AN APPRAISAL OF SURFACE WAVE METHODS FOR SOIL CHARACTERIZATION

Transcription

1 AN APPRAISAL OF SURFACE WAVE METHODS FOR SOIL CHARACTERIZATION By KHIEM TAT TRAN A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA

2 2008 Khiem Tat Tran 2

3 To my father, whose lifetime of hard work has made mine easier 3

4 ACKNOWLEDGMENTS First of all, I thank Dr. Dennis R. Hiltunen for serving as my advisor. His valuable support, encouragement during my research and studies were what made this possible. I thank the other members of my thesis committee, Dr. Reynaldo Roque and Dr. Nick Hudyma. I would like to thank my parents for encouraging my studies. I thank the remaining members of my family for their support. I thank all of my friends who treated me like family. Lastly, I extend thanks to my wife, who has supported my decisions and the results of those decisions for the past 2 years. 4

5 TABLE OF CONTENTS ACKNOWLEDGMENTS...4 LIST OF FIGURES...7 ABSTRACT...9 CHAPTER 1 INTRODUCTION...10 page 1.1 Problem Statement Research Objectives Scope SURFACE WAVE METHODS Introduction Spectral Analysis of Surface Waves Tests (SASW) Field Testing Elements and Procedures Dispersion Curve Analysis Inversion Analysis Multi-Channel Analysis of Active Surface Waves (Active SASW) Field Testing Elements and Procedures Dispersion Curve Analysis Frequency-wavenumber transform (f-k) Slowness-frequency transform (p-f) Park et al. transform Cylindrical beamformer transform Inversion Analysis Multi-Channel Analysis of Passive Surface Waves (Passive MASW) Field Testing Elements and Procedures Dispersion Curve Analysis The 1-D geophone array The 2-D geophone array Inversion Analysis TESTING AND EXPERIMENTAL RESULTS AT TAMU Site Description Tests Conducted The SASW Tests Active MASW Tests Passive MASW Tests Dispersion Results

6 3.3.1 Dispersion Analysis for SASW Tests Dispersion Analysis for Active MASW Spectrum comparison Dispersion curve extraction Dispersion Analysis for Passive MASW Inversion Results Soil Profile Comparison TESTING AND EXPERIMENTAL RESULTS AT NEWBERRY Site Description Tests Conducted The SASW Tests Active MASW Tests Passive MASW Tests Dispersion Results Dispersion Analysis for SASW Tests Dispersion Analysis for Active MASW Tests Dispersion Analysis for Passive MASW Tests Combined Dispersion Curve of Active and Passive MASW Inversion Results Crosshole Tests Soil Profile Comparison CLOSURE Summary Findings Conclusions Recommendations for Further Work...69 LIST OF REFERENCES...70 BIOGRAPHICAL SKETCH

7 LIST OF FIGURES Figure page 2-1 Schematic of SASW setup Dispersion curves from SASW test Inversion result Frequency-Wavenumber Spectrum (f-k domain) Example of data in the x-t domain Signal spectrum and extracted dispersion curve from Park et al. method Signal image and extracted dispersion curve from ReMi Example of SASW data (4ft receiver spacing) Experimental combined dispersion curve for SASW of TAMU Final experimental dispersion curve for SASW of TAMU TAMU-0_122 recorded data in the time-trace (t-x) domain Spectra of TAMU-0_122 obtained by applying methods Normalized spectrum at different frequencies Extracted dispersion curves of TAMU-0_122 obtained by applying 4 methods Extracted dispersion curves of TAMU-88_220 obtained by applying 4 methods Final dispersion curve of TAMU obtained by active MASW Dispersion curves obtained by three techniques Inversion result of of TAMU obtained by SASW Inversion result of of TAMU obtained by Active MASW Inversion result of of TAMU obtained by Pasive MASW Newberry testing site Dispersion curve for SASW of Newberry Newberry active MASW recorded data in the time-trace (t-x) domain

8 4-4 Spectra of Newberry obtained by applying methods Normalized spectrum at different frequencies Extracted dispersion curves of Active MASW obtained by applying 4 signalprocessing methods Combined spectrum of Passive MASW Combined dispersion curve of passive and active MASW Final dispersion curve of combined MASW Dispersion curve comparison Inversion result of Neberry obtained by SASW Inversion result of Neberry obtained by combined MASW Soil profile obtained from Crosshole Test Soil profile comparison of Newberry

9 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Engineering AN APPRAISAL OF SURFACE WAVE METHODS FOR SOIL CHARACTERIZATION Chair: Dennis R. Hiltunen Major: Civil Engineering By Khiem Tat Tran May 2008 Three popular techniques, Spectral Analysis of Surface Waves (SASW), Multi-Channel Analysis of Active Surface Waves (Active MASW) and Multi-Channel Analysis of Passive Surface Waves (Passive MASW), were conducted at two well-characterized test sites: Texas A & M University (TAMU) and Newberry. Crosshole shear wave velocity, SPT N-value, and geotechnical boring logs were also available for the test sites. For active multi-channel records, the cylindrical beamformer is the best method of signal processing as compared to frequencywavenumber, frequency-slowness, and Park, et al. transforms. The beamformer provides the highest resolution of imaged dispersion curves, and its dominance of resolution at low frequencies over other methods allows achieving a reliable dispersion curve over a broad range of frequencies. Dispersion data obtained from all three surface wave techniques was generally in good agreement, and the inverted shear wave profiles were consistent with the crosshole, SPT N- value, and material log results. This shows credibility of non-destructive in situ tests using surface waves for soil characterization. 9

10 CHAPTER 1 INTRODUCTION 1.1 Problem Statement Near surface soil conditions control the responses of foundations and structures to earthquake and dynamic motions. To get the optimum engineering design, the shear modulus (G) of underlying layers must be determined correctly. The most popular method used to obtain the shear modulus is non-destructive in situ testing via surface waves. An important attribute of this testing method is ability to determine shear wave (Vs) velocity profile from ground surface measurements. Then shear modulus is calculated from G=ρV s 2. Three popular techniques, Spectral Analysis of Surface Waves (SASW), Multi-Channel Analysis of Active Surface Waves (Active MASW) and Multi-Channel Analysis of Passive Surface Waves (Passive MASW) have been developed for non-destructive in situ testing, but their accuracy remains a question. This research will apply these three techniques to characterize the soil profiles at two testing sites. The accuracy will be appraised by comparing the soil profiles derived from these techniques with soil profiles derived from cross-hole tests, a highly accurate but invasive testing technique. Non-destructive in situ surface wave testing technique can be divided into three separate steps: field testing to measure characteristics of particle motions associated with wave propagation, signal processing to extract dispersion curves from experimental records, and using an inversion algorithm to obtain the mechanical properties of soil profiles. For SASW, the testing and data analysis steps are well established. However, for the multi-channel techniques, a number of wave field transformation methods are available, but the best method has not been confirmed. Two of the most important criteria for establishing the best method are: 1) From which method can we derive the most credible soil profile? 2) From which method can we maximize the depth of investigation? 10

11 The soil profile derived from the third step is not necessarily unique. It is credible only when we have a good dispersion curve from the second step. Thus, this research will focus on the second step to get the best dispersion curves from among different methods of signal processing. The data recorded during a field test includes both signal and ambient noise. It is necessary to use signal-processing methods to discriminate against noise and enhance signal. The first question can be answered if we can successfully separate the desired signals of surface waves from background noise. The second question can be answered if we can obtain dispersion curves at low frequency. The lower frequency at which we have dispersive relation, the deeper depth of investigation we obtain. The research objectives are as follows: 1.2 Research Objectives 1. To find the best method of signal processing to obtain the most credible dispersion curve for a large range of frequency. 2. To check the accuracy of three surface wave techniques by comparison with results from cross-hole tests. 1.3 Scope For the first research objective, the author has developed programming codes to map the signal spectra of the recorded data by four different methods named as frequency - wavenumber transform (f-k), frequency slowness transform (f-p), Park et al. transform, and cylindrical beamformer transform. The dispersion curves are then obtained by picking points that have relatively strong power spectral values on the spectra. These points carry information of frequency wavenumber (f-k), frequency slowness (f-p) or frequency velocity (f-v) relationships. Straightforward dispersion curves in frequency velocity (f-v) domain can be built by calculation of v=1/p from f-p domain or v=2πf/k from f-k domain. The details of the signal 11

12 processing methods will be described in the chapter 2 and the results will be shown in the chapters 3 and 4. For the second research objective, SASW, Active MASW, and Passive MASW have been conducted in two test sites: 1. A National Geotechnical Experiment site (NGES) at Texas A & M University (TAMU). 2. A Florida Department of Transportation (FDOT) storm water runoff retention basin in Alachua County off of state road 26, Newberry, Florida. Also cross-hole tests were completed at these two sites for comparison. All the test results and comparisons are available in chapters 3 and 4. 12

13 CHAPTER 2 SURFACE WAVE METHODS 2.1 Introduction The motivation for using surface waves for soil characterization originates from the inherent nature of this kind of wave. Surface waves propagate along a free surface, so it is relatively easy to measure the associated motions, and carry the important information about the mechanical properties of the medium. So far, three popular techniques: SASW, Active MASW, Passive MASW have been developed to use surface waves for soil characterization. This chapter will provide a brief summary of these techniques, including the advantages, disadvantages of each. 2.2 Spectral Analysis of Surface Waves Tests (SASW) SASW was first introduced by Nazarian (1984) to the engineering community. Advantages of SASW are a simple field test operation and a straightforward theory, but it also has some disadvantages. This method assumes that the most energetic arrivals are Rayleigh waves. When noise overwhelms the power of artificial sources such as in urban areas or where body waves are more energetic than Rayleigh waves, SASW will not yield reliable results. Also during the processing of data, SASW requires some subjective judgments that sometimes influence the final results. SASW is described as follows Field Testing Elements and Procedures This method uses an active source of seismic energy, recorded repeatedly by a pair of geophones at different distances. The Figure 2.1 shows a schematic of SASW testing configuration. To fully characterize the frequency response of surface waves, these twotransducer tests are repeated for several receiver spacings. The maximum depths of investigation will depend on the lowest frequency (longest wavelength) that is measured. The sources are 13

14 related to the geophone distances, and range from sledgehammers at short receiver spacings (1-2m) to heavy dropped weights, bulldozers, and large vibration shakers at large receiver spacings (50-100m) Dispersion Curve Analysis Each recorded time signal is transformed into frequency domain using FFT algorithm. A cross power spectrum analysis calculates the difference in phase angles (φ(f)) between two signals for each frequency. The travel time (Δt(f)) between receivers can then be obtained for each frequency by: φ( t) Δt( f ) = (2.1) 2π f The distance between geophones is known, thus wave velocity is calculated by: V R X ( f ) = (2.2) Δt( f ) Considering each pair of signals, an estimate of the relationship between wave velocity and frequency over a certain range of frequency is obtained. Gathering the information from different pairs of geophones the combined dispersion curve is derived (Figure 2.2a). Then the combined one is averaged to get the final dispersion curve for inversion (Figure 2.2b) Inversion Analysis Inversion of Rayleigh wave dispersion curve is a process for determining the shear wave velocity profile from frequency-phase velocity dispersion relationship. This process consists of evaluation of theoretical dispersion curves for an assumed profile and comparison with the experimental dispersion curve. When the theoretical dispersion curve and the experimental dispersion relatively match, the assumed profile is the desired solution. The assumed medium is composed of horizontal layers that are homogeneous, isotropic and the shear velocity in each 14

15 layer is constant and does not vary with depth. The theoretical dispersion curve calculation is based on the matrix formulation of wave propagation in layered media given by Thomson (1950). The details of the process are described as follows. a) To determine the theoretical dispersion from an assumed profile: We can use either transfer matrix or stiffness matrix for calculation of the theoretical dispersion. The transfer matrix relates the displacement-stress vector at the top of the layer and at the bottom of the layer. Using the compatibility of the displacement-stress vectors at the interface of two adjacent layers, the displacement-stress vector at the surface can be related to that of the surface of the halfspace. Applying the radiation condition in the half-space, no incoming wave, and the condition of no tractions at the surface, the relationship of the amplitudes of the outgoing wave in the halfspace and the displacements at the surface can be derived: S u P w = B (2.3) Where the 4x4 matrix B is the product of transfer matrices of all layers and the half-space, u and w are the vertical and horizontal displacements at the surface. A nontrivial solution can be obtained if the determinant of a 2x2 matrix composed by the last two rows and the first two columns of matrix B is equal to zero. The characteristic equation 2.4 gives the theoretical dispersion. B B B B = 0 (2.4) Another method to obtain the theoretical dispersion is to use the stiffness matrix that relates displacements and forces at the top and at the bottom of a layer or displacements and 15

16 forces at the top of a half-space. The global stiffness matrix S is diagonally assembled by overlapping all the stiffness matrices of layers and half-space. The vector u of interface displacements and the vector q of external interface loadings can be related: S u = q. The Rayleigh waves can exist without interface loadings so: S u = 0 (2.5) The nontrivial solution of the interface displacements can be derived with the determinant of S being zero. The theoretical dispersion can be achieved from the equation 2.6 S = 0 (2.6) b) To determine a reasonable assumed profile: An initial model needs to be specified as a start point for the iterative inversion process. This model consists of S-wave velocity, Poisson s ratio, density, and thickness parameters. It is necessary to start from the most simple and progressively add complexity (Marosi and Hiltunen 2001). The assumed profile will be updated after each iteration and a least-squares approach allows automation of the process. 2.3 Multi-Channel Analysis of Active Surface Waves (Active SASW) This method was first developed by Park, et al.(1999) to overcome the shortcomings of SASW in presence of noise. The most vital advantage of MASW is that transformed data allow identification and rejection of non-fundamental mode Rayleigh waves such as body waves, nonsource generated surface waves, higher-mode surface waves, and other coherent noise from the analysis. As a consequence, the dispersion curve of fundamental Rayleigh waves can be picked directly from the mode-separated signal image. The obtained dispersion curve is expected to be more credible than that of SASW, and this method can be automated so that it does not require an experienced operator. An additional advantage of MASW is the speed and redundancy of the 16

17 measurement process due to multi-channel recording. Its quick and easy field operation allows doing many tests for both vertical and horizontal soil characterization Field Testing Elements and Procedures In Active MASW, wave field from an active source is recorded simultaneously by many geophones (usually >12) placed in a linear array and typically at equidistant spacings. The active source can be either a harmonic source like a vibrator or an impulsive source like a sledgehammer. Depending on the desired depth of investigation, the strength of source will be properly selected to create surface wave field at the required range of frequencies. If the wave field is treated as plane waves in data analysis, the distance from source to the nearest receiver (near offset) cannot be smaller than half the maximum wavelength, which is also approximately the maximum depth of investigation (Park et al. 1999). However, with cylindrical wave field analysis, this near offset can be selected smaller to reduce the rapid geometric attenuation of wave propagation Dispersion Curve Analysis To determine accurate dispersion information, multi-channel data processing methods are required to discriminate against noise and enhance Rayleigh wave signals. The following will discuss on four methods used for separating signals from background noise Frequency-wavenumber transform (f-k). For a given frequency, surface waves have uniquely defined wavenumbers k 0 (f), k 1 (f), k 2 (f) for different modes of propagation. In other words, the phase velocities c n =ω/k n are fixed for a given frequency. The f-k transform allows separation of the modes of surface waves by checking signals at different pairs of f-k. The Fourier transform is a fundamental ingredient of seismic data processing. For example, it is used to map data from time domain to frequency domain. The same concept is 17

18 extended to any sequential series other than time. The f-k analysis uses 2D Fourier transform that can be written as (Santamaria and Fratta 1998): P e M 1 N 1 2 π 2 π i v m i u l N N u, v = pl, m e (2.7) l= 0 m= 0 Where: N = number of time samples, M = number of receivers in space P u,v = spectral value at wavenumber index u and frequency index v p l,m = recorded data at mth sample of lth receiver This transform is essentially two consecutive applications of a 1D Fourier transform as shown in the following: Input data in (t,x) domain 1D Fourier Transform in the time direction (Data in (f,x) domain) 1D Fourier Transform in the spatial direction (Data in (f,k) domain) One main problem of the 2D transform is the requirement of a large number of receivers to obtain a good resolution in wavenumber direction. Because the geophone spacing dx controls the highest obtainable wavenumber (k max =π/dx min ), the spread length (X) controls the solution (Δk=2π /X). To obtain a good solution the spread length must be large but it is often difficult due to site size restrictions. The usual trick to improve the solution is to add a substantial number of zero traces at the end of field record (zero padding), which essentially creates artificial receiver locations with no energy. Figure 2.4 shows a spectrum in f-k domain where the signals are successfully separated from the background noise. Here we observe that the most energy is concentrated along a narrow band of 18

19 f-k pairs. This narrow band represents of fundamental Rayleigh wave mode of propagation. At a given frequency, wavenumber k is determined by picking the local strongest signal and the dispersion curve is then built by calculating the velocities at different frequencies as: Slowness-frequency transform (p-f). 2 f V ( f ) = π (2.8) k( f ) This procedure developed by McMechan and J.Yedlin (1981) consists of two linear transformations: 1) A slant stack of the data produces a wave field in the phase slowness time intercept (p-τ) plane in which phase velocities are separated. 2) A 1D Fourier transform of the wave field in the p-τ plane along the time intercept τ gives the frequency associated with each velocity. The wave field is then in slowness-frequency (p-f) domain. Firstly, the slant stack is a process to separate a wave field into different slowness (inverse of velocity) and sum up all signals having the same slowness over the offset axis. The calculation procedures as follows: 1) For a given slowness p and a time-intercept τ (figure 2-5), calculate the travel time t at offset x as t = τ + px and retrieve P(x,t), the amplitude of the recorded signal for that x and t. In practice, the recorded value of P(x,t) will often fall in between sampled data in time, and then will be calculated via linear interpolation. 2) This process is repeated for all x in the recorded data and the results are summed to produce: S ( p, τ ) will present a spectral amplitude in the p-τ domain. S ( p, τ ) = P( x, t) (2.9) x 3) Steps 1 and 2 are repeated over a specified range of p and τ to map out the spectral amplitudes in the p-τ domain. Secondly, a 1D Fourier transform of S(p, τ) along the τ direction separates the wave field into different frequencies, which produces data set of spectral amplitudes in the slowness (p) 19

20 frequency (f) domain such as shown in figure 2-6. Here we observe that the most energy (largest spectral amplitudes) is concentrated along a narrow band of p-f pairs. As with f-k, this narrow band represents the fundamental Rayleigh wave mode of propagation. At a given frequency, the phase velocity is calculated as the inverse of the slowness determined from the maximum spectral amplitude. In practice, this process has been observed to produce better identification of Rayleigh waves than does f-k Park et al. transform In the mid to late 1990s, Park, Miller, Zia and others at the Kansas Geological Survey began to develop the now popular SurfSeis software for the processing of multi-channel surface wave data from geotechnical applications. During their development, it was discovered that the two conventional transformation methods, f-k and p-f, did not provide adequate resolution of the wavefield in the cases where a small number of recording channels is available (Park, et al. 1998). Because it is desirable for geotechnical applications to use small arrays, they developed an alternative wavefield transform referred to herein as the Park, et al. transform. This method consists of 4 steps: 1) Apply 1D Fourier transform (FFT) to the wavefield along the time axis, this separates the wavefield into components with different frequencies. The recorded data is changed from (x-t) domain to (x-f) domain: U(x,t) U(x,f). 2) Normalize U(x,f) to unit amplitude: U(x,f) U ( x, f ) U ( x, f ) 3) Transform the unit amplitude in (x-f) domain to (k-f) domain as follows: For a specified frequency (f) and a wavenumber (k), the normalized amplitude at x is multiplied by e ikx and then summed all over the offset axis. This is repeated over a range of wavenumber for each f, and then over all f to produce a 2D spectrum of normalized amplitudes in f-k domain. This can be presented by: ikx U ( x, f ) V ( k, f ) = e (2.10) U ( x, f ) x 20

21 4) Transform V(k,f) to the phase velocity frequency domain: V(k,f) V(v,f) by changing the variables such that c(f)=2πf/k. The spectrum of V(v,f) is shown as an example in figure 2-7. Here we observe that the most energy (largest spectral amplitudes) is concentrated along a narrow band of f-v pairs. This narrow band represents the fundamental Rayleigh wave mode of propagation. At a given frequency, phase velocity is determined by picking the local strongest signal in the narrow band Cylindrical beamformer transform a) Cylindrical wavefield: The previous three transforms, f-k, p-f, Park, are based on a plane wavefield model for the surface wave propagation. A plane wavefield is a description of the motion created by a source located an infinite distance from the receivers. Surface wave testing methods, however, employ a source at a finite distance, and thus the wavefield is cylindrical and not planar. Zywicki (1999) has noted that a cylindrical wavefield can be described by a Hankel-type solution as given by: s iωt ( x, t) = AH ( kx) e 0 (2.11) Where s(x,t) = displacement measured at spatial position x at time t, A= initial amplitude of the wave field, H0 = the Hankel function of first kind of order zero which has the real part and imaginary part are respectively Bessel functions of the first kind and the second kind of order zero. The cylindrical wave equation allows accurate modeling of wave motions at points close to the active source, and this brings advantages in determining dispersion relationship at low frequencies (long wavelengths). At a relatively large distance x, the Hankel function can be expanded as: (Aki and G.Richards 1980) H ( kx) 0 1/ 2 = exp 2 2 πkx i 1 [ i( kx π / 4) ] 1 + O 8kx ( kx) (2.12) 21

22 Neglecting waves that decay more rapidly than 1 / x, the equation 2.12 becomes: 1/ 2 2 H 0( kx) exp[ i( kx π / 4) ] (2.13) πkx This equation clearly shows the 1/ x decay and plane wave nature of the cylindrical wave equation in the far-field. In other words, at a relatively large distance x, the cylindrical wave field approaches the plane wave field. b) Cylindrical wavefield transform: Based upon the cylindrical wavefield model, a cylindrical wavefield transform can be described as follows (Zywicki 1999): 1) Apply 1D Fourier transform to wavefield along the time direction 2) Build a spatiospectral correlation matrix R(f): The spatiospectral correlation matrix R(f) at frequency f for a wave field recorded by n receivers is given by: R11( f ) = R21( f ) R( f ) M Rn1( f ) R R R n2 ( f ) ( f ) M ( f ) L L O L R R R 1n 2n nn ( f ( f M ( f ) ) ) (2.14) * R ( f ) = S ( f ) S ( f ) (2.15) ij i Where R ij (f) = the cross power spectrum between the i th and j th receivers, S i (f) = Fourier spectrum of the i th receiver at frequency f, * denotes complex conjugation. 3) Build a cylindrical steering vector: the cylindrical steering vector for a wavenumber k is built by applying the Hankel function as follows: j [ φ ( H ( k x )), φ( H ( k x )),, ( H ( k ))] T h( k) = exp{ i 1 2 L φ (2.16) Where φ denotes taking the phase angle of the argument in parentheses. T denotes changing a vector from a column to a row or adversely. 4) Calculate the power spectrum estimate of the fieldwave: For a given wavenumber k and frequency f, the power spectrum estimate is determined by: x n 22

23 T P( k, f ) = h( k) R( f ) h( k) (2.17) The spectrum of P (k, ω) allows separating fundamental mode Rayleigh waves from other waves (figure 2.8). Similar to previous methods, here we observe that the most energy (largest spectral amplitudes) is concentrated along a narrow band of f-k pairs. This narrow band represents the fundamental Rayleigh wave mode of propagation. At a given frequency, wavenumber k is determined by picking the local strongest signal and the dispersion curve is then built by calculating the velocities at different frequencies by equation Inversion Analysis The inversion algorithm of this method is the same as that of SASW (part ). The only difference would be that the iterative inversion calculation of MASW is quicker than that of SASW because MASW usually brings smoother dispersion curves that allow quickly achieving the stopping criteria in the inversion process. 2.4 Multi-Channel Analysis of Passive Surface Waves (Passive MASW) Passive wave utilization has been intensively studied recently. It derives from useful inherent characteristics of the passive surface waves. The most important advantage of testing methods using passive waves is the ability to obtain deep depths of investigation with very little field effort. Desired Rayleigh waves from passive seismic arrivals are relatively pure plane waves at low frequencies allow determining Vs profiles up to hundreds meter depth. The shortcoming is that this method is only able to apply for noisy testing sites (urban areas close to roads ) but not for quiet test sites (rural areas) Field Testing Elements and Procedures Passive wave fields (background noise) are recorded simultaneously by many geophones located in 1-D or 2-D arrays. With a requirement of recording waves at long wavelengths, geophone spacing of passive MASW is often larger than that used in active MASW. This leads 23

24 to a need of large testing spaces especially for a 2-D geophone layout. The length of a 1D geophone spread must not be less than the maximum expected wavelength. For a 2-D circular geophone layout, the diameter should be equal to the maximum expected wavelength. It is typical that many sets of data are recorded for each geophone layout and these data will be combined to improve spectra for dispersion analysis Dispersion Curve Analysis The methods of dispersion curve analysis depend on the geophone layouts applied to record data. Two methods have been suggested as follows: The 1-D geophone array. This method was first developed by Louie (2001) and named Refraction Microtremor (ReMi). Two-dimensional slowness-frequency (p-f) transform (part ) is applied to separate Rayleigh waves from other seismic arrivals, and to recognize the true phase velocity against apparent velocities. Different from active waves that have a specific propagation direction inline with the geophone array, passive waves arrives from any direction. The apparent velocity V a in the direction of geophone line is calculated by: V a = v / cos( θ ) (2.18) Where: v = real inline phase velocity, and θ = propagation angle off the geophone line. It is clear that any wave comes obliquely will have an apparent velocity higher than the true velocity of inline waves, i.e., off-line wave signals in the slowness-frequency images will display as peaks at apparent velocities higher than the real inline phase velocity. Dispersion curves are extracted by manual picking of the relatively strong signals at lowest velocities (figure 2-8). 24

25 The disadvantage of ReMi is to require the manual picking, as this depends on subjective judgment, and sometimes influence the final results The 2-D geophone array. Park, et al. (2004) introduced a data processing scheme for a 2D cross layout and then developed for 2D circular layout. This method is extended from the method applied for active MASW tests (part ) Inversion Analysis The inversion algorithm of this method is the same that of SASW (part ). Usually, the dispersion curves from passive MASW are in a small range of low frequencies (<20Hz), so the soil profiles at shallow depths are not very precise. Passive data are sometimes combined with that of active MASW to broaden the range to higher frequencies. The combination of dispersion curves brings better results of soil characterization. Figure 2-1. Schematic of SASW setup 25

26 a) b) Phase Velocity (ft/s) Phase Velocity (ft/s) Frequency (Hz) Frequency (Hz) Figure 2-2. Dispersion curves from SASW test: a) Combined raw dispersion curve and b) Final dispersion curve after averaging a) 1600 experimental Theoretical b) 0 Shear wave velocity (ft/s) Phase Velocity (ft/s) Depth (ft) Frequency (Hz) -60 Figure 2-3. Inversion result: a) Dispersion curve matching, b) Soil profile 26

27 wavenumber, rad/ft frequency, Hz Figure 2-4. Frequency-Wavenumber Spectrum (f-k domain) Figure 2-5. Example of data in the x-t domain 27

28 5 x Slowness, s/ft frequency, Hz Figure 2-6. Slowness-Frequency Spectrum (f-p domain) Figure 2-7. Signal spectrum and extracted dispersion curve from Park et al. method 28

29 Wave number, rad/ft frequency, Hz Figure 2-8. Cylindrical Beamformer Spectrum (f-k domain) Figure 2-9. Signal image and extracted dispersion curve from ReMi 29

30 CHAPTER 3 TESTING AND EXPERIMENTAL RESULTS AT TAMU 3.1 Site Description The data were collected at the National Geotechnical Experiment site (NGES) on the campus of Texas A & M University (TAMU). The TAMU site is well documented, and consists of an upper layer of approximately 10 m of medium dense, fine, silty sand followed by hard clay. The water table is approximately 5 m below the ground surface. Because of space limitations, all the tests including two-sensor and multi-sensor tests were only 1D receiver layout and conducted on a straight line of nearly 400 feet. The positions are marked with one-foot increment from 0 to 400 as TAMU-0_ Tests Conducted On the mentioned line, three kinds of tests, SASW, Active MASW and Passive MASW were conducted for comparison. The details of field-testing elements and procedures of each kind of tests are described as follows The SASW Tests The conducted SASW tests are divided into two categories that were recorded at two positions, TAMU-61 and TAMU-128. The SASW tests were conducted with configurations having the source-first receiver distance equal to inter-receiver distance. At each position, many configurations were used in common midpoint (CMP) style with the inter-receiver distance at 4 ft, 8 ft, 16 ft, 32 ft, 64 ft, and 122 ft. For each receiver layout, the active source was placed both front and behind for recording forward and backward (reverse) wave propagations. The active sources were hammers for the inter-receiver distances up to 16 ft, and shakers for larger distances. 30

31 3.2.2 Active MASW Tests The active MASW tests were conducted with 62 receivers at spacing of 2 feet with the total receiver spread of 122 feet. Two receiver layouts were laid at positions TAMU-0_122 and TAMU-98_220. For each receiver layout, five sets of data were recorded accordingly to five positions of the active source at 10 ft, 20 ft, 30 ft, 40 ft, and 50 ft away from the first receiver. For the record TAMU-0_122, the active source was located at TAMU 132, 142, 152, 162, 172, and for the record TAMU-98_220, the active source was located at TAMU 88, 79, 68, 58, 48 (see Figure 3.1). Each set of data was obtained with 16,348 (2^14) samples, the time interval of ms ( s), and the total recorded period of 12.8 seconds Passive MASW Tests The passive MASW tests were conducted by 32 receivers deployed at inter-spacing of 10 feet spanning a distance of 310 feet at site position TAMU-0_310. For the passive tests, several sets of data were obtained for combining spectra in the dispersion analysis. In this case, 26 sets of data were recorded with 16,348 (2^14) samples, the time interval of ms ( s), and the total recorded period of 32 seconds. 3.3 Dispersion Results In this section, the dispersion curves from SASW, Active MASW and Passive MASW are extracted for inversion. Also, several signal processing methods are applied for Active MASW data to evaluate these methods and obtain the best dispersion curve Dispersion Analysis for SASW Tests The dispersion results of tests at TAMU-61 and TAMU-128 are similar so only tests at TAMU-61 are presented here in detail. The Figure 3-2 shows an example of data obtained with inter-receiver distance of 4 ft and reverse recording (4r). The cross power spectrum (CPS) phase is used to calculate the frequency-dependent time delay. Then with the known receiver distance, 31

32 the phase velocity is determined. The coherence function allows checking wave energy distribution and the ranges of frequency where the signal to noise ratio is high (according to the coherence function close to 1). This information helps to determine the credible range of frequency in which dispersion relationship is obtained. One more criterion should be applied to eliminate the influence of body waves. Only the range of frequency in which the according wavelength is not less than one third and not more than twice of the distance from the source to the first receiver is effectively counted. In this range, the wave field can be considered as relatively pure plane waves. For SASW data recorded at TAMU-61, all twelve sets of data with 6 inter-receiver distances for both forward and backward records are used for dispersion analysis. Each set gives the dispersion relationship in a certain range of frequency. Assembling the information from the 12 sets of data, the combined dispersion curve is derived (Figure 3-3). Many points in the combined dispersion curve are cumbersome in the inversion process, so an averaged curve is desired. In this case, a smoothing algorithm is used to obtain the final dispersion curve (Figure 3-4) Dispersion Analysis for Active MASW The main purpose of this part is to use the real recorded data to check and compare all of the signal processing methods described in the chapter 2: f-k transform, f-p transform, Park, et al. transform, and cylindrical beamformer. Then the spectrum having the best resolution will be selected for extracting the dispersion curve Spectrum comparison For each geophone layout, the data recorded with five active source locations give similar results of spectra, so only data recorded at the closest source (10 feet away from the first geophone) are presented here. Figure 3-5 shows the TAMU-0_122 recorded data in the time- 32

33 trace (t-x) domain. In this untransformed domain, we can only see the waves coming at different slowness (slope), but are not able to distinguish between signals and noise. The signal processing methods are necessarily applied to map the field wave for dispersion analysis. For active MASW, the recorded data were used to check and compare the signal processing methods, f-k, f-p, Park, et al. transform, and cylindrical beamformer. For comparison, the spectra were all imaged in the same domain (figure 3.6 and figure 3.7). The frequency interval, velocity interval, number of frequency steps, and number of velocity steps on these spectra are identical. Also, the spectral values in all images were unity normalized, i.e., the highest value in each spectrum is equal to 1.0, and all other values are relatively compared to one. From these data it is apparent that the Park, et al. transform and the cylindrical beamformer have better imaged dispersion curves at low frequencies (<15Hz) than that of the f-k and f-p transforms. Overall, the spectrum obtained from the cylindrical beamformer has the highest resolution. Resolution of spectra in the frequency-phase velocity (f-v) domain can be separated into 2 components: resolution along the frequency axis and resolution along the phase velocity axis. All four methods apply a 1-D Fourier transform along the time direction to discriminate among frequencies for a given phase velocity, thus the resolutions along the frequency axis for each method are not much different. However, for the resolution along the phase velocity axis, the cylindrical beamformer appears best able to separate phase velocities for a given frequency. To provide further illustration of resolution capabilities, figure 3.8 shows the normalized spectral values of TAMU-0_122 at 4 frequencies: 10, 20, 30, and 40 Hz. For each frequency, the spectral values are normalized to unity, i.e. the maximum value along the phase velocity axis is equal to 1. Even though the strongest peak for each method occurs at similar phase velocities for each frequency, the highest peak of the cylindrical beamformer is most dominant to other local 33

34 peaks on its spectrum, i.e., the cylindrical beamformer reduces side ripples, and most of the energy concentrates at the strongest peak. The sharpest peak of the cylindrical beamformer allows the best separation of phase velocities for any given frequency. Thus, the high resolution along the phase velocity axis contributes to the highest overall resolution of the cylindrical beamformer. This can be understood that the cylindrical wavefield equations present the motions of waves created by an active source more properly than do plane wavefield equations Dispersion curve extraction The dispersion curves from all mentioned signal-processing methods are extracted by selecting the strongest signals at every frequency and shown in figure 3.9 and figure For the recorded data, even though the extracted dispersion curves of the methods are similar, the curves (figure 3.11) obtained by the cylindrical beamformer were selected to present for the test site because of their highest credibility. Because they are also very similar, the two dispersion curves of TAMU-0_122 and TAMU-98_220 were combined, averaged and smoothened to derive the final one for Active MASW testing of TAMU (figure 3.12). This is also rational since it is desirable to compare these results with those from passive MASW, and this data was collected over the full 310 feet length of the array Dispersion Analysis for Passive MASW The data of 1D receiver array at TAMU were analyzed by commercial software Seisopt ReMi that uses the Louie (2001) method of data analysis. This method applies two-dimensional slowness-frequency (p-f) transform to separate Rayleigh waves from other seismic arrivals and to recognize true phase velocity against apparent velocities (see Part ). The combined spectrum from several passive records allows obtaining the dispersion curve over a larger range of frequencies (figure 3.13). 34

35 3.3.4 Dispersion Curve Comparison It is observed from figure 3.14 that the dispersion data from all three techniques is generally in good agreement, particularly at the high and low frequency ranges. However, active MASW dispersion data appear to be higher in a middle frequency range. It is also observed that the active and passive MASW data is smoother than the SASW data. The ripples in the SASW data are mostly produced by slight mismatches in the combined dispersion data from multiple receiver spacings. Each spacing samples a slightly different zone of soil, and lateral variability of soil properties will produce a mismatch in dispersion data. 3.4 Inversion Results After finishing the dispersion analysis, the inversion algorithm (part 2.2.3) is applied to characterize soil profiles from the dispersion curves. The inversion module of commercial software Seisopt and inversion algorithm developed by D.R.Hiltunen & Gardner (2003) are applied to derive the soil profile. Both give similar results which are shown in figure 3-15, figure 3-16, and figure 3-17 for tests: SASW, Active MASW and Passive MASW respectively. Also dispersion curve matching between theoretical curve and experimental curve is shown for reference. In all three cases, the inversion routine was able to match the experimental data very well. However, it is noted for all three cases that the theoretical models are not able to exactly match the experimental data in some localized areas. These fluctuations are due to localized variability in the soil profile that the surface wave inversion algorithm is not able to detect. The maximum depth of investigation depends on the lowest frequency in which the dispersive relationship is achieved and on shear velocity. By using heavy shakers to create the active field wave, the lowest frequency of SASW is 3 Hz and the maximum attainable depth is 65 feet. For active MASW and passive MASW, the lowest frequencies are 6 Hz and 5 Hz; the 35

36 maximum attainable depths are 53 ft and 45 ft respectively. The maximum depth of investigation at TAMU is not very deep even though the lowest frequency is as low as 3 Hz (SASW) because of low phase velocity of soil profile that leads to a moderate maximum wavelength (λmax=v/2π.fmin). The bigger the maximum wavelength, the deeper depth of investigation is obtained. 3.5 Soil Profile Comparison The Vs profiles of TAMU derived from SASW, Active MASW, Passive MASW and cross-hole test are all shown together in the figure Also shown in the figure 3.18 are crosshole Vs measurements, SPT N-values, material logs from a nearby geotechnical boring conducted at the site. First, regarding the shear wave velocity profiles from the three surface wave techniques, it is observed that they are generally in good agreement. Consistent with the dispersion curves, the SASW and passive MASW are in particularly good agreement. However, the active MASW is slightly stiffer (higher velocity) at some depths, which is also consistent with the dispersion data. Second, it is observed that the surface wave based shear wave velocity profiles compare well with the crosshole results, especially at depths from 30 to 50 ft. Above 30 ft, a reversal occurs in the profile attained from the crosshole tests that is not detected by the surface wave tests. The surface wave tests are conducted over a relatively long array length that samples and averages over a large volume of material, whereas the crosshole results are based upon wave propagation between two boreholes that are only 10 ft apart, and thus these data represent a more local condition at the site. Lastly, there appears to be reasonable consistently between the shear wave velocity results and the SPT N-values and material log. In the sand layer above a depth of about 30 ft, the shear 36

37 wave velocities and the N-values are approximately uniform. Below 30 ft, the shear wave velocities and the N-values increase in the hard clay material 3.6 Summary of TAMU Tests Base upon the results presented herein, the following conclusions appear to be appropriate: 1. For active multi-channel records, the cylindrical beamformer is the best method of signal processing as compared to f-k, f-p, and Park, et al. transforms. The beamformer provides the highest resolution of imaged dispersion curves, and its dominance of resolution at low frequencies over other methods allows achieving a reliable dispersion curve over a broad range of frequencies. 2. There is generally good agreement between dispersion results from SASW, active MASW, and passive MASW surface wave tests. 3. The surface wave-based shear wave velocities are in good agreement with the crosshole results, and the shear wave velocities appear consistent with SPT N-values and material logs. Figure 3-1. Schematic of SASW setup for TAMU-0_122 and TAMU-98_220 37

38 Figure 3-2. Example of SASW data (4ft receiver spacing) 1400 Phase Velocity (ft/s) f 4r 8f 8r 16r 16f 32f 32r 64f 64r 122f 122r Frequency (Hz) Figure 3-3. Experimental combined dispersion curve for SASW of TAMU-61 38

39 Combined dispersion curve 1400 Final dispersion curve by smoothing 1200 Phase Velocity (ft/s) Frequency (Hz) Figure 3-4. Final experimental dispersion curve for SASW of TAMU-61 Figure 3-5. TAMU-0_122 recorded data in the time-trace (t-x) domain 39

40 Figure 3-6. Spectra of TAMU-0_122 obtained by applying methods: a) f-k transform b) f-p transform c) Park, et al. transform d) Cylindrical beamformer Figure 3-6. Spectra of TAMU-0_122 obtained by applying methods: a) f-k transform b) f-p transform c) Park, et al. transform d) Cylindrical beamformer 40

41 Figure 3-7. Spectra of TAMU-88_220 obtained by applying methods: a) f-k transform b) f-p transform c) Park, et al. transform d) Cylindrical beamformer 41

42 Figure 3-8. Normalized spectrum at different frequencies (Solid line for cylindrical beamformer, Dashpot line for Park, et al. transform Dashed line for f-k transform, Dotted line for f-p transform) Figure 3-8. Normalized spectrum at different frequencies (Solid line for cylindrical beamformer, Dashpot line for Park, et al. transform, Dashed line for f-k transform, Dotted line for f-p transform) 42

43 f-k transform f-p transform Park et al.transform Cylindrical Beamfomer Phase Velocity (ft/s) Frequency (Hz) Figure 3-9. Extracted dispersion curves of TAMU-0_122 obtained by applying 4 methods f-k transform f-p transform Park et al.transform Cylindrical Beamfomer Phase Velocity (ft/s) Frequency (Hz) Figure Extracted dispersion curves of TAMU-88_220 obtained by applying 4 methods 43

44 Phase Velocity (ft/s) Frequency (Hz) Figure Combined dispersion curve of TAMU from 2 shot gathers TAMU_0-122 TAMU_ Phase Velocity (ft/s) Frequency (Hz) Figure Final dispersion curve of TAMU obtained by active MASW 44

45 b) Phase Velocity (ft/s) Frequency (Hz) Figure The REMI analysis: a) Combined spectrum of Passive MASW at TAMU, b) Extracted dispersion curve by manual picking 45

46 Phase Velocity (ft/s) SASW Active MASW Passive MASW Frequency (Hz) Figure Dispersion curves obtained by three techniques 46

47 a) Experimental dispersion curve Theorectical dispersion curve 1200 Phase Velocity (ft/s) Frequency (Hz) b) 0 Shear Velocity (ft/s) Depth (ft) Figure Inversion result of of TAMU obtained by SASW: a) Dispersion curve matching and b) soil profile 47

48 a) Experimental dispersion Curve Theoretical dispersion curve Phase Velocity (ft/s) Frequency (Hz) b) 0 Shear Velocity (ft/s) Depth (ft) Figure Inversion result of of TAMU obtained by Active MASW: a) Dispersion curve matching and b) soil profile 48

49 a) Experimental dispersion curve Theoretical dispersion curve Phase Velocity (ft/s) Frequency (Hz) b) Shear Velocity (ft/s) Depth (ft) Figure Inversion result of of TAMU obtained by Pasive MASW: a) Dispersion curve matching and b) soil profile 49

50 Figure Soil profile comparison 50

51 CHAPTER 4 TESTING AND EXPERIMENTAL RESULTS AT NEWBERRY 4.1 Site Description The testing site is a single Florida Department of Transportation (FDOT) storm water runoff retention basin in Alachua County off of state road 26, Newberry, Florida (figure 4-1). The test site was approximately 1.6 hectares and was divided into 25 strips by 26 north-south gridlines marked from A to Z with the gridline spacing of 10 ft. Each gridline was about 280 ft in length with the station 0 ft at the southern end of the gridline. Five PVC-cased boreholes extending to the depth of 60 ft were installed for cross-hole tests. 4.2 Tests Conducted SASW, Active MASW, and Passive MASW were conducted in Newberry for comparison of the obtained soil profiles. The details of field testing procedures of each kind of test are described as follows The SASW Tests The SASW tests were conducted on gridline Z with configurations having the source-first receiver distance equal to inter-receiver distance. All configurations were employed with the common midpoint (CMP) at position Z-80 for inter-receiver distances of: 4 ft, 6 ft, 8 ft, 12 ft, 16 ft, 24 ft, 32 ft, 40 ft and 50 ft. For each receiver layout, the source was placed front and behind for recording forward and backward wave propagations. Hammers were used to produce active wave fields Active MASW Tests The active MASW tests were conducted by 31 receivers at spacing of 2 feet with the total receiver spread of 60 feet. The active source was located 30 ft away from the first receiver. Many sets of data were collected by moving both the source and receiver layout 4 ft each. Each set of 51

52 data was obtained with 2048 (2^11) samples, the time interval of ms ( s), and the total recorded period of 1.6 seconds. For comparison with SASW tests, only one set of data collected by a receiver array having the centerline at position Z-80 (same as CMP of SASW) is analyzed in this thesis. For this record, the wave field was produced by an active source at position Z-20, and the receiver spread was at Z-50_ Passive MASW Tests The passive MASW tests were conducted by 32 receivers deployed at inter-spacing of 10 feet spanning a distance of 310 feet at Z-0_310. In order to obtain a good combined spectrum, 15 sets of data were recorded with (2^14) samples, the time interval of ms ( s), and the total recorded period of 32 seconds. 4.3 Dispersion Results This section will express the dispersion results of three surface wave methods. The dispersion curves of active MASW and passive MASW will be combined to broaden the range of frequency for inversion Dispersion Analysis for SASW Tests The fundamental concepts of SASW analysis are the same as that expressed in part For SASW data recorded at Newberry, all 16 sets of data with 8 inter-receiver distances for both forward and backward records are used for dispersion analysis. The combined dispersion curve from 16 data sets and the averaged dispersion curve are shown in the figure 4.2. With very well recorded data, the obtained final dispersion curve is smoother than that of TAMU, and this allows a quicker process of inversion. 52

53 4.3.2 Dispersion Analysis for Active MASW Tests Similar to what was described in chapter 3, the active multi-channel records of Newberry are also analyzed by four signal processing methods. Then the spectrum having the best resolution will be selected for extracting the dispersion curve. Figure 4-3 and figure 4-4 show the data recorded of the active wave field in untransformed domain (x-t) and transformed domain (f-v), respectively. We can easily recognize the desired fundamental mode Rayleigh waves that is successfully separated from other noisy waves in the transformed domain. Here we observe that the most energy (largest spectral amplitudes) is concentrated along a narrow band. This narrow band represents the fundamental Rayleigh wave mode of propagation. As before, the cylindrical beamformer transform shows its dominance by the best resolution spectrum. The best resolution of the cylindrical beamformer transform can be seen more clearly in the figure 4-5 of normalized spectra in which the spectral values are checked for particular frequencies to evaluate the separation of phase velocities. Here we observe that the cylindrical beamformer transform reduces side ripples or most of energy concentrates at the strongest peak. The sharpest peak of the cylindrical beamformer transform allows the best separation of phase velocities for any given frequency. The dispersion curves obtained from the four signal processing methods are shown together in figure 4-6, and the one from the cylindrical beamformer is selected to represent the active MASW tests of Newberry Dispersion Analysis for Passive MASW Tests The passive wave data recorded by 1D receiver array at Newberry are analyzed by commercial software Seisopt ReMi 4.0. The signals of passive waves are not usually very strong so many spectra of data sets should be considered. Each spectrum is only good for a small range of frequency. The combined spectrum allows obtaining dispersive relationship in a larger range. 53

54 The spectrum shown in figure 4-7 is derived by combining that of 15 data sets. Manual picking points at the lowest edge of area in which the signals are relatively strong gives the dispersion curve of passive MASW for Newberry Combined Dispersion Curve of Active and Passive MASW The principal goal of passive MASW is to obtain the dispersion relationship at low frequencies (<15 Hz) but we also need the dispersion property at higher frequencies (>15Hz) for characterization of soil at shallow depths. Combining dispersion curves achieved from both active and passive is a good solution to broaden the range of frequency. For Newberry, the active MASW and passive MASW give the dispersion property at ranges of frequency of 5 to 15 Hz and 10 to 60 Hz, respectively. The combined dispersion curve at the frequencies of 5 to 60 Hz allows attaining the detailed soil profile from ground surface to a great depth. The overlapping of the dispersion curves between frequencies of 10 to 15 Hz shows the agreement of the two methods and brings the credibility of the combined dispersion curve. Some points on the combined dispersion curve cannot be handled in the inversion, so the curve should be simplified by using smoothing algorithm to derive the final dispersion curve shown in the figure Dispersion Curve Comparison It is observed that the dispersion data from combined MASW and SASW is generally in good agreement, particularly at the high frequency range (figure 4-10). However, combined MASW dispersion data appear to be higher, especially at the low frequency range. 4.4 Inversion Results After finishing the dispersion analysis, the inversion algorithm (part 2.2.3) is now applied to characterize soil profiles from the dispersion curves. Two dispersion curves of SASW and combined MASW are used for inversion and the derived soil profiles are shown in figure

55 and figure Also dispersion curve matching between theoretical curve and experimental curve is shown for reference. All dispersion curves of Newberry are typical curves whose phase velocities continuously increase with decreasing frequency. Thus the typical soil profiles with shear velocity increasing with depth increase are obtained. That the slope of dispersion curves changes suddenly from a low value at frequencies more than 20 Hz to a very high value at frequencies less than 20 Hz can be explained by a big increasing step of shear velocity. For SASW, the dispersion property is obtained at the lowest frequency of 12 Hz only and the maximum velocity of about 1800ft/s. This does not allow achieving a great depth of investigation because of the short maximum obtained wavelength (λmax=24ft). The reliable depth of investigation is only about 25 ft. For combined MASW tests, the dispersion property at low frequencies can be derived from passive wave fields. The combined dispersion curve is attained in a broad range of frequency from 5 Hz to 60 Hz and the maximum phase velocity of about 3000 ft/s (λmax=95ft). This allows increasing the credible depth of investigation up to about 70 ft. It is clear that the classified depth is considerately increased by using passive wave fields in soil characterization. 4.5 Crosshole Tests Five PVC-cased boreholes extending to the depth of 60 ft were installed at position J-20, K-10, K-20, K-30 and M-20. The crosshole test was conducted along gridline K with the hammer at K-30, and two receivers at K-20 and K-10. The system including the hammer and two receivers were lowered from the surface by steps of 2 ft. Manual hammer blows created active waves, and the time of wave travel were recorded by the two receivers at different depths. From 55

56 the known distance between two receivers and the difference between times of wave travel recorded by two receivers, the shear wave velocity is calculated (figure 4-13). For the Newberry testing site, the soil profile below the depth of 25 ft is very stiff. By using the manual hammer that only created waves at relatively low frequencies, the time of wave travel in rock were not definitely determined. In this case, a hammer that can produce wave fields at high frequencies is necessary. Unfortunately, such a hammer was not available at the time of testing, so the maximum depth at which we could obtain the shear wave velocity was only 25 ft. 4.6 Soil Profile Comparison Soil profiles of Newberry derived from SASW, combined MASW, and cross-hole test are all shown together in figure First, regarding Vs profiles from combined MASW and SASW, it is observed that they are generally in good agreement. Consistent with the dispersion curves, the SASW and combined MASW are in particularly good agreement for shallow depths up to 18ft that is presented in the dispersion curves at high frequencies. However, the combined MASW is slightly stiffer (higher velocity) at some deeper depths. Second, it is observed that the surface wave based Vs profiles compare well with the crosshole results. However, the Vs profiles at the depth from 10 to 15ft are different. It can be explained that: 1) Crosshole tests were conducted at gridline K that is 180 ft away from the testing line of the nondestructive tests and the Vs profile changes over the test size. 2) The surface wave tests are conducted over a relatively long array length that sample and average over a large volume of material, whereas the crosshole results are based upon wave propagation between two boreholes that are only 10 ft apart, and thus these data represent a more local condition at the site. 56

57 4.7 Summary of Newberry Tests All of the signal processing methods and non-destructive testing techniques described in chapter 2 are applied to analyze the real recorded data of Newberry. Also, the crosshole test is briefly described. The conclusion has been derived as follows: 1) One more time, the cylindrical beamformer transform gives the best resolution of signal imaging for active wave fields. 2) The soil profiles of Newberry derived from SASW, combined MASW are relatively well matched each other. 3) The matching in soil profiles of Newberry derived from non-destructive tests and from cross-hole tests is good but not excellent because the crosshole test was taken far away from the testing line of nondestructive tests. 4) Combining of active MASW and passive MASW shows an excellent solution to increase the depth of investigation. Figure 4-1. Newberry testing site (from Hudyma, Hiltunen, Samakur 2007) 57

58 Combined dispersion curve Final dispersion curve Phase Velocity (ft/s) Frequency (Hz) Figure 4-2. Dispersion curve for SASW of Newberry Figure 4-3 Newberry active MASW recorded data in the time-trace (t-x) domain 58

59 Figure 4-4. Spectra of Newberry obtained by applying methods: a) f-k transform b) f-p transform c) Park, et al. transform d) Cylindrical beamformer 59

60 Figure 4-5. Normalized spectrum at different frequencies (Solid line for cylindrical beamformer, Dashpot line for Park et al. transformdashed line for f-k transform, Dotted line for f-p transform) 60

61 2500 f-k transform f_p transform Park et al. transform Cylindrical Beamformer 2000 Phase Velocity (ft/s) Frequency (Hz) Figure 4-6. Extracted dispersion curves of Active MASW obtained by applying 4 signalprocessing methods Figure 4-7. Combined spectrum of Passive MASW 61