Laboratory-Based Correlation between Liquefaction Resistance and Shear Wave Velocity of Sand with Fines

: This paper presents the results of a laboratory investigation into the effect of non-plastic ﬁnes on the correlation between liquefaction resistance and the shear wave velocity of sand. For this purpose, undrained stress-controlled cyclic triaxial and bender element tests were performed on clean sand and its mixtures with non-plastic silt. It is shown that the correlation between liquefaction resistance and shear wave velocity depends on ﬁnes content and conﬁning effective stress. Based on the test results, correlation curves between ﬁeld liquefaction resistance and overburden stress corrected shear wave velocity for sand containing various contents of ﬁnes are derived. These curves are compared to other previously proposed by ﬁeld and laboratory studies.


Introduction
The velocity of shear wave propagation, V s , is a key soil property, used for soil characterisation, such as the estimation of small-strain shear modulus, liquefaction resistance, seismic response, and assessment of the effectiveness of soil improvement methods used in soils, identification of transportation of pollutants in soils, as well as others.
Liquefaction of sandy soils under cyclic loading conditions is considered one of the major causes of damage to earth structures and foundations. To date, a great research effort has been devoted to improving the knowledge concerning the liquefaction characteristics of natural soil deposits and the ability to predict the nature and the extent of the liquefaction phenomenon. In practice, liquefaction resistance is evaluated from laboratory tests such as cyclic simple shear, cyclic triaxial, and cyclic torsional shear, on undisturbed or reconstituted samples and by field tests. Semi-empirical field-based procedures for evaluating the liquefaction potential during earthquakes are based on correlations between field behaviour and in-situ index tests, such as standard penetration test (SPT), cone penetration test (CPT), Becker penetration test (BPT), and shear wave velocity (Vs).   [1] proposed the oldest and perhaps the most widely used procedure termed the "simplified procedure", developed from evaluations of field observations and field and laboratory test data, in which the cyclic stress ratio, CSR = τ av /p 0 , is correlated with the SPT blow counts, corrected for both effective overburden stress and energy, (N 1 ) 60 , for clean sands and silty sands with fines content greater than 5% and earthquake magnitude, M = 7.5. Through the years the "simplified procedure" has been updated [2] and revised relations for use in current practice have been recommended. Idriss and Boulanger (2004) [3] re-evaluated SPT and CPT case history databases and re-examined the semi-empirical procedures for evaluating the liquefaction potential of saturated cohesionless soils during earthquakes. Cavallaro et al. (2018) [4] determined the shear wave velocity profiles in various areas of the Emilia-Romagna Region, in Italy, by means of a large series of in situ, geophysical and laboratory tests, for the analysis of significant and widespread liquefaction phenomena, observed during the seismic events of May 2012.
a=0.25 (1) where C N is a factor to correct measured V s for overburden stress, p a is a reference stress equal to 100 kPa, and σ v , is the effective overburden stress in Kpa.
Geotechnics 2021, 1, FOR PEER REVIEW 2 geophysical and laboratory tests, for the analysis of significant and widespread liquefaction phenomena, observed during the seismic events of May 2012. The evaluation of liquefaction resistance or cyclic resistance ratio, CRR, based on field evaluation of shear wave velocity, Vs, constitutes a promising alternative procedure compared to the approaches based on penetration-type tests. The correlation between the field CRR, CRRfield, and Vs1, where Vs1 is the overburden stress-corrected shear wave velocity, similar to the traditional procedures for modifying standard and cone penetration resistances [5], has been the subject of numerous field and laboratory studies over the last thirty years, as described below. Tokimatsu and Uchida (1990) [6] proposed a 'best fit' CRRfield-Vs1 curve, which also includes the data presented by [7][8][9] and is based on a combination of in situ measurements of Vs and laboratory liquefaction tests. Kayen et al. (1992) [10] and Lodge (1994) [11] developed field CRRfield-Vs1 curves for sites that did and did not liquefy during the 1989 Loma Prieta earthquake. Similarly, Robertson et al. (1992) [5] developed a CRRfield-Vs1 curve from field performance data and seismic CPT tests. Stokoe (1997, 2000) [12,13] developed semi-empirical liquefaction resistance criteria from field measurements of shear wave velocity (referred to as semi-empirical procedure below). They proposed different CRRfield-Vs1 curves for soils with different fines content, fc, to separate liquefaction from no-liquefaction zones for a magnitude 7.5 earthquake, Figure 1. According to Andrus and Stokoe (2000), [13] the case history data and the CRRfield-Vs1 curves they presented are limited to relatively level ground sites with average depths of <10 m, uncemented soils of Holocene-age, ground-water table depths between 0.5 and 6m, and Vs measurements performed below the water table. In the following figure, Vs1, was obtained from: where CN is a factor to correct measured Vs for overburden stress, pa is a reference stress equal to 100kPa, and σ′v, is the effective overburden stress in Kpa.

Figure 1.
Curves recommended for calculation of CRR from Vs1 measurements along with case history data [13]. Figure 1. Curves recommended for calculation of CRR from V s1 measurements along with case history data [13]. Kayen et al. (2013) [14] reported the results of an 11-year international project to gather 301 new V s site data from China, Japan, Taiwan, Greece, and the United States and develop probabilistic correlations for seismic liquefaction occurrence in sand with various fines contents. At most sites, a continuous harmonic-wave spectral analysis of surface waves method (SASW) was used for V s measurement. They noted that the effect of fines is minor in comparison with other aspects of the analysis, namely, the estimation of uncertainty associated with CSR and V s1 . They found 14 data points that cross beyond the Andrus and Stokoe (2000) [13] clean sand curve into a frontier previously deemed non-liquefiable and suggested that the concept of a limiting upper bound V s1 of 215 m/s for seismic soil liquefaction is unconservative.
Laboratory-based CRR field -V s1 correlations have been presented by [15][16][17][18][19][20][21][22][23][24], Table 1. These refer to clean sand and sand-silt mixtures with fines content, f c , up to 75%. In all the above studies, V s was measured by bender element tests, except for the study by Askari et al. (2011) [21] in which torsional resonant column tests were used, while CRR was estimated from the results of cyclic triaxial tests.
The aim of this work is the investigation of the effect of fines on CRR field -V s1 correlation by means of laboratory tests. For this purpose, a parametric laboratory investigation was conducted by means of bender element and undrained cyclic triaxial tests for the measurement of V s and CRR, respectively, on clean sand and its mixtures with a non-plastic (NP) silt. The test results allow the derivation of CRR field -V s1 correlation curves for the sand and the sand-silt mixtures and their comparison with previously proposed curves in the literature, as described above. The V s measurements are also used for the estimation of the small-strain shear modulus, G max , of the soils, a key parameter for site characterisation, understanding soil behaviour, and the development of soil behaviour models.

Tested Materials
The materials used in the testing program were natural quartz clean sand (S) with well-rounded grains and its artificial mixtures with non-plastic silt (F), a ground product of natural quartz deposits in Assyros, Greece. Tests were conducted on the clean sand and on three groups of mixtures of the sand with the silt, having fines content, f c , of 15, 25, and 35% of the total dry mass of mixtures (noted as S, SF15, SF25, and SF35, respectively). A more detailed description of the mixtures is presented in [28].
The physical properties and grain size distributions of the tested materials are presented in Table 2 and Figure 2, respectively.

Testing Procedure
As stated previously, the testing program comprised bender element and undrained stress-controlled cyclic triaxial tests for the determination of Vs and CRR of the tested materials, respectively. Both types of tests were performed using a closed-loop automatic cyclic triaxial apparatus, designed and manufactured by MTS (Material Test Systems Corporation, Eden Prairie, MN, USA) [28]. Its principle of operation is based on the cooperation of its two main systems, the servo-hydraulic and the electronic, with the application of closed-loop control, firstly, for either the stress or the strain control of the actuator rod, and, secondly, for the control of the pressure inside the triaxial cell.

Specimen Preparation
The specimens (height/diameter = 150 mm/100 mm) were formed by moist tamping at a water content varying between 4 and 12% using the undercompaction method, introduced by [29]. Moist tamping was preferred to other preparation methods, such as pluviation techniques, in order to achieve uniform density and homogeneous distribution of fine particles and to enable the formation of loose specimens, as moist tamping produces specimens of varying densities [30]. Saturation was achieved by percolating through the specimen, from the bottom to the top drainage line, first carbon dioxide gas (CO2) for 20 min and then deaired water. A suction pressure of 15 kPa was applied while dismantling the specimen, measuring its dimensions, and assembling the triaxial cell. In order to ensure full saturation, a series of steps of simultaneous increasing cell pressure and back pressure were performed, while maintaining effective confining stress of 15 kPa. A final back pressure of 200-400 kPa

Testing Procedure
As stated previously, the testing program comprised bender element and undrained stress-controlled cyclic triaxial tests for the determination of V s and CRR of the tested materials, respectively. Both types of tests were performed using a closed-loop automatic cyclic triaxial apparatus, designed and manufactured by MTS (Material Test Systems Corporation, Eden Prairie, MN, USA) [28]. Its principle of operation is based on the cooperation of its two main systems, the servo-hydraulic and the electronic, with the application of closed-loop control, firstly, for either the stress or the strain control of the actuator rod, and, secondly, for the control of the pressure inside the triaxial cell.

Specimen Preparation
The specimens (height/diameter = 150 mm/100 mm) were formed by moist tamping at a water content varying between 4 and 12% using the undercompaction method, introduced by [29]. Moist tamping was preferred to other preparation methods, such as pluviation techniques, in order to achieve uniform density and homogeneous distribution of fine particles and to enable the formation of loose specimens, as moist tamping produces specimens of varying densities [30]. Saturation was achieved by percolating through the specimen, from the bottom to the top drainage line, first carbon dioxide gas (CO 2 ) for 20 min and then de-aired water. A suction pressure of 15 kPa was applied while dismantling the specimen, measuring its dimensions, and assembling the triaxial cell. In order to ensure full saturation, a series of steps of simultaneous increasing cell pressure and back pressure were performed, while maintaining effective confining stress of 15 kPa. A final back pressure of 200-400 kPa was found to be sufficient, as the parameter of pore water pressure, B = ∆u/∆σ, did not increase by further increasing back pressure. In all the tests the parameter B had values from 0.95 to 1.00. After completion of saturation, the specimens were isotropically consolidated under effective isotropic stress, p 0 , ranging from 50 to 300 kPa. A period of time equal to double the consolidation time of the specimens was allowed before testing. During consolidation, the volume change and the axial displacement of the specimens were recorded in order to calculate the post-consolidation void ratio, e.

Bender Element Tests
The bender element system was installed in the cyclic triaxial apparatus. The bender elements were encapsulated and then mounted into inserts which were fixed into specially manufactured top and bottom platens of the cylindrical specimen. A function generator (Agilent 33220A) was used for the excitation of the source sensor (top platen) with an electrical signal. Waves transmitted through the soil specimen were recorded at the other end by the bender element in the base pedestal (receiver). A digital oscilloscope (Agilent 54642A) was used for the display and recording of both the input-source and output-receiver signals. The function generator and the oscilloscope were connected to a computer. The type of electrical signal used to drive the source sensor was a sinusoidal pulse of 10 Volts (amplitude) at a frequency, f, ranging from 3 to 10 kHz. An automated measurements system was developed for signal acquisition and analyses which included recording, appropriate filtering, and automated measurement of travel time of the signal in time and frequency domain [31]. In this work, the start-to-start method was used for the measurement of shear wave travel time in the soil specimen [32]. To account for the near field effect disturbances that are believed to be the influence of P wave signals, that reach before the actual shear waves, as well as signal noises, signal arrival was observed by passing waves of different frequencies [33,34]. According to the start-to-start method, when the first amplitude in the time history of the receiver signal matches the direction of input motion (source signal), the point where the receiver signal takes off from the baseline (horizontal line of zero voltage when there is no signal) is the time of shear wave arrival. In case the first amplitude in the time history of the receiver signal does not match the direction of input motion, the point where the receiver signal first transverses towards the input motion direction and intersects the baseline is the time of shear wave arrival. As the bender element test is considered non-destructive, measurements of V s were performed at various levels of effective mean (isotropic) stress, p 0 , ranging from 30 to 300 kPa. Test details, as well as the results of the V s measurements, are presented in Table 3 for the sand and the mixtures.

Cyclic Triaxial Tests
In the cyclic triaxial tests, the specimens were subjected to a sinusoidally varying axial stress (±σ d ) at a frequency of f = 0.1 Hz under undrained conditions. Typical results of cyclic triaxial tests are presented in Figure 3a,b for sand and a mixture of sand with 15% fines, respectively. Plots of CSR, ε DA , ∆u/p 0 with time, t and q with ε DA and p , are shown. During cyclic loading, the excess pore water pressure, ∆u, builds up and approaches p 0 , when the state of liquefaction is reached (∆u/p 0 ≥ 0.90). For a given sand, the rate of increase of ∆u, its final value and the corresponding double amplitude axial strain, ε DA , depend on p 0 , the density, and the applied cyclic stress ratio, CSR = σ d /2p 0 [28]. The occurrence of ε DA = 5% is customarily used as a reference point to define the state of cyclic softening or liquefaction of both clean sand and sand containing fines [35]. Thus, in order to specify the onset of liquefaction, the number of loading cycles, N, required to reach ε DA = 5%, N l , is determined by running a series of tests with different CSR values. In view of the typical number of significant load cycles from 10 to 20 (10-20 for an earthquake of a 7.5 magnitude) of actual earthquakes, in this work, the onset of liquefaction and, thus, the cyclic resistance ratio, CRR 15 , is considered as the CSR required to produce ε DA = 5% in 15 loading cycles.
Geotechnics 2021, 1, FOR PEER REVIEW 8 typical number of significant load cycles from 10 to 20 (10-20 for an earthquake of a 7.5 magnitude) of actual earthquakes, in this work, the onset of liquefaction and, thus, the cyclic resistance ratio, CRR15, is considered as the CSR required to produce εDA = 5% in 15 loading cycles. Papadopoulou (2008) [28] studied the effect of density, p 0 , and f c on CRR 15 of the soils examined in this work and presented a database of results of undrained stress-controlled cyclic triaxial tests on the sand and the sand-silt mixtures with f c = 15%, 25%, 35%, 40%, and 60%. For each soil type, the V s value, measured at a given density and p 0 , was correlated with the CRR 15 , obtained from the above-described database, Table 3. In a few of the tests, CRR 15 was also measured.

Shear Wave Velocity
The variation of V s with e at various levels of p 0 is presented in Figure 4. For each tested soil, it is shown that V s increases with increasing p 0 , and this increase is significantly greater at the transition of p 0 from 100 kPa to that of 200 kPa. Moreover, for a given p 0 , V s increases with decreasing e, as shear waves travel faster in denser specimens.
The results of the tests also allow for the estimation of small-strain shear modulus, G max , from V s from the following equation: where ρ is the total mass density of the soil. Papadopoulou (2008) [28] studied the effect of density, p′0 , and fc on CRR15 of the soils examined in this work and presented a database of results of undrained stress-controlled cyclic triaxial tests on the sand and the sand-silt mixtures with fc = 15%, 25%, 35%, 40%, and 60%. For each soil type, the Vs value, measured at a given density and p′0, was correlated with the CRR15, obtained from the above-described database, Table 3. In a few of the tests, CRR15 was also measured.

Shear Wave Velocity
The variation of Vs with e at various levels of p΄0 is presented in Figure 4. For each tested soil, it is shown that Vs increases with increasing p′0, and this increase is significantly greater at the transition of p′0 from 100 kPa to that of 200 kPa. Moreover, for a given p′0, Vs increases with decreasing e, as shear waves travel faster in denser specimens.  The results of the tests also allow for the estimation of small-strain shear modulus, Gmax, from Vs from the following equation: where ρ is the total mass density of the soil. Empirical equations proposed for the estimation of Gmax of sand are widely used for soil characterisation in common geotechnical engineering practice and constitutive modelling of soil behaviour. Hardin's empirical equation [36], which takes into account the effect of density and effective stress, is the most widely used for the estimation of Gmax: By combining Equations (2) and (3), Vs can be expressed as follows: Empirical equations proposed for the estimation of G max of sand are widely used for soil characterisation in common geotechnical engineering practice and constitutive modelling of soil behaviour. Hardin's empirical equation [36], which takes into account the effect of density and effective stress, is the most widely used for the estimation of G max : By combining Equations (2) and (3), V s can be expressed as follows: where p a is reference stress assumed to be 100 kPa, p 0 is the mean effective stress, f(e) = e −n is the void ratio function [37], and A, m, and n are parameters that depend on soil type. The values of G max obtained from Equation (2) were used in non-linear regression analysis for the estimation of the parameters A, m, and n in Equations (3) and (4) for the sand and the sand-silt mixtures. The results of this regression analysis are listed in Table 4, while the variation of parameters A and m with f c is plotted in Figure 5. It is shown that the value of parameter A decreases with increasing f c , while the value of the stress exponent m for the artificial mixtures is different from the value of 0.5, which is commonly used in practice for clean sand. e −n is the void ratio function [37], and A, m, and n are parameters that depend on soil type. The values of Gmax obtained from Equation (2) were used in non-linear regression analysis for the estimation of the parameters A, m, and n in Equations (3) and (4) for the sand and the sand-silt mixtures. The results of this regression analysis are listed in Table  4, while the variation of parameters A and m with fc is plotted in Figure 5. It is shown that the value of parameter A decreases with increasing fc, while the value of the stress exponent m for the artificial mixtures is different from the value of 0.5, which is commonly used in practice for clean sand.      Figure 7 shows the variation of CRR15 with e, at p′0 = 50, 100, 200, and 300 kPa, for the sand and the sand-silt mixtures, at values of Dr ranging from 7% to 100%. In the following figure, the results for the sand-silt mixtures with fc = 40% and 60% are also presented [28]. At a given p′0 and density, CRR15 decreases with increasing fc up to a threshold fines content value, fc,th, and increases thereafter with further increasing fc. For the tested sand-silt mixtures, fc,th is 35% and 25% at p′0 = 50-200 kPa and 300 kPa, respectively. The behaviour  Figure 7 shows the variation of CRR 15 with e, at p 0 = 50, 100, 200, and 300 kPa, for the sand and the sand-silt mixtures, at values of D r ranging from 7% to 100%. In the following figure, the results for the sand-silt mixtures with f c = 40% and 60% are also presented [28]. At a given p 0 and density, CRR 15 decreases with increasing f c up to a threshold fines content value, f c,th , and increases thereafter with further increasing f c . For the tested sand-silt mixtures, f c,th is 35% and 25% at p 0 = 50-200 kPa and 300 kPa, respectively. The behaviour of the mixtures at f c,th is characterised by instability and flow liquefaction. Moreover, it is shown that at a given density, CRR 15 decreases with increasing p 0 and that the effect of p 0 on CRR 15 diminishes with increasing f c . The existence of f c,th , has also been observed in previous studies on the effect of f c on the behaviour of sand with fines [38][39][40][41][42][43][44]. The f c,th is an important parameter determining the transition from the sand-dominated to the silt-dominated behaviour of mixtures and is related to their particle packing, mean diameter ratio, and separation distance as well as gradation, mineralogy, and particle shape characteristics [45].

Figure 6.
Variation of normalized small-strain shear modulus, Gmax/f(e), with effective stress, p′0, for the tested soils. Figure 7 shows the variation of CRR15 with e, at p′0 = 50, 100, 200, and 300 kPa, for the sand and the sand-silt mixtures, at values of Dr ranging from 7% to 100%. In the following figure, the results for the sand-silt mixtures with fc = 40% and 60% are also presented [28]. At a given p′0 and density, CRR15 decreases with increasing fc up to a threshold fines content value, fc,th, and increases thereafter with further increasing fc. For the tested sand-silt mixtures, fc,th is 35% and 25% at p′0 = 50-200 kPa and 300 kPa, respectively. The behaviour of the mixtures at fc,th is characterised by instability and flow liquefaction. Moreover, it is shown that at a given density, CRR15 decreases with increasing p′0 and that the effect of p′0 on CRR15 diminishes with increasing fc. The existence of fc,th, has also been observed in previous studies on the effect of fc on the behaviour of sand with fines [38][39][40][41][42][43][44]. The fc,th is an important parameter determining the transition from the sand-dominated to the siltdominated behaviour of mixtures and is related to their particle packing, mean diameter ratio, and separation distance as well as gradation, mineralogy, and particle shape characteristics [45].

Correlation of Shear Wave Velocity with Liquefaction Resistance
For each soil type, the measured Vs value at a given p′0 and density were correlated with CRR15, obtained from the above-described database, Figure 8. To account for the effect of p′0 on the correlation between CRR15 and Vs, Vs was normalized by the stress function, f(p′0) = p′0 m/2 in Figure 9, where m is the stress exponent parameter determined for each soil type as described above, Table 4. It is shown in Figure 9, that the CRR15-Vs/p′0 m/2 curves shift to the left with increasing fc up to 25% and then start to move downwards and towards the right when fc is increased to 35%. As noted above for the tested mixtures, fc,th is 35% and 25% at p′0 = 50-200 kPa and 300 kPa, respectively.

Correlation of Shear Wave Velocity with Liquefaction Resistance
For each soil type, the measured V s value at a given p 0 and density were correlated with CRR 15 , obtained from the above-described database, Figure 8. To account for the effect of p 0 on the correlation between CRR 15 and V s , V s was normalized by the stress function, f(p 0 ) = p 0 m/2 in Figure 9, where m is the stress exponent parameter determined for each soil type as described above, Table 4. It is shown in Figure 9, that the CRR 15 -V s /p 0 m/2 curves shift to the left with increasing f c up to 25% and then start to move downwards and towards the right when f c is increased to 35%. As noted above for the tested mixtures, f c,th is 35% and 25% at p 0 = 50-200 kPa and 300 kPa, respectively. fect of p′0 on the correlation between CRR15 and Vs, Vs was normalized by the stress function, f(p′0) = p′0 m/2 in Figure 9, where m is the stress exponent parameter determined for each soil type as described above, Table 4. It is shown in Figure 9, that the CRR15-Vs/p′0 m/2 curves shift to the left with increasing fc up to 25% and then start to move downwards and towards the right when fc is increased to 35%. As noted above for the tested mixtures, fc,th is 35% and 25% at p′0 = 50-200 kPa and 300 kPa, respectively.  The evaluation of the field CRR field -V s1 relationship from the test results of this work requires the conversion of the laboratory CRR 15 to an equivalent field CRR field and the correction of V s values for overburden stress. In particular, the laboratory CRR 15 obtained from unidirectional cyclic triaxial tests on isotropically consolidated specimens should be corrected for the multidirectional character of earthquake loading and the k 0 conditions of lateral earth pressure at rest that exists in the field. Therefore, to convert laboratory CRR 15 to an equivalent field CRR field , the following correction factors are applied [46]: where r c is a factor to consider multidirectional earthquake loading with a value between 0.9 and 1.0, assumed to be 0.90 [46], K σ = CRR 15,σ v /CRR 15,σ v = 100 the overburden stress correction factor and c r = (1 + 2 · k 0 )/3 is a factor to convert laboratory CRR 15 , determined under isotropic conditions, to field k 0 conditions. For the tested materials, the coefficient of lateral earth pressure at rest, k 0 , was calculated from 1 − sin(ϕ cs ), where ϕ cs is the angle of shearing resistance at a critical state, determined from undrained monotonic triaxial tests [45]. The values of k 0 , ϕ cs , and factor c r , used for each soil type are presented in Table 5.
The evaluation of the field CRRfield-Vs1 relationship from the test results of this work requires the conversion of the laboratory CRR15 to an equivalent field CRRfield and the correction of Vs values for overburden stress. In particular, the laboratory CRR15 obtained from unidirectional cyclic triaxial tests on isotropically consolidated specimens should be corrected for the multidirectional character of earthquake loading and the k0 conditions of lateral earth pressure at rest that exists in the field. Therefore, to convert laboratory CRR15 to an equivalent field CRRfield, the following correction factors are applied [46]:  The overburden stress correction factor, K σ , depends on D r and soil-reconstituted or undisturbed samples-and test type [47,48]. In this work, K σ , was derived from the cyclic triaxial tests, conducted on the tested soils [28]. Figure 10a-d present the variation of K σ with normalized overburden effective stress, σ v /100, at various values of D r for each soil type. For all soil types and σ v below 100 kPa, K σ increases with decreasing σ v at all values of D r examined. Moreover, for a given σ v , lower values of K σ at higher D r are in general indicated. However, for σ v above 100 kPa, different types of variations of K σ with σ v are observed, depending on f c . For the sand and the sand-silt mixtures with and 25%, K σ decreases with increasing σf c = 15% v , with K σ values becoming smaller with increasing D r , Figure 10a to c. Moreover, at a given D r , K σ values at f c = 15% and 25% are lower than the corresponding for the sand. However, for the sand-silt mixture with f c = 35% and σ v above 100 kPa, K σ decreases initially and then increases with increasing σ v , with K σ values becoming smaller with increasing D r , Figure 10d. The minimum K σ values take place at σ v /100 ratios between 1.70 and 3.4. and 25%, Kσ decreases with increasing σ′v, with Kσ values becoming smaller with increasing Dr, Figure 10a to c. Moreover, at a given Dr, Kσ values at fc = 15% and 25% are lower than the corresponding for the sand. However, for the sand-silt mixture with fc = 35% and σ′v above 100 kPa, Kσ decreases initially and then increases with increasing σ′v, with Kσ values becoming smaller with increasing Dr, Figure 10d. The minimum Kσ values take place at σ′v/100 ratios between 1.70 and 3.4. To correct Vs for overburden stress, a factor CN, as given in Equation (1), is commonly used, similarly to the traditional procedures for modifying standard and cone penetration resistances for overburden stress. Salgado et al. (1997) [49] developed relationships between CPT resistance, relative density, vertical effective stress, and lateral earth pressure coefficient at rest, by means of numerical analyses, and expressed the overburden normalization exponent a in Equation (1) as a function of Dr (a = b − cDr). Boulanger (2003) [48] reevaluated the SPT calibration chamber test data on sand, presented by   [50,51], and expressed the exponent a, also as a function of Dr, (a = b·Dr c ). Both the aforementioned functions correspond to sand.
In this work, the exponent a, of factor CN was evaluated using two approaches. In the first approach, it was assumed that a = m/2, where m is the stress exponent parameter in Equations (3) and (4), Table 4. In the second approach, Vs was expressed as a function of confining stress, p , and Dr, according to the results of bender element tests and the exponent a was expressed as a function of Dr in the form of b − c·Dr [49]: Parameters B′, b, c, and d, are soil type-dependent properties, obtained from a nonlinear regression analysis, and their values are presented in Table 6. Figure 11 shows the variation of exponent a, with Dr for the sand and the sand-silt mixtures. The values of the exponent a are calculated from the bender element tests results using the following equation: To correct V s for overburden stress, a factor C N , as given in Equation (1), is commonly used, similarly to the traditional procedures for modifying standard and cone penetration resistances for overburden stress. Salgado et al. (1997) [49] developed relationships between CPT resistance, relative density, vertical effective stress, and lateral earth pressure coefficient at rest, by means of numerical analyses, and expressed the overburden normalization exponent a in Equation (1) as a function of D r (a = b − cD r ). Boulanger (2003) [48] reevaluated the SPT calibration chamber test data on sand, presented by Marcuson and Bieganousky (1997) [50,51], and expressed the exponent a, also as a function of D r , (a = b·D r c ). Both the aforementioned functions correspond to sand.
In this work, the exponent a, of factor C N was evaluated using two approaches. In the first approach, it was assumed that a = m/2, where m is the stress exponent parameter in Equations (3) and (4), Table 4. In the second approach, V s was expressed as a function of confining stress, p 0 , and D r , according to the results of bender element tests and the exponent a was expressed as a function of D r in the form of b − c·D r [49]: Parameters B , b, c, and d, are soil type-dependent properties, obtained from a nonlinear regression analysis, and their values are presented in Table 6. Figure 11 shows the variation of exponent a, with D r for the sand and the sand-silt mixtures. The values of the exponent a are calculated from the bender element tests results using the following equation: In Figure 11, the values of the exponent a, determined by the second approach, are also compared with the values of a = 0.25 and a = m/2. It is shown that for all tested soils, the range of the values of exponent a, determined by the second approach, is close to the value of a = m/2. In particular, for the sand and the examined range of Dr, the variation of In Figure 11, the values of the exponent a, determined by the second approach, are also compared with the values of a = 0.25 and a = m/2. It is shown that for all tested soils, the range of the values of exponent a, determined by the second approach, is close to the value of a = m/2. In particular, for the sand and the examined range of D r , the variation of exponent a is from 0.254 to 0.284, Table 6, which may be considered close to the value of 0.25, used commonly for sand. However, for the sand-silt mixtures, higher values of exponent a are anticipated.
Thus, in this work, the overburden stress-corrected shear wave velocity, V s1 , is calculated from measured V s using Equation (1) with a = m/2: where p a is the reference overburden effective stress equal to 100 kPa. The CRR field -V s1 correlations determined for the sand and the sand-silt mixtures are presented in Figure 12, using the proposed stress exponent a = m/2 and the typical stress exponent a = 0.25, for comparison reasons. Similar to the CRR 15 -V s /p 0 m/2 , the CRR field -V s1 curves move to the left with increasing f c up to 25% and then downwards and to the right with a further increase of f c to 35%. In the mixtures with f c = 15% and 25% there is a significant scatter in the CRR field -V s1 curves when a = 0.25 is used. Moreover, there are indications that the liquefaction resistance of these mixtures is underestimated when a = 0.25 is used.
Geotechnics 2021, 1, FOR PEER REVIEW 18 curves move to the left with increasing fc up to 25% and then downwards and to the right with a further increase of fc to 35%. In the mixtures with fc = 15% and 25% there is a significant scatter in the CRRfield-Vs1 curves when a = 0.25 is used. Moreover, there are indications that the liquefaction resistance of these mixtures is underestimated when a = 0.25 is used. Figure 12. Variation of cyclic resistance ratio, CRRfield, with overburden stress corrected shear wave velocity, Vs1, for the tested materials.
The results indicate that fc has a significant influence on the CRRfield-Vs1 correlation and that at the fc,th mixtures are unstable showing the lowest liquefaction resistance values even though they are in a dense state. Figure 13 presents the CRRfield-Vs1 correlation results determined for the sand, as well as the curves determined for soils with fc ≤ 5% by previous field and laboratory studies for comparison. The CRRfield-Vs1 results for the sand in this work lay on the curves recommended by [10,11] and to the right of the curves recommended by [5,6,13,14]. The curve suggested by [6] has been drawn as reported by [13] (data analysis from twelve different sand types with fc = 0-9.6%, D60 = 0.167-0.324 mm and Cu = 1.4-2.2 and 15 cycles of loading, assuming emin = 0.65, K0 = 0.5 and rc = 0.9). The curve by [13] has been drawn for fc = 0%, as suggested in their paper. All the data and curves, obtained from previous laboratory studies [15,[17][18][19][20][21][22][23][24], lay to the left of the results of this work. This difference may reflect differ- The results indicate that f c has a significant influence on the CRR field -V s1 correlation and that at the f c,th mixtures are unstable showing the lowest liquefaction resistance values even though they are in a dense state. Figure 13 presents the CRR field -V s1 correlation results determined for the sand, as well as the curves determined for soils with f c ≤ 5% by previous field and laboratory studies for comparison. The CRR field -V s1 results for the sand in this work lay on the curves recommended by [10,11] and to the right of the curves recommended by [5,6,13,14]. The curve suggested by [6] has been drawn as reported by [13] (data analysis from twelve different sand types with f c = 0-9.6%, D 60 = 0.167-0.324 mm and C u = 1.4-2.2 and 15 cycles of loading, assuming e min = 0.65, K 0 = 0.5 and r c = 0.9). The curve by [13] has been drawn for f c = 0%, as suggested in their paper. All the data and curves, obtained from previous laboratory studies [15,[17][18][19][20][21][22][23][24], lay to the left of the results of this work. This difference may reflect differences in the mineralogy, grain, and grading characteristics of the soils and testing conditions. The maximum estimated V s1 value is of the order of 244 m/s at D r = 100%, as compared to the limiting upper value of 215 m/s, proposed in the semiempirical procedure and the upper range of values from 177 to 222 m/s, observed for the results of previous laboratory studies.
Geotechnics 2021, 1, FOR PEER REVIEW 19 Figure 13. Variation of cyclic resistance ratio, CRRfield, with overburden stress corrected shear wave velocity, Vs1, for soils with fc ≤ 5%. Figure 14 presents the CRRfield-Vs1 correlation results determined for the sand-silt mixture with fc = 15% together with results of previous field and laboratory studies for comparison. The CRRfield-Vs1 correlation data for the sand-silt mixture (D50 = 0.30 mm, Cu = 8.8) of this work lay to the left of the curves recommended by all previous field and most laboratory studies [15,21,23], and practically coincide with those reported by [24] for an artificial sand-silt mixture with fc = 15% and similar grading characteristics (D50 = 0,28 mm, Cu = 9.7) and rounded grains. The maximum estimated Vs1 value is of the order of 144 m/s at Dr = 70%, as compared to the limiting upper value of 204 m/s, proposed in the semiempirical procedure and the upper range of values from 157 to 181 m/s, observed for the results of previous laboratory studies. Figure 13. Variation of cyclic resistance ratio, CRR field , with overburden stress corrected shear wave velocity, V s1 , for soils with f c ≤ 5%. Figure 14 presents the CRR field -V s1 correlation results determined for the sand-silt mixture with f c = 15% together with results of previous field and laboratory studies for comparison. The CRR field -V s1 correlation data for the sand-silt mixture (D 50 = 0.30 mm, C u = 8.8) of this work lay to the left of the curves recommended by all previous field and most laboratory studies [15,21,23], and practically coincide with those reported by [24] for an artificial sand-silt mixture with f c = 15% and similar grading characteristics (D 50 = 0.28 mm, C u = 9.7) and rounded grains. The maximum estimated V s1 value is of the order of 144 m/s at D r = 70%, as compared to the limiting upper value of 204 m/s, proposed in the semi-empirical procedure and the upper range of values from 157 to 181 m/s, observed for the results of previous laboratory studies. Figure 15 presents the CRR field -V s1 correlation results determined for the sand-silt mixture with f c = 25% together with results of previous field and laboratory studies for comparison. The CRR field -V s1 correlation data for the sand-silt mixture of this work lay to the left of the curves recommended by all previous field and laboratory studies. laboratory studies [15,21,23], and practically coincide with those reported by [24] for a artificial sand-silt mixture with fc = 15% and similar grading characteristics (D50 = 0,28 mm Cu = 9.7) and rounded grains. The maximum estimated Vs1 value is of the order of 144 m at Dr = 70%, as compared to the limiting upper value of 204 m/s, proposed in the sem empirical procedure and the upper range of values from 157 to 181 m/s, observed for th results of previous laboratory studies. Figure 14. Variation of cyclic resistance ratio, CRRfield, with overburden stress corrected shear wav velocity, Vs1, for soils with 5 < fc ≤ 15%.  Finally, Figure 16 presents the CRRfield-Vs1 correlation results determined for the sand-silt mixture with fc = 35% together with results of previous field and laboratory studies for comparison. The CRRfield-Vs1 correlation data for the sand-silt mixture of this work (D50 = 0.27 mm, Cu = 24.6) lay, again, to the left of the curves recommended by [13] and are in good agreement with the curves of [5,10,14]. They practically coincide with the results reported by [15,21,24] for artificial sand-silt mixtures with fc = 35% and have similar grading characteristics. The maximum estimated Vs1 value is of the order of 150 m/s at Dr = 100%, as compared to the limiting upper value of 194 m/s, proposed in the semi-empirical procedure, and the upper range of values from 149 to 171 m/s, observed for the results of previous laboratory studies.
The results from the previously reported field and laboratory studies and the work presented in this paper, indicate that the effect of fines is much more distinct in the case Figure 15. Variation of cyclic resistance ratio, CRR field , with overburden stress corrected shear wave velocity, V s1 , for soils with 15 < f c ≤ 25%.
Finally, Figure 16 presents the CRR field -V s1 correlation results determined for the sand-silt mixture with f c = 35% together with results of previous field and laboratory studies for comparison. The CRR field -V s1 correlation data for the sand-silt mixture of this work (D 50 = 0.27 mm, C u = 24.6) lay, again, to the left of the curves recommended by [13] and are in good agreement with the curves of [5,10,14]. They practically coincide with the results reported by [15,21,24] for artificial sand-silt mixtures with f c = 35% and have similar grading characteristics. The maximum estimated V s1 value is of the order of 150 m/s at D r = 100%, as compared to the limiting upper value of 194 m/s, proposed in the semi-empirical procedure, and the upper range of values from 149 to 171 m/s, observed for the results of previous laboratory studies.
The results from the previously reported field and laboratory studies and the work presented in this paper, indicate that the effect of fines is much more distinct in the case of the laboratory-based CRR field -V s1 correlation. Factors contributing to the difference between the field and laboratory-based CRR field -V s1 correlation may include stress history, fabric, ageing, and the type of laboratory test used to estimate liquefaction resistance. It is worth noting that grain characteristics of natural silty sand are more complex than that of the artificial sand-silt mixtures with binary packing, as tested in this work and most previous laboratory investigations. Natural sand has an infinite number of particle diameters with varying shape characteristics and may contain particles whose behaviour is dictated by interacting surface forces. Moreover, laboratory tests are element tests, whereas field measurements of V s may also be affected by soil stratigraphy and boundary conditions.

Conclusions
The following conclusions can be drawn from the results of bender element and cyclic triaxial tests conducted on sand and its mixtures with an NP silt: The correlation between CRR and Vs of sand containing NP fines depends on factors, such as fc and p′0. When Vs is normalized with respect to p′0, a good correlation between CRR and stress normalized shear waves velocity, Vs/p′0 m/2 , irrespective of stress level is observed. The stress exponent m depends on fc. The sand-silt mixture with fc = 35%, forms a lower bound for the CRR15-Vs/p′0 m/2 correlation; (ii) The fc-dependent stress exponent, m/2, can be used in the overburden stress correction of Vs; (iii) The type of the estimated CRRfield-Vs1 correlation is similar to the correlation between CRR and Vs/p′0 m/2 and depends significantly on fc. The sand-silt mixture with fc = 35% forms the lower bound for this correlation; (iv) The comparison of derived CRRfield-Vs1 correlation results in this work with previous field and laboratory studies indicates that besides fc, other factors, such as mineralogy, grain and grading characteristics, fabric, ageing, and stress history may be important.

Conclusions
The following conclusions can be drawn from the results of bender element and cyclic triaxial tests conducted on sand and its mixtures with an NP silt: (i) The correlation between CRR and V s of sand containing NP fines depends on factors, such as f c and p 0 . When V s is normalized with respect to p 0 , a good correlation between CRR and stress normalized shear waves velocity, V s /p 0 m/2 , irrespective of stress level is observed. The stress exponent m depends on f c . The sand-silt mixture with f c = 35%, forms a lower bound for the CRR 15 -V s /p 0 m/2 correlation; (ii) The f c -dependent stress exponent, m/2, can be used in the overburden stress correction of V s ; (iii) The type of the estimated CRR field -V s1 correlation is similar to the correlation between CRR and V s /p 0 m/2 and depends significantly on f c . The sand-silt mixture with f c = 35% forms the lower bound for this correlation; (iv) The comparison of derived CRR field -V s1 correlation results in this work with previous field and laboratory studies indicates that besides f c , other factors, such as mineralogy, grain and grading characteristics, fabric, ageing, and stress history may be important.

Conflicts of Interest:
The authors declare no conflict of interest.

List of Notations
V s shear wave velocity CRR cyclic resistance ratio or liquefaction resistance CRR lab cyclic resistance ratio measured at the laboratory CRR field field cyclic stress ratio V s1 overburden stress-corrected shear wave velocity f c fines content C N factor to correct measured shear wave velocity for overburden stress p a reference stress equal to 100 kPa σ v effective overburden stress (vertical effective stress) CSR cyclic stress ratio equal to σ d /2p 0 D 50 mean grain size D 10 diameter corresponding to 10% finer C u coefficient of uniformity e max maximum void ratio e min minimum void ratio ε DA double amplitude axial strain k 0 coefficient of lateral earth pressure at rest R u excess pore water pressure ratio CRR CTX cyclic resistance ratio or liquefaction resistance from cyclic triaxial tests G max linear elastic shear modulus G s specific gravity of soil grains B degree of saturation, B = ∆u/∆σ ∆u excess pore water pressure f frequency p 0 effective isotropic stress (mean effective stress)-(confining stress) e void ratio after consolidation ρ total mass density of a soil CRR 15 cyclic resistance ratio or liquefaction resistance at 15 cycles of loading ±σ d sinusoidally varying axial stress N number of loading cycles N l number of loading cycles at ε DA = 5% t Time A parameter dependent on soil type m parameter dependent on soil type n parameter dependent on soil type D r relative density f c,th threshold fines content τ l cyclic shear strength r c factor to consider multidirectional loading CRR 15,σ ν = 100 cyclic resistance ratio at 15 cycles of loading and at σ ν = 100 kPa CRR 15,σ ν cyclic resistance ratio at σ ν K σ correction factor for the level of vertical effective stress c r factor to convert stress ratio to cause liquefaction to field k o conditions CRR 15,p 0 cyclic resistance ratio at 15 cycles of loading and at p 0 ϕ cs angle of shearing resistance at critical state B parameter obtained from a nonlinear regression B parameter obtained from a nonlinear regression a parameter obtained from a nonlinear regression b parameter obtained from a nonlinear regression c parameter obtained from a nonlinear regression d parameter obtained from a nonlinear regression D 60 diameter corresponding to 60% finer