Spectral Analysis Of Surface Waves Research Articles

Comparison of different dispersion evaluation methods and a case history with the inversion to a soil model, related admittance functions, and the prediction of train‐induced ground vibration

ABSTRACTGround vibrations due to different technical sources are analysed in theory and experiment for the dispersion of Rayleigh waves and the admittance spectra. Both tasks are theoretically based on the same concept: The admittance function in frequency‐wavenumber domain yields the dispersion as its maxima, and the admittance function in space domain is obtained by integrating it over the wavenumbers. On the experimental side, many signal processing methods have been applied to many sites and have been developed by the authors in the last 35 years, i.e., time‐domain methods, including the cross‐correlation method, and frequency‐domain methods such as the spectral analysis of surface waves with two or multiple sensors, the wavenumber‐transform method, and the spatial autocorrelation method. All methods are presented by their basic formula and by at least one example site. Different sensor arrays and deterministic and stochastic sources have been tested for the spatial autocorrelation method and the wavenumber‐transform method at several sites. In addition, all frequency‐domain methods are presented for a specific layered site comparing their quality. The evaluated dispersion curves are very similar, but a somewhat higher frequency range has been found for the fastest method, i.e., the multi‐sensor spectral‐analysis‐of‐surface‐waves method. The theoretical solutions have been used for the inversion of the measured dispersion to the soil profile of the specific layered soil. The theoretical soil model has subsequently been used to predict the ground vibration spectra of hammer and railway excitation that exhibit a good agreement with the corresponding measurements. Thus, the contribution shows the benefit of active and passive seismic methods for the prediction of railway vibration, including a new version of the spatial autocorrelation method for technical vibrations. On the other hand, technical and namely railway vibrations are considered a seismic source for the exploration of near surface soils.

Comparison between Laboratory and Field Stiffness by Wave Measurements

Abstract The present work aims to establish a relationship between field and laboratory moduli obtained from mechanical wave measurements. Spectral analysis of surface waves was performed on a clayey sand trial layer during tests in a full-scale trial. Laboratory triaxial tests involving S-wave measurements with bender elements and accelerometers were conducted on specimens under similar conditions, and the shear modulus was determined. Both laboratory and field methodologies for the determination of the shear modulus were based on S-wave propagation through the tested material; thus they involved similar stress and strain levels. A reasonable relationship was observed between field and laboratory moduli, taking into account field conditions (moisture content and void ratio) and stress state.

Verification study for a surface wave method based on harmonic wavelet analysis waves using a large-scale model testing site

In this study, a large-scale model testing site was constructed to show the feasibility of a surface wave method based on harmonic wavelet analysis of waves (HWAW) for evaluating the lateral variation of the shear wave velocity (VS) profile (or two-dimensional shear wave velocity image) by initially determining the local VS profile. The testing site consists of four different stiffness layers, including an inclined layer boundary. In this site, 104 geophones were embedded and used to determine the wave velocities of each layer at seven test locations. The wave velocities measured by the embedded geophones were used as reliable reference values for the verification study. The HWAW, SASW (Spectral Analysis of Surface Wave), and down-hole methods were performed on the constructed model testing site, and the test results were compared to reference values. The verification study demonstrated the promising potential of the HWAW method in determining the two-dimensional VS image (or the lateral variation of the shear wave velocity profiles) by interpolating the 1D profiles of local fields subdividing the entire field in a lateral direction.

An explicit relation for the apparent phase velocity of Rayleigh waves in a vertically heterogeneous elastic half-space

S U M M A R Y This paper presents the mathematical derivation of an explicit relation for the apparent (or effective) phase velocity of Rayleigh waves in a vertically heterogeneous, isotropic elastic half-space for harmonic excitation. As a kinematical feature, the apparent phase velocity captures the superposition, in a spatial Fourier series, of the individual modes of propagation of Rayleigh waves and describes the speed of propagation of a composite waveform generated by a vertically oscillating point load. The relation, which is a function of the distance from the source, frequency and depth, depends explicitly on the modal phase and group velocities of Rayleigh waves, and their corresponding wavenumbers and eigenfunctions, which can be computed directly from the solution of the Rayleigh-wave eigenproblem. A practical scenario for the application of the notion of apparent Rayleigh-wave phase velocity is the modelling of the dispersion curve in the well-known surface wave measurement methods ‘spectral analysis of surface waves’ (SASW) and ‘multichannel analysis of surface waves’ (MASW). Apart from a theoretical motivation, the availability in surface wave testing of an explicit formula for the calculation of the apparent Rayleigh-wave phase velocity may lead to the development of a new class of inversion algorithms capable of taking into account the influence of all the modes of surface wave propagation. To demonstrate the exactness of the explicit relation, the predicted values of apparent phase velocity are compared to those computed synthetically from a numerical simulation of SASW and MASW testing for three case studies, which show both single as well as multiple mode dominance effects.

Estimating Subsurface Shear Velocity with Radial to Vertical Ratio of Local P Waves

Online Material: Code for computing V S by the r/z ratio method; seismogram plots. In contrast to the western United States where seismicity is high and seismic networks are dense, the central and eastern United States (CEUS) is covered with sparse seismic networks. The relatively low seismicity in the CEUS has also led to a limited dataset of waveform data from local earthquakes, hindering the development of reliable ground‐motion prediction equations in the CEUS. This situation has been changing with the Earthscope Transportable Array (USArray) program that started installing about 1000 broadband and short‐period stations in the CEUS starting in 2009, and will fully cover the CEUS soon. Such large numbers of stations provide a rich dataset for ground‐motion studies in the United States. Also, the increasing number of Advanced National Seismic System (ANSS) broadband stations with high‐sampling rate substantially augments the waveform data. Site responses at each seismic station need to be obtained before the waveform data can be used for ground‐motion studies. For example, Boore (2003) and Atkinson and Boore (2006) find that site amplification needs to be taken into account for ground‐motion modeling in eastern North America, especially for high frequencies. Site response is controlled by the subsurface shear‐velocity profile, and the velocity structure of the top ten to hundreds of meters is particularly important (Wald and Mori, 2000; Boore, 2006). Therefore an essential part of site‐response modeling is determining subsurface velocity structure. A detailed review of methods for determining subsurface velocity structure was made by Boore (2006). Theoretically, invasive methods such as borehole logging provide the most accurate measurement of velocity structure, but their cost prohibits extensive application in site‐response studies. Noninvasive geophysical exploration methods are more often used in determining shallow velocity structure, and these include spectral analysis of surface waves (SASW), multichannel …

Field Survey of Compressibility of Municipal Solid Waste

This paper presents a study on the compressibility of municipal solid waste (MSW) by means of a field survey in Valdemingomez Landfill in Madrid, Spain. Organic matter content was 59%, there was no waste segregation and field compaction, nor internal drainage systems for gas and leachate. Solid waste management changed significantly since then in Madrid, but former characteristics of this landfill are similar to those of present inadequate MSW disposal sites in more than 60% Brazilian municipalities. Initially a geotechnical exploration of the landfill was carried out by mechanically drilled boreholes with Standard Penetration Tests, determination of in-situ density and moisture content, and geophysical methods. Subsequently, vertical and horizontal displacements caused by a surcharge load applied by a trial soil embankment were measured, as well as settlements due to biodegradation of the organic materials, for 19 months. Displacements were monitored by topographical references, inclinometer, continuous lines of settlement, and a sliding micrometer. Young’s modulus was estimated 1900 kN/m2 . Shear modulus increased from 7 to 31 MPa with depth according to results of spectral analysis of surface waves. The auscultation campaign indicated that primary settlements occurred during approximately 100 days and that accumulated secondary settlements amounted to 0.600 m, representing 55% of the total settlements.

Comparison of In Situ and Laboratory Shear Wave Velocity Measurements in Compacted Backfill

Abstract The construction of a new nuclear power plant requires an excavation over 27.4 m (90 ft) deep. The excavation is backfilled with compacted sandy soils. The power plant is embedded about 12.2 m (40 ft) below grade; thus bearing on about 15.2 m (50 ft) of compacted backfill. During licensing and design of the plant, the shear wave velocity profile of the proposed backfill was estimated using results from laboratory testing [combined resonant column and torsional shear (RCTS)] and in situ shear wave velocity measurements. RCTS tests were conducted on representative samples of potential borrow sources. In situ velocity measurements, which included spectral-analysis-of-surface waves (SASW) and cross-hole seismic testing methods, were conducted on a 6.1-m- (20-ft-) thick embedded test pad of the potential borrow. During construction of the production backfill, in situ shear wave velocity measurements, using SASW methods, were taken at four levels during backfill placement, spaced nominally 6.1 to 7.6 m (20 to 25 ft) apart. The fourth and final level of testing was conducted nominally at plant grade. Cross-hole seismic testing through the backfill was also conducted at this level. This paper compares the results of estimated values made during the licensing and design phases of the project, based primarily on laboratory test results, with in situ shear wave velocity measurements made during the actual construction. In particular, SASW results from the first two levels of backfill tested [about 7.6 and 15.2 m (25 and 50 ft) of backfill] are evaluated. Results from the final two test levels of backfill, along with results of cross-hole testing, were not available at this writing. The comparison of laboratory results and in situ testing provides good agreement. The assumptions made to develop the estimated values during the licensing phase are compared to the as-built measurements of shear wave velocity accounting for actual backfill materials and construction practices reflected in the in situ values.

A Mobile Acoustic Subsurface Sensing (MASS) System for Rapid Roadway Assessment

Surface waves are commonly used for vibration-based nondestructive testing for infrastructure. Spectral Analysis of Surface Waves (SASW) has been used to detect subsurface properties for geologic inspections. Recently, efforts were made to scale down these subsurface detection approaches to see how they perform on small-scale structures such as concrete slabs and pavements. Additional efforts have been made to replace the traditional surface-mounted transducers with non-contact acoustic transducers. Though some success has been achieved, most of these new approaches are inefficient because they require point-to-point measurements or off-line signal analysis. This article introduces a Mobile Acoustic Subsurface Sensing system as MASS, which is an improved surface wave based implementation for measuring the subsurface profile of roadways. The compact MASS system is a 3-wheeled cart outfitted with an electromagnetic impact source, distance register, non-contact acoustic sensors and data acquisition/processing equipment. The key advantage of the MASS system is the capability to collect measurements continuously at walking speed in an automatic way. The fast scan and real-time analysis advantages are based upon the non-contact acoustic sensing and fast air-coupled surface wave analysis program. This integration of hardware and software makes the MASS system an efficient mobile prototype for the field test.

Study of the Effect of Temperature Changes on the Elastic Modulus of Flexible Pavement Layers

In general, the stiffness of flexible pavement is influenced by environmental changes, whereby temperature and rainfall affect the asphalt layer and non-asphalt layer, such as the subgrade, respectively. Normally, the effect of temperature on flexible pavement can be measured using two methods. The first is a destructive test whereby core samples are tested in a laboratory using a Universal Testing Machine (UTM). The second is a non- destructive in situ test using equipment such as a Falling Weight Deflectometer (FWD) and Spectral Analysis of Surface Waves (SASW). This study was conducted to investigate the effect of temperature at different tensile levels on the Soekarno-Hatta and Purwakarta Cikampek roads in Bandung, West Java, Indonesia. It is observed that different tensile levels and testing methods result in various elastic modulus values of flexible pavement. The higher the temperature applied to the flexible pavement layer, the more the elastic modulus values decrease. In contrast, the lower the temperature imposed on the flexible pavement layer, the more the elastic modulus values increase. Different testing methods (FWD, UTM and SASW) on the flexible pavement layer are also affected by temperature changes.

SASW analysis through inversion of combined dispersion curve using reliability of data from several receiver-configurations

In spectral analysis of surface waves (SASW analysis), experimental dispersion curves are generated at different inter-receiver distance, and they are combined to obtain the soil profile over a large range of depth with the available wide frequency range. In this paper, the contribution of various inter-receiver distances in generation of combined dispersion curve is proposed to be based on the reliability of dispersion data over the representative range of wavelength. A weighted averaging approach has been adopted for generation of combined dispersion curve from individual experimental dispersion curves. Weights were calculated based on a triangular reliability distribution function that takes into account the gradual existence of near field and far field effect on the data. The analysis also includes a systematic data reduction procedure to account for the scatter in dispersion curve to reduce the complexity during inversion procedure. Incorporating all these aspects, an automated procedure of analysis and interpretation is proposed, which can be used for soil site profiling with several receiver-configurations in SASW technique.

On the height of fall of dropping mass in SASW measurements for asphaltic road pavements

A number of spectral analysis of surface waves (SASW) tests were performed on asphaltic road pavements by dropping a metallic 6.5 kg sphere, from a height (H) ranging from 1 to 3 m. Various combinations of source to first receiver distance (S) and receiver spacing (X) were employed. By increasing the height of the fall of the dropping mass, the maximum wavelength (λmax), up to which the shear wave velocity profile can be predicted with the usage of the SASW measurements, was found to increase continuously. The height of fall of the dropping mass also seems to affect the admissible range of the wavelength for given combinations of X and S. Irrespective of different chosen combinations of S, X and H, a unique combined dispersion curve was generated in all the cases for a given pavement site as long as the threshold minimum value of the coherence function is greater than 0.90.

Road Pavement Stiffness Determination using SASW Method

The Spectral Analysis of Surface Waves (SASW) method is an in-situ seismic technique for the evaluation and assessment of road pavement. The method is based on the theory of stress waves propagating in elastic media with the key elements being the generation and detection of Rayleigh wave motion. A set of transient impact source with a range of frequencies is used to generate the Rayleigh wave energy that is able to propagate along the surface layer of the pavement. Through two vertical accelerometers, the motion of the wave for each range of frequency is recorded and calculated using a dynamic signal analyzer. A dispersion curve is then constructed from the cross-power spectrum of the Fast Fourier Transform (FFT) that results in the phase velocity versus wavelength plot. An iterative inversion is then carried out to obtain the shear wave velocity profile with depth and the corresponding dynamic modulus of each pavement units. This paper presents a case study carried out on a new road pavement construction site. It was found that the profile of the dynamic shear and Young’s modulus versus depth obtained from SASW method

Comparisons of dry ERT, diachronic ERT and the spectral analysis of surface waves for estimating bedrock depth in various Mediterranean landscapes

Bedrock depth provides important information for many applications, such as groundwater modelling, the estimation of soil water availability and crop production potential. Direct estimates of bedrock depth from destructive soil observations are discontinuous and too expensive to be used in large areas. Geophysical methods are often cited as possible alternatives; however, their ability to provide reliable estimations of bedrock depth relies greatly on local site characteristics. Therefore, this study examines the ability of Electrical Resistivity Tomographie (ERT) in dry conditions, diachronic ERT and the Spectral Analysis of Surface Waves (SASW) method to determine bedrock depth (BD) in different geopedological contexts that are representatives of the Mediterranean landscape (Southern France). SASW was performed using the data that were measured in the field with classical seismic equipment (impulse source and geophones) along a transect in each study site. In the same place, transects of ERT (Wenner–Schlumberger array, 1-m electrode spaced) were measured under wet and dry conditions. To calibrate the geophysical measurements, 131 boreholes (from two to 5m deep) were interpreted to determine the bedrock depth. Dry ERT, diachronic ERT and SASW were found to have highly variable performances for the estimation of bedrock depth in all geopedological contexts. SASW correctly estimated the bedrock depth (RMSE=0.3–0.7m) in all situations except in the case of shallow soils. Conversely, dry ERT only estimated bedrock depth (RMSE=0.2m) in the case of a high contrast of the resistivity between the soil and bedrock. By analysing the pattern of the water uptake by grapevine, diachronic ERT determined the bedrock depth in the case of very low contrasts in resistivity (RMSE=0.5). According to a prior pedological knowledge such soil maps, the combination with the use of a sensor based on different physical parameters may enhance the bedrock detection.

Imaging a near‐surface feature using cross‐correlation analysis of multi‐channel surface wave data

In this study, we demonstrate that cross‐correlation gathers of multi‐channel and multi‐shot configurations provide accurate estimations of shear‐wave velocity (Vs) perturbations from Rayleigh wave data for the reconstruction of two‐dimensional (2D), high‐resolution velocity distributions without requiring the systematic calculation of surface wave dispersion, as in the spectral analysis of surface waves (SASW). Data acquisition for cross‐correlation analysis is similar to that for a 2D seismic common midpoint reflection survey. The data processing involved is similar to the coda wave interferometry used for seismological data but differs in the sense that the cross‐correlation of the original waveform is calculated for active source seismic data. Data processing in cross‐correlation analysis consists in the following three steps: first, cross‐correlations are calculated for every trace in each shot gather with the same offset trace of a reference shot to flatten the linearly sloping events of surface waves. A common receiver location stack section can then be obtained, which allows for the assessment of lateral variations in the elastic properties of the medium. Second, the maxima of the time‐shifted cross‐correlation gathers and the maxima of the shot gathers’ envelope traces are picked for different frequencies and trace values having the same receiver location are averaged to calculate Vs perturbations, as described in the theory of coda wave interferometry. Finally, a 2D Vs profile is reconstructed by applying the lateral Vs perturbation to a homogeneous Vs velocity profile obtained by inversion of the surface wave dispersion of the reference shot gather. Analyses of waveform data from numerical modelling and field observations indicate that this new method is valid and greatly improves the accuracy and resolution of near‐surface imagery using surface waves and reconstructed subsurface velocity distributions compared with a conventional SASW or multi‐channel application.

Frozen and Unfrozen Shear Wave Velocity Seismic Site Classification of Fairbanks, Alaska

AbstractRelationships between seismic site classification and surficial geology for the city of Fairbanks, Alaska, for both frozen (winter) and unfrozen (summer) surface conditions are investigated in this article. The work is based on 59 shear wave velocity (Vs) profiles collected using the spectral analysis of surface waves (SASW) method. Forty-three Vs profiles were collected during the summer when the ground surface was fully thawed, and 16 Vs profiles were collected by reoccupying some of the test locations during fully frozen winter ground surface conditions. Relationships between mean Vs over the top 30 m of the subsurface (Vs30m) and surficial geologic units in Fairbanks were developed, permitting estimates of seismic site classification throughout the city for both frozen and unfrozen conditions. Much of Fairbanks was determined to have been founded on NEHRP Site Class D material when unfrozen. When frozen, the Vs of the near-surface material increased significantly (by 700% on average). However,...

Briefing: Study of the relationship between stiffness parameters for base materials

The stiffness of the base layer is an important parameter for designing the pavement thickness needed to support traffic loads. It is normally related to the California bearing ratio (CBR). The spectral analysis of surface waves (SASW) method is introduced here as an in situ non-destructive seismic technique to obtain the CBR and dynamic cone penetrometer (DCP) values. They are found from measurement of wave velocity and correlation with the dynamic properties of the pavement system. In this study, the relationship between the shear wave velocity and dynamic stiffness of the SASW was found to correlate well with the DCP and CBR values. The empirical correlation of CBR to dynamic stiffness in terms of elastic modulus was found to be similar to a previously suggested correlation. Preliminary analysis also indicates that the empirical model could be used to predict the modulus of pavement base layer.

Spectral Analysis of Surface Wave for Empirical Elastic Design of Anchored Foundations

Helical anchors are vital support components for power transmission lines. Failure of a single anchor can lead to the loss of an entire transmission line structure which results in the loss of power for downstream community. Despite being important, it is not practical to use conventional borehole method of subsurface exploration, which is labor intensive and costly, for estimating soil properties and anchor holding capacity. This paper describes the use of an empirical and elasticity-based design technique coupled with the spectral analysis of surface wave (SASW) technique to provide subsurface information for anchor foundation designs. Based on small-strain wave propagation, SASW determines shear wave velocity profile which is then correlated to anchor holding capacity. A pilot project involving over 400 anchor installations has been performed and demonstrated that such technique is reliable and can be implemented into transmission line structure designs.

Impulse Response Dynamic Stiffness Decay in Aging General Aviation Airfield Pavements

Managing pavements requires a reliable pavement performance indicator. The current study examines the feasibility of using the impulse response (IR) method to provide a reliable, mechanistic measure of current and future pavement performance. In an extension of the pavement family approach, IR-inferred dynamic stiffness (kd) decay models were generated for pavements with asphalt concrete (AC) and portland cement concrete (PCC) surfaces. AC pavement family subdivisions devised with the total thickness of structurally capable layers were found to yield the most significant correlations. Grouping data from all IR tests on PCC pavement sections into one family yielded a coefficient of determination of large significance with low scatter in the data. A statistically significant correlation could not be established for AC pavement between IR-estimated kd and the low-strain modulus (ESEIS) inferred by the method of spectral analysis of surface waves. In PCC pavements, a weak correlation was observed between kd and ESEIS. Though the sample used for comparison with structurally distressed sections was small, results suggested that in AC pavements, visually inferred traffic-related distresses did not correlate with structural failure. For PCC pavements, visual identification of structural distresses was more accurate than for AC pavements.

Compressive Strength Prediction of Porous Concrete Using Nondestructive Tests

This research focused on a prediction of compressive strength in porous concrete based on the ratio of air-entrained agents in the concrete slab using nondestructive testing methods such as the Impact Echo (IE) method, Spectral Analysis of Surface Wave (SASW) method and Free-Free Resonance (FFR) test. The method that best predicts the strength of the concrete slab can be derived from a relationship between compressive strengths and stress wave velocities. Concrete slab specimens of varying air content, were formed with a mix ratio of air-entrained agent of 0%, 0.15%, 0.3%, 0.7% and 1.5% by weight. These slabs were tested and analyzed to measure the stress wave velocities in order to develop a correlation with compressive strengths. The plot between the stress waves and compressive strengths showed a stiff slope up to an air ratio of 4% with a less steep slope beyond this point. In the process of predicting the compressive strength of concrete slab specimens, the prediction of compressive strength based on the compression wave velocity caused an average error of 4.9% in the compression wave velocity, and the prediction of compressive strength based on the surface wave velocity caused an average error of 2.2% in the surface wave velocity.

Combining seismic and electric methods for predicting bedrock depth along a Mediterranean soil toposequence

Bedrock depth provides important information for many environmental and agricultural applications, such as shallow groundwater monitoring, the determination of soil water availability, and the estimation of crop production potential. Direct estimates of bedrock depth from destructive soil observations are discontinuous and too expensive to be used in large areas. Geophysical methods are often cited as possible alternatives. However, their ability to provide reliable estimations of bedrock depth is known to depend greatly on local site characteristics. Therefore, combining geophysical methods based on different physical parameters may help to provide better predictions. This study examines the ability of the Spectral Analysis of Surface Waves (SASW) method combined with the classical high resolution Electrical Resistivity Tomography (ERT) method to predict soil depths in a 500m ranged Mediterranean hillslope (Southern France) with increasing soil depths along the slope. SASW was performed using the data measured in the field with classical seismic equipment (impulse source and geophones distributed along a line). In the same place, eight transects of ERT (Wenner–Schlumberger array, 1m electrode spaced) were measured under wet and dry conditions. To calibrate the geophysical measurements, 81 boreholes (from two to 5m deep) were interpreted to determine the bedrock depth, which was defined as the occurrence in the depth of heterogeneous marine Miocene loose sandstone with centimetric laminations. ERT and SASW were found to have highly variable performances for predicting separately the bedrock depth along the hillslope. SASW correctly predicted the bedrock depth in the lower part of the hillslope, whereas the data from ERT were disrupted by shallow permanent groundwater. Conversely, ERT correctly predicted bedrock depth within the upper part of the hillslope, whereas a high variability of SASW data near the topsoil caused difficulties for bedrock depth prediction. From these results, it was possible to define an estimator of bedrock depth according to the presence of shallow groundwater, which varies along the slope, such that more importance is given to ERT estimates in the upper part of the hillslope and more importance is given to SASW in the lower part. This study shows the usefulness of such a sensor combination to estimate soil properties when the uncertainties of making predictions vary according to the geophysical methods.