section, while a Fourier–Bessel transformation captures the complete Rayleigh-wave signal. Waves of finite bandwidth in the multivalued section propagate with positive group-velocity and negative phase-velocity. Their eigenfunctions appear conventional and contain no conspicuous feature.

Propagation of Rayleigh waves at the boundary of an orthotropic elastic solid: Influence of initial stress and gravity

Propagation of harmonic plane waves is considered in an orthotropic elastic medium in the presence of initial stress and gravity. Roots of a quadratic equation define the propagation of one quasi-longitudinal wave and one quasi-transverse wave in a symmetry plane in this medium. These two waves are coupled in the identical phase to define the propagation of Rayleigh waves at the boundary of the medium. Two conditions at the stress-free boundary translate into a complex frequency equation, which explains the dispersive behavior of this Rayleigh wave. For the presence of radical terms, this complex equation is rationalized into a real algebraic equation. Only one root of this algebraic equation satisfies the mother frequency equation and hence represents the propagation of dispersive Rayleigh waves at the boundary of the orthotropic solid. The influence of initial stress and gravity on velocity and polarization of Rayleigh waves is observed through a numerical example.

Effects of Two-Temperature, Rotation, Initial Stressed Magnetic Field on Rayleigh Wave in Half-Plane

Abstract In the present paper, we consider the governing equation for generalized thermoelastic media under the effect of magnetic fleld, rotation, initial stress, and two-temperature parameter for Rayleigh wave in half-space. The secular equation of Rayleigh wave is also deduced using surface wave solution, which also satisfy the radiation condition for thermally insulated/isothermal surface. The velocity and amplitude attenuation factor of Rayleigh wave is also computed for a particular material. The effect of two-temperature, rotation, and initial stress parameters on velocity of propagation and amplitude attenuation factor is shown graphically.

Tomographic Imaging of the Agung-Batur Volcano Complex, Bali, Indonesia, From the Ambient Seismic Noise Field

The Agung-Batur Volcanic Complex (ABVC), part of the Sunda volcanic arc, is the source of some of the most hazardous volcanic activity in Indonesia. The ABVC has undergone many small (VEI 1-2) eruptions since historical records began in the early 19th century, but Mt. Agung has experienced much larger (VEI 5) eruptions, both in the modern (1963) and historical (1843) eras, as well as several times during the past 2000-3000 years. The 1963 eruption caused more than 1000 deaths, and a more recent eruption in 2017 caused the evacuation of 140,000 people. Delineating the magma structure beneath ABVC is an important first step in understanding the physics of these eruptions. This paper presents the first local-scale study of Rayleigh wave group velocity structure and the seismic velocity structure beneath the ABVC using ambient seismic noise tomography. Seismic data were collected using 25 seismometers deployed across the ABVC during early January to March 2019. The local seismic network provides good resolution beneath both Mt. Agung and Mt. Batur. We obtained 158 Rayleigh Green’s Functions, extracted by cross correlating noise simultaneously recorded at available station pairs. We used sub-space inversion to calculate group velocity at different periods and to estimate the lateral variations in group velocity for given periods. 2-D tomographic maps obtained from the inversion of the group velocity of Rayleigh waves clearly showed some pronounced velocity anomalies beneath the ABVC. We applied the Neighbourhood Algorithm (NA) technique to invert the Rayleigh wave dispersion curves to obtain shear wave velocity (Vs) vs. depth profiles. These profiles indicate a low Vs of about 1 km/s underlying the volcanic complex between Mt. Agung and Mt. Batur at depths up to 2 km, which we suggest is due to a combination of low-Vs volcanic deposits as well as a shallow hydrothermal fluids system associated with magma fluids and/or gases produced by magma intrusion at depths > 7 km.

Seismic characterization of a clay-block rupture in Harmalière landslide, French Western Alps

SUMMARYIn late June 2016, the Harmalière clayey landslide (located 30 km south of the city of Grenoble, French Alps) was dramatically reactivated at the headscarp after a 35-yr-long period of continuous but limited activity. The total involved volume, which moved as sliding blocks of various sizes, was estimated to be about 2 × 10 6 m3. Two seismometers were installed at the rear of the main headscarp in August 2016, on both sides of a developing fracture delineating a block with a volume of a few hundred cubic metres. For 4 months, they continuously recorded seismic ambient vibrations and microearthquakes until the block broke. Five seismic parameters were derived from the monitoring: the cumulative number of microearthquakes (CNe), the seismic energy (SE), the block resonance frequency (fB), the relative variation in Rayleigh wave velocity (dV/V) deduced from noise cross-correlations between the two sensors and the associated correlation coefficient (CC). All parameters showed a significant precursory signal before the rupture, but at very different times, which indicates the complexity of the rupture mechanism in this clay material.

Shear wave velocity and radial anisotropy structures beneath the central Pacific from surface wave analysis of OBS records

The central Pacific plate is an ideal area to study the dynamics of the lithosphere-asthenosphere system, as this region is far away from other dynamics systems, such as subduction zones and volcanic hotspots of mantle plumes, and has experienced simple oceanic evolution. In this study, we collect three-component continuous seismic data and differential pressure gauge data recorded by 15 broadband ocean bottom seismometers (OBSs) from the NoMelt experiment. We process continuous seismic noise data to obtain phase velocities of the fundamental (6-30 s) and first high (5-11 s) mode Rayleigh waves and fundamental mode Love waves (5-12 s). We apply a two-plane-wave method to teleseismic Rayleigh waves to obtain the fundamental mode phase velocities at 20-150 s periods, and apply high-resolution linear Radon transform to teleseismic Love waves to obtain phase velocities for the fundamental mode Love waves at 28-48 s periods. Then, we jointly invert the average phase velocities of Rayleigh and Love waves to construct 1-D isotropic shear wave velocity and radial anisotropy from the seafloor to 150 km depth beneath the NoMelt region. Our 1-D model shows a low velocity zone (LVZ) beneath a high velocity lid. By comparing our results with the predictions of partial melt models, we suggest the LVZ is attributed to the presence of a small amount of melt in the asthenosphere. Strong radial anisotropy (5-6%) is observed in the crust. But the mantle lithosphere is characterized by weak radial anisotropy (< 1%), consistent with the corner mantle flow history at the mid-ocean ridge during the formation of new oceanic plates. Strong radial anisotropy (4-5%) is observed in the asthenosphere, which is consistent with the global surface wave tomography results and numerical simulation studies, reflecting the strong shear strain of asthenosphere related to the motion of oceanic plate over the underlying asthenosphere.

Study on fracture process zone near mode II and mode III dynamic crack tip

Determination of the configuration and size of fracture process zone (FPZ) at dynamic crack tip is still a problem unsolved completely at present. In this paper, based on elastic dynamic theory and stress functions, a method for evaluating the configuration and the size of FPZ is proposed and the feasibility of the method is demonstrated. The configuration and size of the FPZ near the crack tip in dependence on crack propagation velocity are determined by using the Von Mises and Tresca criteria, respectively. Numerical results show that FPZ at mode II and mode III dynamic crack tip is distributed symmetrically with respect to crack plane and increases with the crack propagation velocity. FPZ changes more rapidly when the Rayleigh wave velocity is approached. The effects of Poisson’s ratio on FPZ are discussed. Analysis reveals an intricate dependence on Poisson’s ratio in plane strain condition.

Application of a general expression for the group velocity vector of elastodynamic guided waves

In the field of elastodynamic guided waves, the calculation of the group velocity vector is closely tied with the numerical techniques used to calculate the waveguide's dispersion curves. These techniques often require mode sorting – which can be difficult for densely packed dispersion curves – or access to large matrices. In this paper, we implement Biot's general energy expression in order to derive the group velocity vector of elastodynamic guided waves. We demonstrate the flexibility and applicability of the expression by using it to calculate the group velocity of partial waves, Rayleigh waves, and Lamb waves. We also use it to calculate the skew angle of a guided wave in a transversely-isotropic plate and suggest how it may be used for 2D-arbitrary cross-sections. Explicit expressions for the group velocity are provided for each of these applications, thereby allowing insightful comparison between them. In particular, we compare the group velocity of Lamb waves and the partial waves of which they are composed. The primary benefit of the proposed expressions is that they enable the group velocity to be accurately calculated at a specific frequency and a specific wavenumber by using only the material parameters and the wave's displacement profile. More generally though, they give analysts more options for calculating group velocity and skew angle.

Surface wave surveys for imaging ground property changes due to a leaking water pipe

This study demonstrates the use of Multi-channel Analysis of Surface Waves (MASW) to measure changes in Rayleigh wave velocity relating to both the initial trench construction and subsequent simulated failures (water leaks) of a buried water-pipe. The MASW field trials were undertaken in conjunction with a wider suite of geophysical monitoring techniques at a site in South-west England, within an area of clayey sandy SILT. The Rayleigh wave velocity through a soil approximately equals the shear wave velocity, which in turn is predominantly dependant on the shear modulus of the soil (G) and this can be inferred to give a measure of the relative strength of a soil. It is proposed that the time-lapse measurement of Rayleigh wave velocity may be used to monitor ongoing changes in soil strength and therefore the MASW technique could perform a significant role in monitoring the initiation/progression of any internal processes within a geotechnical asset, before they would otherwise be identified through visual inspection alone.

Insight Into the Wave Scattering Properties of the Solfatara Volcano, Campi Flegrei, Italy

In this study we inferred statistical properties related to the scatterers within a volcanic area, the Solfatara crater, located in the Campi Flegrei caldera, Southern Italy. We analyzed active seismic data recorded in a 3D geometry during the first RICEN experiment, held in September 2013. After extraction of seismic sections, we evaluated the coherent and incoherent intensities, averaging over sources and receivers sharing the same source-station distance. We thus computed the ratio between the two intensities over the surface waves, which is almost sensitive to the scattering mean free path in the area. We found that the intensity ratio exponentially decreases with distance, while the final plateau can be recognized only if the average is performed moving sources and receivers over the whole domain of investigation. We report that the scattering mean free path exhibits a small increase between 7.5 Hz and 10 Hz from 50 m to 60 m, and then it decreases down to about 10 m, at a frequency of 21.5 Hz. Since the scattering mean free path can be determined assuming a constant Rayleigh group velocity of 65 m/s, we modelled it as generated by a single scatterer of cylindrical shape in a homogeneous medium. We found that the average size of the scatterer is about 10 m, with a small increase of the Rayleigh wave velocity inside the scatterer. The scatterers are here interpreted as regions richer in water with respect to the background and eventually due to the condensed steam running below the investigated area.

Feasibility of freeze-thaw damage analysis for asphalt mixtures through dynamic nondestructive testing

Invisible freeze-thaw damage is commonly associated with many durability problems in asphalt pavement. Therefore, the freeze-thaw damage of asphalt pavement should be detected in situ to evaluate the pavement condition. This study aimed to explore the feasibility of freeze-thaw damage analysis for asphalt mixtures through dynamic nondestructive testing. Free–free resonance testing method and Rayleigh wave testing technology were selected for this analysis. Natural frequency, damping ratio, and Rayleigh wave velocity were used to describe the freeze-thaw damage. Optimal experimental parameters were proposed by analyzing the effect of test parameters on the stability and accuracy of results. Variations in the dynamic parameters of asphalt mixtures under freeze-thaw action were analyzed. Results showed that natural frequency, damping ratio, and Rayleigh wave velocity changed regularly during the freeze-thaw process and could be used to analyze the damage after freeze-thaw cycles. The effects of different types of asphalt mixture on the dynamic test parameters during the freeze-thaw process were also examined. Nondestructive testing revealed that the type of asphalt and the gradation of asphalt mixture affected the damage degree of freeze-thaw cycles. The sensitivities of the different test parameters of the freeze-thaw damage were compared via principal component analysis, and the second-order damping ratio was proposed as a reasonable parameter to identify the in situ freeze-thaw damage in asphalt pavement.

Fractal Characteristics of Transverse Crack Propagation on CRTSII Type Track Slab

Objectives of this study are to examine influence of the surface crackles fractal characteristics of CRTSII track slab on its propagation velocity and stress intensity factor (SIF) and to improve the service performance of track slab. In this paper, fractal dimension D of transverse crack on the surface of CRTSII track slab was calculated by image processing, digital image technology, and box-counting method. Based on the fractal structure of transverse crack on track slab surface, a fractal transverse crack propagation model was established. The impact of fractal effect on the surface crack propagation velocity and SIF of CRTSII track slab was analyzed quantitatively. The fractal dimension D of transverse crack is 1.0652 on the surface of CRTSII track slab. The actual measured crack propagation velocity V0 on the surface of the track slab can be corrected as the true crack propagation velocity V. When the V0/Cr=0.899&lt;1, the SIF K′L1.0652,t,V of transverse dynamic fractal crack propagation on the surface of track slab has been equal to 0, and the V0 is always lower than Rayleigh wave velocity. In addition, the true attenuation rate of SIF for CRTSII track slab surface transverse dynamic crack propagation is faster than the actual measured value.