Influence of particle size on the correlation between

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Influence of particle size on the correlation between shear wave velocity and cone tip resistance

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Mourad Karray, Guy Lefebvre, Yannic Ethier, and Annick Bigras

Abstract: The construction of the Péribonka dam involved deep compaction of its foundation using vibroflotation and dynamic compaction. Surface wave testing was used, in addition to classical tests (cone penetration tests (CPTs) and standard penetration tests (SPTs)) for the assessment of vibrocompaction. More than 900 shear wave velocity (Vs) and 1000 CPT profiles were obtained. This set of tests performed prior to and following vibrocompaction constitutes an important data bank, used in this study to establish a relationship between normalized shear wave velocity, Vs1, normalized tip resistance, qc1, and mean grain size, D50. Using the Péribonka project data obtained on fairly coarse sands in conjunction with the Canadian Liquefaction Experiment (CANLEX) project data obtained on fine sands has confirmed the significant effect of particle-size distribution on the relationship between Vs and qc. The paper proposes a correlation between Vs1, qc1, and D50 for uncemented and Holocene-age granular soils in continuity with the relation developed by Wride et al. from the CANLEX project. Key words: Péribonka, modal analysis of surface waves (MASW), shear wave velocity, cone penetration resistance, grain size, modal analysis, surface waves, Canadian Liquefaction Experiment (CANLEX). Résumé : La construction du barrage de Péribonka a nécessité un compactage profond de sa fondation par vibro-flottation et compactage dynamique. Des essais d’onde de surface, en plus des essais typiques (essais au cône de pénétration (CPT) et essais de pénétration standards (SPT)), ont été utilisés pour le contrôle du compactage. Plus de 900 profils de vitesses d’onde de cisaillement (Vs) et 1000 profils de CPT ont été obtenus. Cette série d’essais réalisée avant et après vibro-compaction constitue une banque de données importante qui est utilisée dans cette étude pour établir une relation entre la vitesse normalisée de l’onde de cisaillement, Vs1, la résistance en pointe, qc1, et le diamètre moyen des particules, D50. L’utilisation des données du projet Péribonka obtenues sur des sables relativement grossiers, avec les données du projet « Canadian Liquefaction Experiment (CANLEX) » obtenues sur des sables fins, a permis de confirmer l’effet significatif de la granulométrie sur la relation entre Vs et qc. L’article propose une corrélation entre Vs1, qc1 et D50 pour des sols granulaires non cimentés de l’holocène en continuité avec la relation développée par Wride et al. lors du projet CANLEX. Mots‐clés : Péribonka, analyse modale des ondes de surface (« MASW »), vitesse de l’onde de cisaillement, résistance à la pénétration du cône, granulométrie, analyse modale, ondes de surface, « Canadian Liquefaction Experiment (CANLEX) ». [Traduit par la Rédaction]

Introduction Unlike the characterization of argillaceous deposits where laboratory testing plays a major role in identifying the mechanical parameters, the characterization of sandy deposits is essentially based on in situ testing, laboratory testing generally being limited to the determination of identification characteristics, such as grain size distribution. The standard penetration test (SPT) to determine blow Received 12 July 2009. Accepted 17 October 2010. Published at www.nrcresearchpress.com/cgj on 12 April 2011. M. Karray and G. Lefebvre. Department of Civil Engineering, Université de Sherbrooke, Sherbrooke, QC J1K 2R1, Canada. Y. Ethier. Departement de génie de la construction, École de technologie supérieure, Montréal, QC H3C 1K3, Canada. A. Bigras. Hydro-Québec, 855, Ste Catherine Est, 19e étage, Montréal, QC H2L 4P5, Canada. Corresponding author: M. Karray (e-mail: [email protected]). Can. Geotech. J. 48: 599–615 (2011)

count or penetration index, N, has been by far for several decades the test most frequently used to characterize sandy deposits. A broad expertise was developed to correlate penetration index N with the material density, density index, and shear strength (friction angle, f0 ). The cone penetration test (CPT) for determining the tip resistance (qc) and friction resistance ( fs), although seldom used until quite recently in North America, is now part of the in situ characterization tools available in many countries. Finally, the in situ measurement of the shear wave velocity (Vs), which expresses material rigidity, being directly associated with the shear modulus in the elastic domain (Gmax ¼ rVs2 , where r is the density of material), has lately been used more often due to (i) the development of new measurement techniques, such as the seismic cone penetration test (SCPT), and (ii) the availability of methods using surface waves (spectral analysis of surface waves (SASW), modal analysis of surface waves (MASW)). In every case, empirical relationships must be used to determine the density index, compressibility or f0 angle and, as an alternative, the liquefaction susceptibility, from

doi:10.1139/T10-092

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N, qc or Vs. As as result, the development and verification of such empirical relationships plays a major role in the geotechnical characterization of granular soil deposits. The development and verification of empirical relationships to establish equivalences between N, qc, and Vs is thus very useful for comparing the characterization results obtained with either of these investigation techniques and for implementing the expertise developed from the different test types. Any empirical relationship involving the in situ characteristics of soil deposits is likely to be influenced by geology-related regional features. The development or verification of empirical relationships using experimental data obtained at sites located in Quebec and Eastern Canada is therefore likely to constitute an important contribution to the practice of geotechnics in Eastern Canada. The construction of the Péribonka dam in Northern Quebec (Canada) began with the placement of an approximately 10 m thick sand and gravel fill on the river bottom, also consisting of granular materials down to great depths. Prior to the installation of a plastic concrete diaphragm wall and the commencement of the embankment dam construction, the fill and foundation materials were compacted by vibroflotation. A number of boreholes were made with SPT testing during the pre-construction geotechnical investigations. However, vibroflotation soil compaction was essentially monitored with MASW (Karray 1999) and CPT testing was performed prior to and following vibroflotation (Karray et al. 2010). The objective of this study is to analyse the Péribonka results from cone penetration tests (CPTs) and MASW tests (determination of Vs) to develop and (or) verify the available relationship used to establish equivalencies between Vs1 and qc1. The paper also examines the effect of mean grain size (D50) on the relationship between Vs1 and qc1 using the Péribonka data obtained on gravelly coarse sands (0.2 mm < D50 < 10 mm) in conjunction with the Canadian Liquefaction Experiment (CANLEX) project data obtained on fine sands (0.16 mm < D50 < 0.25 mm). This study focuses on relatively young granular soil deposits with mineralogical and geological properties similar to those encountered at the Péribonka and CANLEX sites.

State of knowledge Analysis of the diversity and complexity of soils makes for a difficult task because of their many geologic origins, ages, constituents, grain size, mineralogy, fabrics, and histories. Therefore, parameters interpreted from SPT, CPT or shear wave velocity tests need to be correlated with one another. The objective of the state of knowledge presented herein is not to cover every study performed on SPT, CPT or Vs measurement tests. Only the elements relevant to the goals of this study, i.e., a comparison between the results generated in granular deposits by the three in situ test types previously listed, are mentioned herein. Table 1 presents a few correlations between Vs and qc and between Vs and N. Effective stress effect An important number of empirical relationships have been developed over the years to determine the in situ properties of cohesionless soil deposits including the void ratio, density index, grain shape, and age factor from qc–CPT (Schmert-

Can. Geotech. J. Vol. 48, 2011

mann 1976; Jamiolkowski et al. 1985, 2001; Baldi et al. 1986; Kulhawy and Mayne 1990; Tanizawa et al. 1990), N– SPT (Meyerhof 1957; Kokusho et al. 1983; Skempton 1986; Hatanaka and Feng 2006), and Vs (Hardin and Richard 1963; Robertson et al. 1995a). The in situ measurements can be influenced by a number of factors that are probably interrelated, such as compressibility, grain-size distribution, mineralogy, and grain shape. For a given uncemented soil of Holocene age ( 2.6) and 0.5 for sandy type soils (Ic < 2.6). Equations [6] and [7] suggest that the soil behaviour index (Ic) can be related to the mean grain size (D50). Péribonka site and the available data The Péribonka main dam is an embankment dam built on deposits found at the bottom of the river and is generally constituted of subrounded to subangular and well-graded gravelly sand to gravel. The sediments appear to be a fluvioglacial deposit formed during the last ice age 7800 to 9800 years ago (Bernatchez 1997). An initial subrounded gravely sand filling, generally 10–12 m in thickness, was dumped on the alluvia forming a platform at elevation 180 m (1 to 3 months of age at the moment of testing). This filling and the foundation alluvia were then compacted prior to the installation of a plastic concrete diaphragm wall. Accordingly, the soils (fill and foundation) at the Péribonka site are of Holocene age (less than 10 000 years old), are uncemented, and are predominantly of quartz minerals with feldspar (quartzo-feldspathic) and some ferromagnesium (Table 2). The vibroflotation was monitored through CPTs and the shear wave velocity (Vs) was determined by MASW tests.

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CPT and MASW testing programs were conducted prior to and following vibroflotation. The Vs profiles were determined prior to and following vibrocompaction at 2 m intervals along six MASW lines, each line measuring 120 to 210 m in length (Fig. 1). The details of the MASW procedure and shear wave velocity results at Péribonka dam are presented by Karray et al. (2010). Several CPT tests were performed, especially following compaction, so that a large number of direct comparisons could be made between qc and Vs profiles located close to one another. The detailed CPT tests results performed within a short distance of the MASW sounding lines are presented by Karray and Lefebvre (2007). For analysis purposes, the compaction platform was divided into three areas. Area 1, or the central area around the dam axis, includes lines 15 upstream, 15 downstream, 10 upstream, and 10 downstream. On either side of the axis of the dam (Fig. 1), area 2, or the downstream area, includes lines 50 downstream and 100 downstream, while area 3 is designated as the transverse line perpendicular to the axis of the dam (Fig. 1). A total of 99 qc profiles were compared one by one with the Vs profiles located within a short distance, including 39 in area 1, 29 in area 2, and 31 in area 3. The distance between the compared qc and Vs profiles is less than 5 m in 62% of the cases and less than 7.5 m in 91% of cases (Karray and Lefebvre 2007). There are fewer boreholes with SPT testing (Fig. 1), and these boreholes allow relatively few comparisons between Vs and N. However, the sampling performed in the boreholes, especially in area 1, is important with respect to identifying the tested materials (D50).

Analysis procedures Basis for comparison between qc and Vs Velocity profiles available at 2 m intervals on MASW sounding lines and qc profiles obtained prior to or following vibrocompaction located generally within 5 to 7.5 m were identified and selected to constitute Vs–qc sets locally by making a distinction between pre- and post-vibrocompaction conditions. The localization of these sets is based on the MASW sounding line PMs (metric point). In some cases, qc and N profiles were considered up to 15 or so metres from the MASW lines due to a lack of closer profiles, particularly with regard to SPTs (used for identification). The distances between the qc or N profiles and the MASW lines are noted for each set (Karray and Lefebvre 2007). The Vs profile considered in this set is an average profile generally based on two adjacent Vs profiles. The sets of qc and Vs profiles are compared in terms of normalized values for a 100 kPa effective earth load (vertical). In some cases, the qc profiles show strong irregularities that are considered here as being associated not with the material density but rather with contacts with coarse elements. Representative points have been defined on the profiles approximately every metre down and the marked irregularities in the qc profiles were neglected, as illustrated in Fig. 2a. A value for Vs has been considered at the same elevation; each of the profile sets thus providing approximately 15 or so representative points used to establish the correlations. The value of qc1N is used in Fig. 2 instead of qc1 to provide scale for qc, which is compatible with that for Vs1. The Published by NRC Research Press

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Table 2. General description of soils: CANLEX (Robertson et al. 2000) and Péribonka sites. Site Péribonka

Soil description Gravelly coarse sand

CANLEX

Fine sand

Average D50 (mm) ∼1.9 ∼0.2

Approximate age at time of testing 1 to 3 months (fill); 7800–9800 years (foundation) 2 months to 4000 years

Mineralogy Quartzo-feldspathic with ferromagnesium

Angularity Subrounded to subangular

Quartz with small amounts of feldspar and mica

Subrounded to subangular, subrounded or angular depending on site

Fig. 1. Locations of the various tests performed on the compaction platform at the Péribonka dam site.

friction measured in the CPTs is processed in terms of the normalized friction ratio (F), as defined in eq. [4]. As illustrated in Fig. 2b, the friction profile is highly irregular due to the gravel content and has been smoothed (best fit) for analysis purposes. The normalized friction profile can then

be compared with the appearance of Vs1 profiles, which are shown in Figs. 2a and 2b. Forms of Vs–qc relationships The Péribonka data, both prior to and following vibrocomPublished by NRC Research Press

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Fig. 2. (a) Sample representative points defined in the Vs1 and qc1N profiles; (b) best fit of the normalized friction and representative points defined in the Vs1 and F profiles.

paction, includes 1084 data points to correlate Vs and qc. In contrast, there are few sets of profiles to compare Vs and N. Therefore, the contribution of the Péribonka data processing primarily concerns the correlation between Vs and qc. As illustrated in Table 1, the form of the empirical relationships established between Vs and qc (Table 1b) or between Vs and N (Table 1a) varies somewhat from one study to another. A purely statistical analysis of the Péribonka data led to another relationship (Vs1 = 149qc10.205) with a form that probably differs from those in Table 1b and could be valid for soils similar to those encountered in Péribonka (see Fig. 3). Robertson, Wride, and their collaborators have presented the results for three studies (Robertson et al. 1992; Fear and Robertson 1995; Wride et al. 2000; Table 1b) which led to Vs–qc relationships having simple and identical forms, i.e.,   1=a ½8 Vs1 ¼ Yðqc1 Þa or qc1 ¼ Vs1 Y where Y is a constant determined from the experimental data. For the three above-mentioned studies (Robertson et al. 1992; Fear and Robertson 1995; Wride et al. 2000), exponent “a” ranges from 0.23 to 0.25 and exponent 1/a ranges from 4 to 4.35. In the paper presented for the interpretation of in situ test results from the CANLEX sites, Wride et al. 2000 ended up using 0.25 for the exponent “a”. Thus, the exponent a = 0.25 will be used in this study. The relationships established by Wride et al. (2000) and Robertson et al. (1992) have furthermore the advantage of having been established for relatively uncemented young sand deposits (Holocene age), such as those encountered in

Fig. 3. Vs1 as a function of qc1N for area 1, prior to and following vibrocompaction.

Eastern Canada (Quebec), versus those encountered further south, which are frequently much older. The study conducted by Wride et al. (2000) is particularly interesting because the relationship was established for six different well-documented sites (CANLEX project), all presenting rather loose uniform fine sands (0.16 < D50 mean value < 0.25 mm). Note that the soils at the CANLEX sites are of Holocene age, uncemented, and are composed primarily of quartz minerals with small amounts of feldspar and mica (Robertson et al. 2000). The Published by NRC Research Press

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properties of CANLEX and Péribonka soils are compared in Table 2. The sandy materials encountered in Péribonka are rather well graded and coarser, with a D50 mean value around 1.8 mm and a somewhat significant gravel portion. The use of the relationship established by Wride et al. (2000) and of the CANLEX experimental data is therefore likely to show the effect of particle-size distribution on the Vs–qc relationship. The Péribonka data includes measurements taken prior to and following vibrocompaction, which should also enable verifying whether the same relationship can account for the density index variation. Validation approach Most of the boreholes with particle-size determination are located near the axis of the dam. The materials are thus relatively well identified in this area (area 1). Two MASW lines are also located a short distance away on either side of the dam axis, with soundings taken prior to and following vibrocompaction. Area 1, which includes these four MASW sounding lines 15 and 10 m on each side from the axis of dam, will be used to identify the Vs–qc relationships. Areas 2 and 3 will be used for validation purposes.

Analysis of the results Identification of Vs1–qc1 empirical relationships For each set of Vs1–qc1N near lines 15 upstream and 15 downstream prior to vibrocompaction and near lines 10 upstream and 10 downstream following vibrocompaction, Vs1 is shown as a function of qc1N in Fig. 3 (area 1). The dots appearing in Fig. 3 are the representative points identified on the different profiles as illustrated in Fig. 2. The pre-compaction and post-compaction data are well separated (Fig. 3). A majority of the pre-compaction values range from 150 to 280 m/s in terms of Vs1 and from 20 to 120 in terms of qc1N. Following compaction, these values are higher: between 220 and 340 m/s for Vs1 andfrom 90 to 330 for qc1N. Each point of Fig. 3 can be examined individually using the following relation: ½9

Vs1 ¼ Yðqc1 Þ0:25

or ½10

Y¼

Vs1 ðqc1 Þ0:25

allowing to determine the Y value for each point. The Y values computed for each point are shown as a function of elevation in Figs. 4a and 5a for the pre- and post-vibrocompaction conditions, respectively. The 95% confidence intervals are also shown in these figures. The confidence intervals are used to show the proportion of points that may be expected to contain the true mean and the end points of the confidence interval are referred to as the confidence limits. However, prior to compaction, the Y values are between 90 and 185, for a mean value of 141.0 ± 24.6 (Fig. 4a), while following compaction Y ranges between 110 and 170, with a mean value of 131.5 ± 15.2 (Fig. 5a). The mean values for D50 and Y = Vs1/qc10.25 determined at the Péribonka site are compared with those for the six CANLEX

project sites in Table 3. The mean Y values determined for the fairly coarse Péribonka sand are much higher than those evaluated for the six CANLEX project fine sand sites (Table 3). An adequate number of particle-size distribution tests were performed on samples taken from area 1 boreholes, near the axis of the dam. The D50 values and 95% confidence intervals of these particle-size distributions are shown as a function of elevation in Figs. 4b and 5b for the boreholes made prior to and following vibrocompaction, respectively. The D50 values range generally from 0.2 to 10 mm, with approximately mean values of 2.15 and 1.77 mm determined separately for the pre- and post-vibrocompaction boreholes (Table 3). Note that the the arithmetic D50 values cannot be normally distributed and the determination of a regression factor results in very low values. However, it will be shown later that the grain-size effect follows the normal distribution. The mean values for D50 determined independently for the boreholes made prior to vibration decrease in comparison with those made following vibration, just like the Y values (Table 3), in line with the trend observed when comparing the Péribonka and CANLEX data. The high values for Y = Vs1/qc10.25 in Péribonka in comparison with those for CANLEX appear to be related to D50 values approximately 10 times higher in Péribonka than at the CANLEX project sites (Table 3). The relationship between Vs and qc therefore appears to be influenced by the particle-size distribution irrespective of the density index. The Y value can also be affected by other factors, such as age, cementation, mineralogy, and grain characteristic. However, the Péribonka and CANLEX soils are uncemented soils and can be considered similar in terms of age, grain characteristic, and mineralogy (Table 2). The D50 values vary noticeably in the materials tested in Péribonka (Figs. 4b and 5b), which could probably explain part of the dispersion seen in Fig. 3. Polynomial best-fit curves are plotted in Figs. 4b and 5b for the D50 and Y = Vs1/qc10.25 values, for pre- and post-compaction conditions. These best-fit curves show some differentiation between the fill andfoundation materials in terms of Y as well as in terms of D50. For simplification purposes, the elevation for the fill– foundation boundary can be set at elevation 170. It can first be noted in Figs. 4b and 5b that, following vibrocompaction, the D50 values decreased in the fill and increased in the foundation. One could think that the coarser fill materials were dragged into the foundation and replaced with less coarse injected materials. The smoothing curves for the Y values as a function of the elevation show generally the same trends as those for the D50 values both prior to and following vibrocompaction, which tends to confirm the influence ofe D50 on the relationship between Vs1 and qc1. The function for the influence ofe D50 on the Y = Vs1/ qc10.25 ratio has been determined in two ways: first by considering only the individual values for Péribonka (Figs. 6a and 6b) and then by considering the mean values for Péribonka and the CANLEX sites (Figs. 7a and 7b). The mean grain size (D50) cannot be determined fromqc or Vs tests. Thus, D50 values shown in Figs. 6a and 6b were obtained for each of the Y values in Figs. 4a and 5a by linking the elevation to the D50 value through the polynomial best-fit curves shown in Figs. 4b and 5b. These curves define a D50 interval ranging from 0.5 to 3.6 mm in comparison with the 0.3 to 10 mm interval shown by the experimental points (Figs. 4b and 5b). Published by NRC Research Press

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Fig. 4. Variation of (a) Y = Vs1/qc10.25 and (b) D50 as a function of the elevation; area 1 prior to vibrocompaction. av, average.

Fig. 5. Variation of (a) Y = Vs1/qc10.25 and (b) D50 as a function of the elevation; area 1 following vibrocompaction.

The influence functions defined independently in Figs. 6a, 6b, 7a, and 7b are identical for all practical purposes. Considering the D50 effect, the relationship between Vs1 and qc1 can therefore be written as ½11

Y¼

Vs1 ¼ 125:5D0:115 50 ðqc1 Þ0:25

where Vs1 is given in m/s, qc1 in MPa, and D50 in mm. A set of qc and Vs profiles can also lead to a good approximation

of the mean grain size (D50) or the mean grain-size factor (FD50) using the following equation:   Vs1 ½12 FD50 ¼ ðD50 Þ0:115 ¼ 125:5ðqc1 Þ0:25 The correlation proposed here, between Vs1 and qc1, indicates that for uncemented young soil deposits having similar mineralogy, as in the case of Péribonka and CANLEX sites (silica based sands), the effect of particle grain size differs Published by NRC Research Press

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Y 134.2 134.2 134.2 134.2 129.0 129.0 129.0 128.7 128.7 128.7 104.1 104.1 104.1 104.1 104.1 104.1

Validation

D50 1.86 (0.68) 1.86 (0.68) 1.86 (0.68)) 1.86 (0.68) 1.86 (0.7) 1.86 (0.7) 1.86 (0.7) 1.87 (0.67) 1.87 (0.67) 1.87 (0.67) 0.197 (0.0314) 0.197 (0.0314) 0.197 (0.0314) 0.197 (0.0314) 0.197 (0.0314) 0.197 (0.0314)

Grain-size factor (FD50) distribution Figures 8a and 9a compare, respectively, the mean grainsize factors (FD50) calculated from the 10 pre-vibro and the 29 post-vibro sets of Vs and qc profiles in area 1 (using eq. [12]) and those calculated from D50 values obtained directly from borings (FD50 = D500.115). In the two cases, the predicted FD50 values from (Vs, qc) sets show a large scatter, but vary similarly as a function of depth to those obtained from borings. Figures 8b and 9b compare the distribution of the predicted factor FD50 from (Vs, qc) to that from borings before and after compaction. It is interesting to see that in the two cases the FD50 factors are normally distributed with a good agreement especially after compaction. The average FD50 factor (from borings) before compaction is about 1.07 ± 0.15 mm corresponding to a mean grain size of 1.8 mm with a lower limit (mean – 1 standard deviation) of 0.48 mm and a higher limit (mean + 1 standard deviation) of 5.7 mm. After compaction, the FD50 factor is around 1.062 ± 0.122 mm corresponding to a mean grain size of 1.7 mm, a lower limit of 0.58, and a higher limit of 4.4 mm.

Note: Values within brackets represent the standard deviations. n/a, not applicable.

CANLEX

Péribonka – area 3

Péribonka – area 2

Areas Péribonka – area 1

Sites Line 15 upstream (prior to vibro) Line 15 downstream (prior to vibro) Line 10 upstream (following vibro) Line 10 downstream (following vibro) Line 50 downstream (prior to vibro) Line 100 downstream (prior to vibro) Line 50 downstream (following vibro) Transverse line (prior to vibro) Transverse line (following vibro) Transverse line (gulley) (following vibro) Mildred Lake Massey Kidd J-pit LL Dam Highmont Dam

No. of points 62 53 150 158 53 49 229 81 86 163 n/a n/a n/a n/a n/a n/a

D50 mean (mm) 2.067 (0.85) 2.158 (0.82) 1.81 (0.61) 1.73 (0.58) 2.39 (0.76) 2.23 (0.84) 1.67 (0.56) 2.15 (0.82) 1.80 (0.61) 1.78 (0.570 0.16 0.2 0.2 0.17 0.2 0.25

Y = Vs1/qc10.25 145.9 (30) 136.8 (20.5) 130.3 (18) 133.0 (15.0) 141.7 (26) 145.3 (27.9) 122.9 (17.5) 135.3 (23) 123.8 (13.0) 127.9 (20.9) 95.6 (12.1) 110.2 (4.6) 110.8 (5.0)0 101.1 (6.3) 107.8 (11.4) 99.3 (7.5)

D50 2.15(0.92) 2.15 (0.92) 1.77 (0.66) 1.77 (0.66) 2.3 (0.8) 2.3 (0.8) 1.7 (0.56) 2.1 (0.82) 1.78 (0.58) 1.78 (0.58) — — — — — —

Y 141.0 141.0 131.5 131.5 143.5 143.5 122.9 135.3 126.5 126.5 — — — — — —

(24.6) (24.6) (15.2) (15.2) (26.7) (26.7) (17.5) (23) (18.7) (18.7)

Mean values per area Mean values per line

Table 3. Inventory of the analysed data (Vs1–qc1 and D50 comparison points) and mean values; Péribonka and CANLEX projects.

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(20.0) (20.0) (20.0) (20.0) (22.7) (22.7) (22.7) (20) (20) (20) (6.32) (6.32) (6.32) (6.32) (6.32) (6.32)

from one test type to another (MASW versus CPT), as recognized by previous studies (CPT versus SPT, eqs. [6] and [7]).

Areas 1, 2, and 3 As previously indicated, the mean grain size (D50) given in Table 3 for area 2 and 3 are estimated by linking the elevation to the D50 value through the best-fit curves shown in Figs. 4b and 5b obtained from the sampling performed in the boreholes especially in area 1. Due to the limited number of borings in areas 2 and 3, one can think that the mean D50 values can be very similar to that in area 1. To verify the variation between these areas, the CPT data (qc1N, F) given for the different areas has been reported (Figs. 10a, 10b, and 10c) into the chart proposed by Robertson (1990) following the procedure suggested by Wride et al. (2000) for soils with Ic < 2.6 (qc1N). The Robertson chart makes it possible to classify the soil in nine categories ranging from sensitive, fine grained soil to gravelly soil. The categories for normally consolidated soil generally increase with the decreasing of the soil behaviour index, Ic, previously described, or with the increasing of mean grain size (D50). The majority of the areas 1, 2, and 3 points are found in zone 6 with mean values of Ic found equal to 1.6, 1.54, and 1.55, respectively (Figs. 10a, 10b, 10c). According to the values of Ic, the soils in areas 2 and 3 appear probably slightly coarser, but can be considered globally similar to the soil in area 1. Figure 11 shows all the values of Vs1 as a function of qc1 obtained from the three different areas (1083 sets of points) and the proposed relationship (eq. [11]) evaluated first for the mean D50 value of 1.8 mm (Figs. 8b and 9b) and then for D50 values ranging from 0.48 to 5.7 m to cover a significant portion of the range of the D50 values encountered in the materials tested at Péribonka (Figs. 8b and 9b). A majority of the Vs1–qc1N points (>70%) are found inside the interval limited by the FD50 factor for values of 0.48 and 5.8 mm, and are relatively well centered around the mean value for D50 (1.8 mm) especially for qc1N lower than 250. Note that the high values of qc1N (>250) can be associated with the presPublished by NRC Research Press

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Fig. 6. Variation of Y = Vs1/qc10.25 as a function of the value for D50; individual data for area 1 in Péribonka: (a) log–log scale and (b) arithmetic scale. r2, squared correlation coefficient.

ence of cobble in the soil foundation. A large part of the Vs1– qc1N dispersion observed in Fig. 3 could therefore be associated with the variation of the D50 value. The proposed relationship for the envelope boundaries (D50 = 0.2 and 10 mm), including nearly all the D50 values obtained from sieve tests (Figs. 4b and 5b), are also presented in Fig. 11. Soil classification, Ic versus D50 The majority of the Péribonka data are found in zone 6 (Fig. 10d) with a mean value of Ic = 1.57. According to the Robertson (1990) chart, the Péribonka soil is classified in

terms of behaviour as a sand ranging from clean to silty sand (Fig. 10d). In addition, some data fall into zone 5 (sand mixtures, silty sand to sandy silt) and some otherd into zone 7 (gravelly). As the soil in the Péribonka dam is identified as gravelly coarse sand, and the Robertson chart is based on CPT results only (qc and F), this could indicate that the effect of grain-size distribution on the CPT results is different than the effect of the shear wave velocity measurement. This is in agreement with the finding of the suggested equation. The Péribonka results combined with those of the CANLEX project gives an opportunity to represent the behaviour Published by NRC Research Press

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Fig. 7. Variation of Y = Vs1/qc10.25 as a function of the value for D50; mean values for the Péribonka and CANLEX sites: (a) log–log scale; (b) semi-log scale.

index, Ic, in the case of sandy soils in terms of D50. Figure 12 presents the Ic mean values obtained from the two sites as a function of D50 ½13

Ic ¼ 1:69D0:12 50

where D50 is in mm. Note that this correlation is available only for uncemented granular soils (silica based) with Ic < 2.6 and D50 ranging between 0.2 and 10 mm. The correlation between Ic and D50 based on Péribonka and CANLEX results is also compared in Fig. 12 with the relation obtained by the substitution of eq. [5] into eq. [6] (based on CPT and SPT test results)

½14

Ic ¼ 4:6  2:944D0:26 50

where D50 is in mm. Note that the transfer from the ratio qc/ (N)60 to the ratio qc1/(N1)60 in the case of eq. [5] is possible because the two parameters (qc and (N)60) are normalized by the same factor (eqs. [1] and [2]). Figure 12 shows that eq. [14] (obtained from N and qc) overpredicts the Ic value in the case of the CANLEX project and underpredicts Ic in the Péribonka case. It appears thus that the relations proposed by Kulhawy and Mayne (1990) and Lunne et al. (1997) are not consistent with the Péribonka and CANLEX results. The extension of the relation obtained using Péribonka Published by NRC Research Press

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Fig. 8. Comparison of envelopes of the mean grain-size influence factor FD50 values from borings with calculated FD50 from proposed correlation for area 1 prior to vibrocompaction: (a) variation of FD50 as a function of elevation; (b) distribution of FD50. m, mean; s, standard deviation.

(D50 = 1.8 mm) and CANLEX (D50 = 0.197 mm) results to cover a important part of granular material (0.002 < D50 < 20 mm) seems to be in good agreement with the entire results (Fig. 12). In fact, the extension of this relation to higher values of D50 (>1.8) indicates a value of Ic ≈ 1.28 for D50 ≈ 10 mm. The value of Ic ≈ 1.28 corresponds approximately to the lower limit observed for the Péribonka data when re-

ported into the Robertson (1990) chart (Fig. 10d) and the value of D50 ≈ 10 mm corresponds to the upper limit obtained from the sampling performed in the boreholes (Figs. 4b and 5b). In addition, the extension of the proposed relation to lower values of D50 (D50 < 0.2) is in good accordance with the soil description given by Robertson (1990). The Péribonka results probably suggest that zone 6 into Published by NRC Research Press

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Fig. 9. Comparison of envelopes of the mean grain-size influence factor FD50 values from borings with calculated FD50 from proposed correlation for area 1 following vibrocompaction: (a) variation of FD50 as a function of elevation; (b) distribution of FD50.

the Robertson (1990) chart could be divided into two zones: 6f and 6c. Zone 6f (1.7 < Ic < 2.05) corresponds to the actual description and zone 6c (1.3 < Ic < 1.7) corresponds to a zone where the soil can be described as a coarse sand ranging from clean to gravelly sand.

Conclusion The effectiveness of vibrocompaction in Péribonka was essentially monitored with penetration tests (CPT) and MASW tests. This set of tests performed prior to and following comPublished by NRC Research Press

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Fig. 10. CPT-based soil behaviour type classification: (a) area 1, (b) area 2, (c) area 3, and (d ) all data.

paction constitutes an important data bank that can be used to establish a relationship between Vs and qc, which enables making a direct profile-to-profile comparison at 100 or so locations on the site. The result for the six CANLEX project

sites and the form of the relationship proposed in the CANLEX project (Wride et al. 2000) were also used in this study. Using the CANLEX project data established on fine sands and the Péribonka project data obtained on fairly coarse Published by NRC Research Press

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Fig. 11. Values for Vs1 as a function of qc1N prior to and following vibrocompaction for areas 1, 2, and 3.

Fig. 12. Correlation between mean grain size (D50) and soil behaviour index (Ic).

sands has confirmed the significant effect of particle-size distribution on the relationship between Vs and qc. The relationship identified in this study for uncemented and relatively young granular soils with mineralogical properties similar to those at the Péribonka site (silica based sands) and with D50 ranging between 0.2 and 10 mm is ½15

Vs1 ¼ 125:5ðqc1 Þ0:25 D0:115 50

where Vs1 is in m/s, qc1 in MPa, and D50 in mm. This relation was found identical for all practical purposes, whether it is determined only from the Péribonka data or from the mean values for Péribonka and the CANLEX project. Evaluating the density index for in situ cohesionless materials is very essential in civil engineering projects whether for, among others, evaluating the liquefaction potential or for monitoring compaction. However, such an evaluation is difficult and frequently affected by a degree of inaccuracy. Using Published by NRC Research Press

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different investigation techniques is then useful, especially if reliable correlations exist between the results of the different types of investigation. The study also confirmed to some extent the influence of mean grain size on Vs. However, this influence could be investigated favorably in a laboratory under properly controlled conditions.

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Acknowledgement The authors thank Hydro-Québec for having given us the opportunity to realise this study and for permission to publish these results.

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Can. Geotech. J. Vol. 48, 2011 standard penetration test. Electric Power Central Research Institute, Japan. Report 383026. Kulhawy, F.H., and Mayne, P.H. 1990. Manual on estimating soil properties for foundation design. Electric Power Research Institute (EPRI), Palo Alto, Calif. Lunne, T., Robertson, P.K., and Powell, J.J.M. 1997. Cone penetration testing in geotechnical practice. Blackie Academic & Professional (Chapman & Hall), Glasgow, UK. Mayne, P.W., Mitchell, J.K., Auxt, J.A., and Yilmaz, R. 1995. U.S. national report on CPT. In Proceedings of the International Symposium on Cone Penetration Testing, CPT’95, Linköping, Sweden, 4–5 October 2995. Report 3:95. Swedish Geotechnical Society (SGI), Linköping, Sweden. Vol. 1, pp. 263–276. Meyerhof, G.G. 1957. Discussion on soil properties and their measurements. In Proceedings of the 4th ICSMFE, London, 12– 24 August 1957. Butterworth Scientific Publications, London. Session 2, Vol. III, 110. Ohta, Y., and Goto, N. 1978. Empirical shear wave velocity equations in terms of characteristic soil indexes. Earthquake Engineering & Structural Dynamics, 6(2): 167–187. doi:10.1002/eqe. 4290060205. Piratheepan, P., and Andrus, R.D. 2002. Estimating shear wave velocity from SPT and CPT data. Final report to U.S. Geological Survey, Award number 01HQR0007. Clemson University, Clemson, S.C. Raptakis, D.G., Anastasiadis, S.A.J., Pitilakis, K.D., and Lontzetidis, K.S. 1995. Shear wave velocities and damping of Greek natural soils. In Proceedings of the 10th European Conference on Earthquake Engineering, Vienna, 28 August – 2 September 1995. Edited by G. Duma. A.A. Balkema, Rotterdam, the Netherlands. pp. 477–482. Rix, G.J., and Stokoe, K.H. 1991. Correlation of initial tangent moduli and cone penetration resistance, calibration chamber testing. Edited by A.B. Huang. Elsevier. pp. 351–362. Robertson, P.K. 1990. Soil classification using the cone penetration test. Canadian Geotechnical Journal, 27(1): 151–158. doi:10.1139/ t90-014. Robertson, P.K., and Wride, C.E. (Fear) 1998. Evaluating cyclic liquefaction potential using the cone penetration test. Canadian Geotechnical Journal, 35(3): 442–459. doi:10.1139/cgj-35-3-442. Robertson, P.K., Woeller, D.J., Kokan, M., Hunter, J., and Luternaur, J. 1992. Seismic techniques to evaluate liquefaction potential. In Proceedings of the 45th Canadian Geotechnical Conference, Toronto, Ont., 26–28 October 1992. pp. 5-1–5-9. Robertson, P.K., Sasitharan, S., Cunning, J.C., and Sego, D.C. 1995a. Shear-wave velocity to evaluate in-situ state of Ottawa sand. Journal of Geotechnical Engineering, 121(3): 262–273. doi:10. 1061/(ASCE)0733-9410(1995)121:3(262). Robertson, P.K., Fear, C.E., Woeller, D.J., and Weemees, I. 1995b. Estimation of sand compressibility from seismic CPT. In Proceedings of the 48th Canadian Geotechnical Conference, Vancouver, B.C., 25–27 September 1995. BiTech Publishers Ltd., Richmond, B.C. Vol. 1, pp. 441–448. Robertson, P.K., Wride, C.E. (Fear), List, B.R., Atukorala, U., Biggar, K.W., Byrne, P.M., et al. 2000. The CANLEX project: summary and conclusions. Canadian Geotechnical Journal, 37(3): 563–591. doi:10.1139/cgj-37-3-563. Schmertmann, J.H. 1976 The shear behavior of soil with constant structure. In Laurits Bjerrum memorial volume — contributions to soil mechanics. Edited by N. Janbu, F. Jørstad, and B. Kjaernsli. Norwegian Geotechnical Institute (NGI), Oslo, Norway. pp. 65–98. Skempton, A.W. 1986. Standard penetration test procedures and the effects in sands of overburden pressure, relative density, particle size, aging and overconsolidation. Géotechnique, 36(3): 425–447. doi:10.1680/geot.1986.36.3.425. Published by NRC Research Press

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