evaluation of the multi-channel surface wave analysis approach for the monitoring of multiple...

© 2010 European Association of Geoscientists & Engineers 611

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Evaluation of the multi-channel surface wave analysis approach for the monitoring of multiple soil-stiffening columns

A. Madun1,3*, I. Jefferson1, D.N. Chapman1, M.G. Culshaw1,4, K.Y. Foo2 and

P.R. Atkins2

1 School of Civil Engineering, University of Birmingham, Edgbaston, Birmingham,B15 2TT, UK2 School of Electronic, Electrical and Computer Engineering, University of Birmingham, B15 2TT, UK3 Faculty of Civil and Environmental Engineering, University of Tun Hussein Onn, Parit Raja Batu, Pahat Johor 86400, Malaysia4 British Geological Survey, Kingsley Dunham Centre, Keyworth, Nottingham, NG12 5GG, UK

Received December 2009, revision accepted August 2010

ABSTRACTSurface wave spectral analysis is a well-known technique in the characterization of layered media, where individual layers are assumed to be laterally homogeneous. This technique was later extend-ed into the multi-channel surface wave analysis approach by using an array of sensors to offer higher signal-to-noise ratio and faster data collection as well as in aiding the identification of sur-face wave propagation from the source. The objective of this article is to assess the performance of the MASW technique for the monitoring of multiple soil-stiffening columns. The key difference in this application is the strong lateral heterogeneity due to the columns, while being relatively homo-geneous in depth. The application of this technique may alleviate the constraints associated with traditional field techniques such as plate loading tests, dynamic probing and field vane shear tests. A laboratory-scale experiment was carried out using materials with controlled properties in order to validate the proposed technique. Two concrete mortar blocks were built, one as a control and another with mild-steel columns installed. A piezo-ceramic transducer was acoustically coupled to the block using a padded weight in order to introduce a stepped-frequency excitation from the sur-face. Four accelerometers were used to capture the excitation signal. Data were collected from multiple excitations and averaging was then applied to maximize the signal-to-noise ratio. By recon-figuration of the exciter and receivers’ arrangement, the area containing the columns was sequen-tially surveyed. The experimental measurements were processed to obtain the phase velocity as a function of wavelength. Approximated inversion was then applied in order to obtain the phase velocity versus depth and this was repeated for all survey points in order to build a 2D plot of phase-velocity across the line of survey and with respect to depth. The results provided experimental evidence on the performance of this technique in the assessment of stiffening columns, evaluated against the requirements of spatial resolution of columns, the consistency of phase-velocities within the columns and the comparison of the measured stiffness profile against known empirical values.

al. 1996). Traditionally, the measurement of the stiffness profile is carried out by using laboratory and in situ, invasive field tests. However, geophysical methods, such as surface wave analysis, offer a non-intrusive and non-destructive approach to carry out the measurements. Moreover, geophysical approaches provide a cost effective way to assess site conditions, while overcoming the issue of sample disturbance in traditional investigative approaches.

INTRODUCTION Ground improvement work is crucial in reducing the deforma-tion of weak soils that may arise from loads imposed by civil engineering structures. The monitoring of the quality of ground improvement is therefore important in ensuring the integrity of the foundation on which the structure is built. One of the main parameters of interest is the ground stiffness profile (Matthews et

Near Surface Geophysics, 2010, 8, 611-621 doi:10.3997/1873-0604.2010047

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© 2010 European Association of Geoscientists & Engineers, Near Surface Geophysics, 2010, 8, 611-621

tifying the frequency-velocity dispersion of the surface wave. A swept-frequency signal is used and multiple closely-spaced receivers are deployed for sampling redundancy. This enables a selective strategy in the choice of offset distance and frequency to optimize the detection of surface waves while mitigating con-tamination from body waves. The multi-channel data are also processed with a wavefield-transformation method that directly produces an image where a dispersion pattern is recognized in the transformed energy distribution. The desired dispersion prop-erty, such as that of the fundamental surface wave mode, can then be extracted. In addition, surface wave analysis using a stepped-frequency excitation approach has been demonstrated by Gunn et al. (2006) for the assessment of a railway embankment, by Moxhay et al. (2001) in measuring the stiffness of a stone column and for site characterization by Matthews et al. (1996). In the majority of applications, the heterogeneous boundaries of the medium are not known a priori. A key distinction to this application is that the locations of the soil stiffening columns are known and can therefore be individually assessed. The focus of this paper is on assessing the viability of the multiple-receiver approach for the evaluation of multiple soil-stiffening columns. It is worth noting that in this specific case, the densities and stiff-ness of the material under test are laterally varied. The key con-tribution of this work is the application of a multiple-receiver strategy in combination with the spectral analysis of surface waves to detect and isolate anomalies in phase velocity caused by the contrast of material in the lateral dimension. The approach is unique in the implementation of a step-frequency transmission to maximize the signal-to-noise ratio and to simplify frequency selection for the extraction of dispersive surface waves. This also significantly extends the previous work on applying a single-channel surface wave analysis on a stone column or dynamically stiffened ground in field case studies documented by Redgers et al. (2008).

THEORETICAL BACkGROUND The MASW method can generally be separated into two main steps of data collection and signal processing for spectral analy-sis. For data collection, there is usually a seismic source, generat-ing a signal x(t) and multiple receivers deployed to acquire the seismic data, represented by y

1(t)…y

n(t) where n is the index of

the array of receivers. The common options for a seismic source are usually a manually controlled mass dropped to induce a broadband impulsive signal into the ground, or an electro-mechanical shaker controlled by a digital source. The earlier option is the simplest, while the latter allows precise control and variations of the source signal characteristics both in terms of bandwidth and time duration. The receivers usually consist of geophones for field testing or accelerometers in laboratory-scale testing. The arrangement of the transmitter and receiver arrays is subject to the near and far offset constraints (Heisey et al. 1982).

The parameters that control the quality of the ground treat-ment can be measured using laboratory tests. However, the proc-ess of sample retrieval required for laboratory testing often introduces additional difficulties associated with sample distur-bance and the reliability of the sample in representing the entire site. As a result, sample retrieval from the field for laboratory testing may not be sufficient in replacing field testing. Penetration testing, dynamic probing, field vane shear tests and plate loading tests are examples of conventional field-test techniques used for quality control testing. A comparison between geophysical seis-mic-based techniques and conventional geotechnical load-testing methods for the measurement of the ground stiffness profile was presented by Matthews et al. (1995), drawing the conclusion that geophysical testing can deliver results of significant quality. The majority of surface wave applications for civil engineer-ing have been used to characterize laterally homogeneous soils and pavements (Forbriger 2003). These are based upon spectral analysis of surface waves (SASW), continuous surface wave analysis and more recently, on multi-channel analysis of surface wave (MASW). Jefferson et al. (2008) showed how SASW can be used to assess qualitatively changes to ground properties later-ally after vibro-replacement stone columns treatment had taken place. Moxhay et al. (2001) and Redgers et al. (2008) applied the continuous surface wave analysis technique to measure the stiffness-depth profile of dynamically stiffened ground and vibro-replacement stone columns, making the assumption that the columns and soils are a single block in the lateral dimension. Their results produced a profile of the average of shear-wave velocity versus depth between the stiffening columns and the surrounding soil. The analysis used in such approaches assumes that the soil behaves as a layered half-space that is laterally homogeneous and isotropic. Thus, the results represent the mean velocity of the whole horizontal layer corresponding to the respective wavelength. The conventional surface wave techniques using a single-pair of receivers yield one-dimensional results of phase velocity ver-sus depth. To resolve anomalies in a laterally heterogeneous medium, it is necessary to obtain a plot of the phase velocity versus depth as a function of lateral distance and hence, the MASW technique is more suitable. Such a method provides information with greater resolution in the lateral dimension and can therefore be used to obtain a qualitative assessment of the variability of geotechnical properties such as stiffness and strength. This enables the detection of features such as voids, fractures and soft spots (Gordon et al. 1996). The implementa-tion of this technique usually involves the deployment of an array of multiple receivers with the seismic source. It has been suc-cessfully demonstrated by Xu and Butt (2006), Nasseri-Moghaddam et al. (2007) and Phillips et al. (2004) for the detec-tion of subsurface cavities and Tallavo et al. (2009) for the detection of buried timber trestles. Another unique aspect of the MASW technique, as described by Park et al. (1999), is the signal processing approach for iden-

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calculated between a pair of receivers, the normalized coherence becomes a measure of variance, over multiple snapshots or time, between the received signals. The normalized coherence can then be calculated as (Ifeachor et al. 1993):

(5)

where p is the index of P, the total number of repetitive collec-tions for each frequency step. μ(Y(f)) is the mean of the complex spectrum across the repetitive collections at each step frequency f and * represents the complex conjugate operation. The signal-to-noise ratio can be calculated from the normalized coherence using

(6)

The phase velocity, as a function of frequency, between any two receivers, can be calculated from their corresponding phase dif-ference. The phase difference at a particular frequency, Δφ(w) , is the angle of the complex spectrum value and expressed as:

(7)

here m and n are the receivers between which the four-quadrant phase difference is calculated. It should be noted that using only a single phase difference measurement is usually more sensitive to error from noise and interference from other modes of wave propagation. Therefore, it is recommended that if the signal-to-noise ratio is sufficiently high across reasonable bandwidths, then a best fit phase-frequency gradient is used as a method of averaging to calculate the time-delay. The time-delay associated with the phase difference observed between the two receivers can be derived from:

(8)

The frequency-dependent phase velocity, v(f), can then be obtained using the distance between the two receivers m and n, Δ

mnx, such that:

(9)

The plot of phase velocity versus frequency is the dispersion curve. To obtain the phase-velocity with respect to depth, the frequency values need to be inverted into depth. This is based upon the observation that surface waves with lower frequencies penetrate to greater depths. The process of inversion can be gen-erally divided into three main categories (Matthews et al. 1996; Menzies 2001): approximation, iterative minimization and finite element modelling. The approximation method is the simplest

These constraints are associated with the wavelength of the signals and, therefore, determine the maximum and minimum frequencies that are useful for spectral analysis. The empirical rule for the near-offset constraint of the distance between the source and the first receiver, d

min is recommended in the litera-

ture (Al-Hunaidi 1993; Matthews et al. 1996; Park et al. 1999) as a function of the surface wave wavelength, λ, to be approxi-mately:

(1)

The far-offset is associated with the attenuation of the surface waves when the receiver is far away from the seismic source. This constraint is approximately:

(2)

In addition, the spacing between the receivers, Δx, should be within the constraint of

(3)

to avoid spatial aliasing when comparing the phase between any pair of receivers. λmax and λmin are the wavelengths corresponding to the minimum and maximum frequencies, respectively. A more detailed study on the data acquisition of high-frequency Rayleigh-waves was carried out by Xia et al. (2006). For signal processing and spectral analysis, the time-domain signals are discretely sampled, yn (k) , by an analogue-to-digital converter and N-points are stored on a computer where the processing and the subsequent spectral analysis are carried out. To adequately capture the spectrum of the signals, the sampling rate, fs, of the analogue-to-digital converter should be at least twice the maximum bandwidth of the signal and usually higher in practice. The discrete Fourier transform (implemented using the FFT algorithm) is then applied to the signal to obtain the discrete spectrum of the signal, Yn(f):

(4)

where f is the discrete frequency of the signal, N = Tfs, while

k and T are the discrete-time and time-duration of the signals. The signals are usually zero-padded in the time domain prior to the application of a radix-2 FFT algorithm. As the quality of the observed phase velocity is strongly dependent upon the fidelity of the phase information, one may wish to observe the coherence of the received signals with respect to frequency, as a degrada-tion of the signal-to-noise ratio at a particular frequency would imply that the phase data for that frequency are unreliable. The coherence of the received signals is represented by its normal-ized cross-spectrum between the pairs of received signals. This allows one to obtain a measure of the signal-to-noise quality as a function of frequency. In cases where the phase difference is

A. Madun et al.614


neous and heterogeneous materials, measured between a pair of receivers on one position. For a homogenous material, the gradi-ent of the phase differences from which the phase velocities of the surface waves can be derived is near constant, hence the cor-responding plot in Fig. 1(b) showing the same velocity at differ-ent depths. However, in a heterogeneous material, the dispersion curve manifests a changing gradient with respect to frequency, depicting a variation of Rayleigh-wave phase velocity with respect to frequency. The frequency axis is converted to depth using the approximations given in equations (10) and (11), while the phase velocities are calculated using equation (9). Figure 2(a) illustrates a trivial case of strong lateral heterogeneity where homogeneity with depth can be assumed, or that heterogeneity with depth is relatively insignificant. This is analogous to the situation of the soil in proximity to a stiffening column. Figure 2(b) illustrates the usual scenario of heterogeneity in soil due to layers of varying properties at different depths, more akin to soil following dynamic compaction.

but least exact. The method is based upon the assumption that the amplitude of the surface wave is attenuated linearly as a function of depth and can usually be represented by a direct relationship of:

(10)

where the wavelength, λ(f), is

(11)

The approximation in equation (10) is common for a vertically homogeneous site, as documented in the literature (Jones 1958; Heukolom and Foster 1962; Ballard and Mclean 1975; Abbiss 1981). The iterative optimization technique is based upon the concept introduced in the early work by Thomson (1950) and Haskell (1953). It is based upon iteratively optimizing the param-eters of the soil profile until a good match between the measured dispersion-curve and the dispersion-curve derived from the esti-mated soil profile is achieved. This technique is computationally intensive but offers greater accuracy in a sharply heterogeneous medium. Finite element modelling is a forward-solver technique based upon obtaining a theoretical solution to the wave propagation model through the soil. The approximation method is herein chosen for its relative simplicity, as the consideration in this work involves a relatively shallow depth, in which the material within the columns can be considered to be reasonably homogeneous with depth (Christoulas et al. 1997; Ellouze et al. 2010) and the focus is on assessing multiple, spatially dense, lateral heterogeneities. In a solid and homogeneous medium, the Rayleigh-wave phase velocity, vr, can be converted into shear-wave velocity, vs, which for an elastic medium is approximately:

(12)

where v is a Poisson’s ratio (Richart et al. 1970). The maximum shear modulus of the material, Gmax, which describes the behav-iour of the ground under load (Matthews et al. 2000), is related to the mass soil density, ρ and the shear-wave velocity through the relationship:

(13)

The error in maximum shear modulus arising from the approxi-mation of the Poisson’s ratio for soil and rock materials in the conversion of Rayleigh-wave phase velocity into shear- wave velocity is usually less than 10% (Menzies 2001). Using the above relationships, the measurements of the Rayleigh-wave phase velocity enables the evaluation of the stiffness profile of the ground, as well as the associated effect of the improvement work that had been carried out. A simplified example is illustrated in Fig. 1. Figure 1(a) shows the ideal dispersion curve for arbitrary, vertically homoge-

FIGURE 1

A simplified example to illustrate the a) phase-frequency relationships for

homogeneous and heterogeneous materials and b) their corresponding

inverted depth versus Rayleigh-wave velocity profile.



inter-column spacing of about 2 m (Muir et al. 2000). Using this as a guideline, the steel columns were installed with a length, diameter and spacing ratio of 15:2:6, such that the inter-column spacing was 120 mm and yielding an overall scaling factor of 16. The concrete mortar material was chosen because its geotech-nical properties such as moisture content were relatively easy to control and vary insignificantly throughout the duration of the experiment. Also, the compression, shear and surface wave velocities for concrete mortar as a function of density and Poisson’s ratio are well documented (Jones 1962; Khan et al. 2006). The reason for using mild steel rods was to enhance the contrast of material density, thus providing a stronger variation of lateral homogeneity and subsequently aiding in the identifica-tion and analysis of the associated anomalies. A portable ultrasonic velocity profiler was used to measure the P-wave velocity on the first block, which did not contain steel rods and the measurement was 2350 m/s. The Rayleigh-wave phase velocity of homogeneous in the concrete mortar block was expected to be approximately 1000 m/s (Khan et al. 2006). For the steel bars, the measurement of P-wave velocity from the

ExPERImENTAL SETUP AND CALIBRATIONTo study and evaluate the viability of this method, a laboratory-scale experiment was carried out. The purpose of performing a laboratory-scale experiment, instead of a field test, is that the process of data collection can be pre-calibrated and that the truth data regarding the material can be measured a priori. In this setup, two concrete mortar blocks were constructed measuring 720 mm × 600 mm × 450 mm in length, width and depth respectively. The concrete mortar blocks were constructed using a mixture of fine sand with 10% cement and 13% water. The mixed concrete was poured into a wooden frame, then compacted using a concrete vibrator. The second block was constructed with mild steel rods embedded before the cement-sand mixture solidified. The mixture was left to solidify for 24 hrs and cured with a moist blanket to avoid the occurrence of cracks. The rods measured 38 mm in diameter and 300 mm in length. The dimension of the steel columns and their spacing closely followed the ratio of that in an actual ground improvement site. Although the dimensions of stone columns vary depending on circumstantial treatment requirements, typical measurements are in the region of 10 m in length and 0.6 m in diameter, with an

FIGURE 2

The illustration of a a) laterally heterogeneous scenario compared to b)

a case of depth heterogeneity in a layered material.

FIGURE 3

a) Illustration of the laboratory-scaled model and equipment setup and

b) photo of the concrete mortar block with sensing accelerometers where

the first sensor-pair on the left was located on one of the columns.

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of receivers consisted of up to 4 piezoelectric accelerometers. The receiver array was then moved after each measurement in order to obtain data with a higher spatial resolution. This was repeated in order to extend the length of survey passing over a steel column. It is worth noting that having a limited number of receivers does not preclude the practical use of a larger number of receivers in the field. The total number of receivers deployed is limited by the constraints as discussed in the section ‘Experimental setup and calibration’ and the sufficiency of signal-to-noise ratio at the furthest receivers, beyond which the excitation source would have to be moved along with the receivers to cover an extended length or area. Therefore, the number of receivers deployed in a multi-channel approach is usually a compromise between the economic cost of the equip-ments and the time required to conduct the survey. As the laboratory model was scaled down, the frequency of the signal for surface excitation was scaled higher accordingly. The distance between the source and the first receiver, d, was set as 50 mm. Using the constraints given in equations (1) and (2) and assuming a Rayleigh-wave phase velocity of 1000 m/s, the applicable frequency range was between 6.7–60 kHz. However, due to the frequency constraints of the sensing accelerometers, the upper frequency was limited to 10 kHz. The excitation wave-form consisted of a 1 s continuous wave shaded with a Tukey-window to reduce spectral side-lobes and increase the dynamic range of the narrow band of interest. Using a stepped-frequency approach, the frequency of the sinusoidal wave was varied from 3–10 kHz with a step-size of 10 Hz. For each frequency step, 5 repetitive measurements were obtained for averaging and for the calculation of the normalized coherence.

ultrasonic velocity profiler was 4950 m/s. The theoretical Rayleigh-wave phase velocity for the mild-steel bar was calcu-lated to be 2970 m/s using parameters of elastic modulus, Poisson’s ratio and density of material of 210 GPa, 0.3 and 7850 kg/m³, respectively (Bauccio 1993). An illustration of the laboratory setup is shown in Fig. 3. A script was written within the Matlab environment to conduct the experiment using a computer. The computer was connected to a National Instruments data acquisition system, in which a 16-bit analogue output module (NI-9263) generated the transmission waveforms. An audio power amplifier was used to drive the piezo-ceramic transducer with the excitation signals. On the receive side, the sensors consist of four piezoelectric accelerom-eters (ICP 352C42 by PCB Piezotronics) with a frequency range of 1 Hz to 10 kHz that were coupled to the surface with cyanoacrylic adhesive. The accelerometers were connected to an analogue signal conditioner and were then sampled by a 24-bit sigma-delta analogue-to-digital converter module (NI-9239) with a sampling rate of 50 kHz. Collected data were stored and processed after the completion of a data acquisition session. To minimize ambient noise, the concrete mortar block was isolated from the ground with acoustic absorbers. The piezo-ceramic transducer was acoustically coupled to the surface using a weight padded with acoustic absorbers. A thin layer of conductive gel was applied between the transducer and the concrete mortar surface in order to reduce air-voids and improve coupling.

ExPERImENTAL PROCEDUREThe multi-channel approach considered in this work is based upon a relatively small number of receiver channels. The array

FIGURE 4

Sequence of the data collection

process to survey the surface

across the columns.



and angle, respectively, represent the spectral amplitude and phase. As a stepped-frequency transmission was implemented, the complex value corresponding to the frequency of the trans-mission with which the received signal is associated was selected and stored. This was repeated for all the repeated transmissions at the same frequency and then for all the frequency steps across the whole range. This yielded a new spectral series of complex FFT values as a function of the stepped frequencies. Therefore, the data were reduced to the stepped-frequency spectral repre-sentation for the 4 sensor channels, with 5 multiple sets as there were 5 repetitive snapshots for each frequency step during data acquisition. The next step was to obtain the phase difference between the receivers. Among the 4 sensors, there were 3 phase difference measurements between adjacent sensor pairs. For each of these adjacent sensor pairs, the phase difference is obtained by per-forming a complex conjugate multiplication in the spectral domain. For example, to obtain the phase difference between adjacent sensors A and B, the FFT of the signal from sensor A was multiplied with the complex conjugate of the FFT of the signal from sensor B. Since there were multiple snapshots, the spectra used in the multiplications were that of the average. Figure 5 shows the phase difference measurements obtained from the data set with no columns and from the first set of meas-urement with columns. In an ideal, homogeneous medium with

Measurement was first performed on the block containing no steel columns to obtain a control data set. The equipment was then set up on the concrete mortar block that contained the steel columns. A series of measurements were performed by repeti-tively moving both the excitation source and sensing accelerom-eters after completing each set of measurements until the area across the columns was surveyed. The sequence is shown in Fig. 4. Such an arrangement is only possible in situations where the locations of the soil-stiffening columns are known. As this is true in most ground improvement works, the knowledge of the columns’ locations is used for planning the survey in order to avoid ambiguities associated with boundaries between layers. There were 15 unique lateral survey positions and the columns were located at the 3rd, 8th and 13th positions respectively. Each set of measurements required a time duration of approximately 90 min.

DATA PROCESSING AND RESULT ANALYSISEvery complete set of measurements contains received signals from the 4 sensing channels, spanning the frequency range of 3–10 kHz with a step-size of 10 Hz. After the completion of each data collection session, the data were loaded into Matlab for processing. The first step was to apply an FFT on all the data to obtain the spectral representation of the received signal. The results were a series of complex values of which the magnitude

FIGURE 5

The phase differences for the 3 sensor-pairs from a) measurements on

concrete mortar without columns and from b) the first set of measure-

ments on the concrete mortar with columns.

FIGURE 6

The normalized coherence between channels A and B from a) measure-

ments on concrete mortar without columns and from b) first set of meas-

urements on the concrete mortar with columns.

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minimum threshold of 0.995 for the normalized coherence was applied and the frequencies with coherence that exceeded the threshold were selected. This threshold corresponded to a signal-to-noise ratio of approximately 20 dB and an equivalent phase measurement standard deviation of approximately 6 degrees. The next step was to obtain the Rayleigh-wave phase velocity measurements. The effective frequency range, as predicted by equations (1) and (2), was from 6.7 kHz up to the accelerome-ter’s upper frequency limitation of 10 kHz. Since the constraints were only an approximation, a frequency range of between 6–10 kHz was chosen for processing. As there were only a very small number of frequencies that exceeded the threshold, this frequency range was divided into sub-bands of 400 Hz each. The velocities were calculated from the phase measurements using equation (9). Within each sub-band, the velocities that corre-sponded to the qualifying frequencies were averaged. In sub-bands that contained no qualifying frequencies, the average value from the higher sub-band was used. A low-pass interpola-tion filter was then applied to smooth and resample the data by a factor of 4, producing velocities that correspond to 100 Hz step increments. The results are shown in Fig. 7. Figure 7(a) shows the result corresponding to the first set of measurements (based upon the sequence described in Fig. 4) from 6–10 kHz. It can be observed from Fig. 5(a) (and similarly from other measurement

no boundaries, the differential phase response is expected to be a linear function of frequency. However, the result in Fig. 5(a) shows that the measurements were corrupted by boundary reflec-tions as well as the mutual interference between the body and surface waves, while Fig. 5(b) demonstrates that the presence of columns introduced additional reflections due to the sharp varia-tion in material density between the columns and the concrete mortar. This resulted in significant distortion in the phase response. Measurement from the C-D sensor pair located direct-ly on top of the first column demonstrated the most severe distor-tion. This was likely to be caused by a combination of two fac-tors, the lack of energy entering the column due to reflections and interference from reflections within the column. This was also reflected in the lack of signal coherence at the receivers over a relatively large number of frequencies. The observed correla-tion of phase response is discussed in the section ‘Conclusions’. The normalized coherence was then calculated for each of the sensor pairs using equation (5). The plots of normalized coher-ence for the case without columns and with columns are shown in Fig. 6. The normalized coherence is a measure of the signal quality in terms of the signal-to-noise ratio and was therefore used as a criterion in choosing the frequencies that contained phase measurements with higher accuracy. As phase measure-ments are very sensitive to degradation in signal-to-noise ratio, a

FIGURE 7

a) The plot of phase velocity versus frequency for the first set of meas-

urements with columns and b) the 2D pseudosection across all the lat-

eral survey positions.

FIGURE 8

a) The plot of shear-wave velocity versus depth (b) and the average shear

wave across depth for all the lateral survey positions.



energy near the surface for some frequency components. From the perspective of the multi-channel surface wave analysis technique, the unique aspect of this target application is the pattern and proximity of lateral heterogeneity introduced by the columns. The energy introduced by the seismic source needs to contend with multiple changes in material density due to the arrangement and spacing of the columns, each introducing reflections and additional attenuation to the wave. Therefore, this may reduce the upper limit for the useful distance between the source and the furthest receiver, hence increasing the number of required array movements. The effect of reflections and attenua-tion on the source energy should also be taken into consideration in determining the optimal source-array configuration. It is also worth noting that measurements obtained for the column itself are more vulnerable to self-interference due to internal reflec-tions caused by the heterogeneous transition of acoustic imped-ance at the column-pile boundary. The elliptical propagation of surface waves may have contributed to the variation of measured velocity with depth. As the wavelength increases, the elliptical propagation of the surface wave may not be fully contained within the steel bar and would traverse across the column-pile boundary. The minimum requirement for spatial resolution, for the pur-pose of assessing the columns and surrounding soil, is the width of the column as the column width is usually smaller than the distance between them in a typical field scenario. This require-ment allows columns to be individually assessed without the influences from non-column material. Given the knowledge of the column location, it is possible to plan the survey to meet this requirement. The trade off is an upper constraint on the usable frequencies due to spatial aliasing, as the spacing between receivers is limited by the column width. In a real application, although the material within the column is homogeneous, the soil between the columns is likely to be layered and it may be challenging in a real application to resolve all the layers in the soil due to the small distance between the columns, as the high spatial density of columns present a con-straint to achieve sufficient depth in the soil as large receiver spacing may include a column instead of just the soil in between. Due to the constraints on receiver spacing, it is likely that the length of the column can only be accurately inferred at the expense of the individual column’s stiffness measurement because the larger receiver spacing will include both the column and the surrounding soil. The interaction between the body waves and surface waves as a function of distance from the source and frequency are often difficult to predict in practice. The switch-over between the dominating waves is usually not instantaneous and therefore mutual interference (self-noise) can occur over a range of dis-tances from the source. With the use of a stepped-frequency approach in this research, it can be observed from the result in Fig. 5(a) that there exists a correlation of phase-difference between the sensor-pairs that becomes weaker at higher frequen-

sets not shown herein) that the velocities at frequencies lower than 7 kHz had larger deviations from the expected Rayleigh-wave phase velocity for the material of concrete mortar and mild-steel column. This was likely to have been caused by inter-ference from other wave modes at these lower frequencies. As such, the remaining data sets were processed using the range of 6.8–10 kHz. The results from all 6 sets of measurements were merged to form a 2D Rayleigh-wave phase velocity map as a function of frequency and lateral survey positions in Fig. 7(b). Anomalies in the form of higher velocities were observed at positions 3, 8 and 13, where the columns were located. The frequencies were then inverted using equations (10) and (11) with the measured velocities to calculate the wavelength and subsequently, estimates of depth. This yielded a 2D pseudosection of phase velocities as a function of depth and lateral positions. The Rayleigh-wave phase velocities were converted into shear-wave velocities by a factor of 1.088 based upon equation (12) and shown in Fig. 8. The pseudosection in Fig. 8(a) contains only a sparse number of discrete measurements that correspond to certain depths. Where more discrete samples are available, either via the use of a wider frequency range or in cases where there are more frequencies that contain accurate phase measurements, the shear-wave velocity values can be interpolated to obtain a smoothed data set. In this case, given the a priori knowledge that both the con-crete mortar and the steel columns were relatively homogeneous with respect to depth, it was possible to average the shear-wave velocity measurements across the different depths, producing the result shown in Fig. 8(b). For comparison, the Rayleigh-wave phase velocities in the three mild-steel columns, averaged along depth, were 3128 m/s, 2685 m/s and 2525 m/s. The average Rayleigh-wave phase velocity in the concrete mortar was 1173 m/s. These experimen-tal results compare to the expected values of 2970 and 1000 m/s for the columns and concrete mortar respectively. Based upon equations (12) and (13), the maximum error of stiffness profile estimation in this experiment was approximately 15% in the columns and 17% for the concrete mortar.

DISCUSSIONIn this work, the use of steel columns in concrete mortar pro-vided the advantages that the geotechnical properties of the materials are well characterized but also introduced constraints in the direct extrapolation of the results for site applications. The main difference is in the sharp variation of material density caused by the steel-to-concrete mortar interface. As the reflec-tion coefficients at the boundary between two materials are pro-portional to the contrasts in density, the reflections are usually less severe in real sites as the variation in density between stiff-ening rock columns and the surrounding soil is usually smaller. The gradient of density variation is also less sharp as the sur-rounding soil may mix into the rock column after compaction. This implies that the signal will experience some level of refrac-tion and depending on the pattern of refraction, may reduce the

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CONCLUSIONSThe feasibility of using surface-wave analysis techniques with multi-channel acquisition specifically for the non-intrusive assess-ment of multiple soil stiffening columns has been demonstrated. A laboratory experiment scaled from a typical ground improvement site was carried out using concrete mortar and mild-steel columns, both of which are materials with well-known stiffness profiles and therefore allowed detailed evaluation to take place. The Rayleigh-wave velocities corresponding to the mild steel columns and the concrete mortar were estimated, from the measure-ments, to be 2779 and 1173 m/s respectively. These compare with the expected velocities of 2970 and 1000 m/s, demonstrating a rea-sonable agreement between the measured and known stiffness pro-file of the materials. The experimental measurements also identified challenges asso-ciated with the practical use of this technique, which are unique to the assessment of multiple columns. On a typical site with a dense arrangement of soil-stiffening columns, the reflections, refractions and attenuations caused by the boundaries of material density, the close proximities of the columns resulting in the possible constraints on source-array configuration and the effect of self-interference on the measurements of the individual columns are issues that need to be investigated in greater detail. Being able to take into account these factors would improve the accuracy of the measurements, leading to greater confidence in the result. Further works that are being carried out are the construction of an Oxford-clay soil and sand column model to investigate materials that better matches a real scenario and the design of an optimal receiver array deployment that maximizes the rate of column assessment on a typical ground improvement site. This provides a powerful tool to assess the effects of stiffening columns in a non-destructive and non-invasive way.

ACkNOWLEDGEmENTSThe authors would like to thank the University of Tun Hussein Onn, Malaysia and the Ministry of Higher Education, Malaysia, for their generous sponsorship of this research. The authors also thank Dr Andrew Thomas and Mr Saiful Wazlan for their assist-ance and input towards the research.

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evaluation of the multi-channel surface wave analysis approach for the monitoring of multiple...

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