A laboratory-based study correlating cone penetration test resistance to the physical parameters of uncemented sand mixtures and granular soils

Engineering Geology 255 (2019) 11–25

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A laboratory-based study correlating cone penetration test resistance to the physical parameters of uncemented sand mixtures and granular soils

T

Michael Ghalia,b, Mohamed Chekiredc, Mourad Karraya,

⁎

a

Department of Civil Engineering, Université de Sherbrooke, Sherbrooke, Quebec J1K 2R1, Canada Department of Civil Engineering, Faculty of Engineering, Helwan University, Cairo, Egypt c Institut de recherche d'Hydro-Québec (IREQ), Varennes, Quebec J3X 1S1, Canada b

ARTICLE INFO

ABSTRACT

Keywords: Cone penetration tip resistance Sleeve friction Mean grain size Uniformity coefficient Two-dimensional angularity of particles Experimental investigation Improved relationship

The influences of gradation curve properties and particle shape on the cone penetration test (CPT) resistances of normally consolidated clean sand under different relative densities were studied. The proposed empirical correlations were developed based on the experimental results of a laboratory CPT using an axisymmetric field simulator. The tests were performed on 18 different gradations of disturbed and premixed clean sands and 25 different gradations of fully spherical glass beads. The gradation curves and particle shapes of the tested sands were developed using laser scanning and image analyses. For a constant relative density, it was demonstrated that while the cone penetration tip resistance and the sleeve friction were slightly positively related to the mean grain size, they were significantly positively related to the uniformity coefficient and negatively related to the two-dimensional angularity of particles. A comparison between the trend in behavior of the current proposed empirical formulas with the frequently used empirical equations formulated in terms of relative density was presented. The applicability and limitations of the proposed relations were verified on a large dataset from the literature and on highly accurate field data of two sites in Canada.

1. Introduction Cone penetration testing is widely used for in-situ investigations because its measurements are cost-effective, rapid, continuous, and reliable (Robertson, 2016). Cone penetration tip resistance, qc, and sleeve friction, ƒs, are used to classify soil based on behavioral characteristics that are often classified as a soil behavior type (SBT) (Schneider et al., 2008; Robertson, 2016). A number of researchers (Robertson and Campanella, 1983; Bolton, 1986) have suggested that qc and ƒs are useful for estimating the real in-situ DR as well as the peak angle of shearing resistance. In addition, increased observation of soil liquefaction phenomena under vibration conditions have led other researchers (Carraro et al., 2003) to use cyclic cone penetration resistance to evaluate the liquefaction potential of soil. For these reasons, several

specifications (ASTM D5778-12, 2012) now demand in-situ measurements for cone penetration resistance. However, field measurements of qc and ƒs evaluate the geotechnical properties for a particular location under specific conditions, where a cone penetration test (CPT) is performed. Therefore, numerous researchers (Hsu and Huang, 1999; Kim et al., 2008; Lee et al., 2011; Yang and Russell, 2016) have carried out laboratory calibration chamber testing to allow laboratory investigation of the geotechnical parameters affecting CPT resistances under controlled conditions. Empirical correlations of qc with some geotechnical parameters of sand have been developed based on field penetration testing results in addition to laboratory investigations of physical parameters. However, several synaptic physical factors influence the cone penetration testing of similar sandy soils and have led to divergent results. In particular, the

Abbreviations: CPT, Cone penetration test; SBT, Soil behavior type; D50, Mean particle size; A2D, Two-dimensional angularity of particles; Cu, Uniformity coefficient; e, Void ratio; emax, Maximum void ratio; emin, Minimum void ratio; emax- emin, Void ratio range; σ'v, Effective overburden stress; σ'h, Effective lateral stress; Pa, Atmospheric reference pressure = 100 kPa; u2, Penetration water pressure immediately behind the cone tip; DR, Relative density; qc, CPT tip resistance; qc1, Standardized qc to a reference pressure of 100 kPa; qt, CPT tip resistance corrected for pore water effects; qt1, Standardized qt to a reference pressure of 100 kPa; qt1 N, Normalized dimensionless cone resistance corrected for water effects; ƒs, CPT sleeve friction; fs1, Standardized ƒs to a reference pressure of 100 kPa; Ic, Soil behavior type index; n, Variable SBT stress exponent ≤ 1.0; Qt, Dimensionless water corrected cone tip resistance; Qcn, Stress-normalized dimensionless CPT tip resistance; Qtn, Dimensionless n normalized cone tip resistance; Fr%, Standardized friction ratio; d, Penetration probe/cone diameter; fI, Physical parameters factor for the CPT tip resistance; fII, Physical parameters factor for the CPT sleeve friction ⁎ Corresponding author. E-mail addresses: [email protected] (M. Ghali), [email protected] (M. Chekired), [email protected] (M. Karray). https://doi.org/10.1016/j.enggeo.2019.04.015 Received 8 September 2018; Received in revised form 17 April 2019; Accepted 18 April 2019 Available online 19 April 2019 0013-7952/ © 2019 Elsevier B.V. All rights reserved.

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Table 1 A review of some empirical qc-DR correlations. Reference

Proposed correlations

Eq. No.

C1

Schmertmann (1976)

qc = C0. (σ'v) . exp [C2. DR]

Baldi et al. (1986) & Robertson and Cabal (2010)

DR =

Kulhawy and Mayne (1990) Mayne (2006)

qc1 2 DR

=

1 C2

Jamiolkowski et al. (2001)

DR 2 =

Qcn C0

(4)

12 (emax

- Where, C0, C1, C2 are empirical soil constants depending on the soil characteristics as well as the OCR. - Where, Qcn = (qc / Pa) / (σ'v / Pa)0.5 for qc and Pa are in kPa while C0 = 15.7 and C2 = 2.41 for moderately compressible, normally consolidated, unaged and uncemented sands. - Where qc1 is in MPa, qc1 = qc(Pa / σ'v)0.5.

(3)

( ). ln ( )

DR % = 100

Robertson and Cabal (2010)

(2)

emin )0.80

qt1N 305 Q A QC QOCR

- Where qt1N = (qt / Pa) / (σ'v / Pa)0.5; Qc is the sand compressibility factor with values 0.9, 1.0, 1.1 for high, medium, and low compressibility, respectively; QOCR = OCR0.2; QA is the aging factor = 1.2 + 0.05log(t/100), and t is time in years. - Where, Qtn is the updated normalized cone resistance associated to SBTn chart and can be estimated after Robertson, 2009 & 2016 - where qt and σ'v are in kPa

(6)

0.50

(8)

Qtn 350

DR % = 100 0.268 ln

qt ( v)

(14)

1.292

Notes and descriptions

Table 2 List characteristics of tested glass beads. Sample Code

Description

D50 (mm)

Cu

A2D

emax

emin

Sample Code

Description

D50 (mm)

Cu

A2D

emax

emin

GB-1 GB-2 GB-3 GB-4 GB-5 A-1 A-2 A-3 A-4 A-5 B-1 B-2 B-3

Glass Glass Glass Glass Glass Glass Glass Glass Glass Glass Glass Glass Glass

0.35 0.50 1.00 2.00 3.00 0.50 1.00 2.00 3.00 4.00 0.50 1.00 2.00

1.00 1.00 1.00 1.00 1.00 2.50 2.50 2.50 2.50 2.50 4.00 4.00 4.00

– – – – – – – – – – – – –

0.68 0.67 0.66 0.66 0.65 0.61 0.56 0.53 0.51 0.50 0.51 0.47 0.44

0.49 0.49 0.50 0.50 0.52 0.45 0.42 0.40 0.39 0.39 0.38 0.35 0.33

B-4 B-5 C-1 C-2 C-3 C-4 C-5 D-1 D-2 D-3 D-4 D-5

Glass Glass Glass Glass Glass Glass Glass Glass Glass Glass Glass Glass

3.00 4.00 0.50 1.00 2.00 3.00 4.00 0.50 1.00 2.00 3.00 4.00

4.00 4.00 8.00 8.00 8.00 8.00 8.00 12.50 12.50 12.50 12.50 12.50

– – – – – – – – – – – –

0.42 0.4 0.43 0.39 0.37 0.36 0.35 0.42 0.39 0.36 0.33 0.33

0.31 0.30 0.32 0.30 0.29 0.27 0.27 0.32 0.30 0.28 0.26 0.26

beads beads beads beads beads beads beads beads beads beads beads beads beads

beads beads beads beads beads beads beads beads beads beads beads beads

Table 3 List characteristics of tested sands. Sample Code

Description

Gs

emax

emin

D50 (mm)

Cu

D50a (mm)

Cua

A2Db

E-1 E-2 E-3 F-1 F-2 G-1 G-2 G-3 H-1 H-2 S-1 S-2 PS-1 PS-2 PS-3 PS-4 PS-5 PS-6

Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean Clean

2.71 2.71 2.71 2.71 2.71 2.74 2.74 2.74 2.72 2.72 2.72 2.71 2.71 2.71 2.71 2.71 2.71 2.71

0.75 0.75 0.68 0.84 0.79 0.92 0.83 0.78 0.81 0.81 0.84 0.86 0.82 0.82 0.83 0.82 0.82 0.81

0.45 0.47 0.42 0.48 0.46 0.46 0.45 0.46 0.47 0.47 0.36 0.33 0.39 0.40 0.41 0.42 0.41 0.40

1.20 1.70 2.25 1.30 1.95 0.45 0.80 1.90 3.10 3.70 0.35 0.25 0.40 1.20 1.70 2.30 2.75 3.55

1.65 2.55 3.50 1.25 2.15 2.50 3.20 5.00 6.85 6.85 2.32 2.39 2.10 2.00 2.03 2.03 1.99 1.99

0.85 1.15 1.60 0.85 1.30 0.30 0.50 1.30 1.85 2.10 0.25 0.18 0.30 0.80 1.10 1.60 1.80 2.20

1.59 2.62 3.66 1.25 2.25 2.50 3.00 4.53 6.36 6.50 2.40 2.40 2.00 2.00 2.00 2.00 2.00 2.00

490 490 490 600 600 650 650 650 780 780 450 450 490 490 490 490 490 490

a b

sand sand sand sand sand sand sand sand sand sand sand sand sand sand sand sand sand sand

Grading curves for natural soils were executed using image analysis and laser scanning. Calculated according to Miura et al. (1997) and Lees (1964a, 1964b).

DR, void-ratio range (emax–emin), D50, Cu, A2D, and percentage of fine content (Fc%) exert significant influence on the technical properties of sandy materials (Santamarina and Cho, 2004). These parameters have a complex impact not only on CPT resistance measurements but also on each other. For example, although the international specifications and guidelines (ASTM D2487-11, 2011) include D50 and Cu in their soil classification, the effect of particle shape on gradation measurements of sand is barely considered. Ghali et al. (2018a) suggested that the difficulty in solving this interrelated nature of the above-mentioned

geotechnical parameters may be the result of the following three factors:

• no standard quantitative description exists in the geotechnical domain to characterize particle shape, • sieve analysis lacks accuracy when the particle shape is involved as • 12

the volume of the retained particles on any sieve varies considerably with the particle shape (Lees, 1964a, 1964b; Fernlund, 2005), and geotechnical parameters such as D50 and void-ratio range affect each

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Fig. 1. Characterization of tested samples: (a) Gradation curves based on sieve analysis. (b) Gradation curves based on laser scanning and image analysis. (c) General images of samples under Leica MZFL-III fluorescence stereozoom microscope. (d) Definition of A2D after Miura et al. (1997) & Ghali et al. (2018a) and the A2D estimation chart modified after Lees et al. (1964a, 1964b).

other.

particle shape effect on soil gradation.

Therefore, many of the existing empirical relationships may require some refinement through isolation of the interlocking effects of the physical parameters of sands. Hence, the objective of this study is to develop more reliable empirical correlations for CPT resistance measurements for the physical characteristics of normally consolidated sands. The research program utilized an assembly (designed and manufactured after Ghali et al., 2018b) as the calibration chamber for the CPT on sands and granular materials (glass beads). This simulator allowed for a range of controlled boundary stiffness conditions in the laboratory and the performance of laboratory parametric studies that described an acceptable range of lateral- and vertical-site stiffness conditions. Experiments with disturbed samples of fully spherical glass beads having specific gravities close to that of natural silica sand were conducted to eliminate particle shape and stress history effects and therefore permit laboratory parametric studies on D5i under specific DR and σ'v to be more easily conducted. In addition, to perform parametric studies, gradation curves of the tested sands were developed by laser scanning and image analysis techniques that allowed isolation of the

2. Basic state of knowledge The in-situ DR of cohesionless soils, as defined in Eq. (1), is usually considered an intermediate soil parameter to correlate the in-situ void ratio under the effective overburden stresses in the field with the voidratio range. For this reason, many researchers have attempted to relate DR to qc.

DR =

emax e emax emin

(1)

Table 1 summarizes the frequently utilized formulas for predicting the in-situ DR from CPT measurements. In detail, Schmertmann (1976) first attempted a correlation based on CPT performed in calibration chambers, as shown by Eq. (2) (Table 1). This correlation is applicable for normally consolidated, uncemented, unaged, fine-to-medium clean sands. Based on extensive data obtained from calibration chamber testing on Ticino sand, Baldi et al. (1986) modified the formula to estimate the DR from the dimensionless stress-normalized CPT tip 13

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Fig. 2. The CPT laboratory simulator: (a) a schematic representation, (b) digital photo of a running test.

resistance, Qcn. Robertson and Cabal (2010) presented a modified version of this relation as shown in Eq. (3) (Table 1). Kulhawy and Mayne (1990) reported the Standardized qc1/DR2 as a function of the void-ratio range as illustrated in Eq. (4) (Table 1). Many researchers (Robertson and Wride, 1998) agreed to define qc1 as

qc1 = qc .

Pa

area. Typical values of a range from 0.5 to 1.0. Robertson and Cabal (2010) proposed that a constant of 350 instead of 305 (Eq. (6)) in Table 1) was more reasonable for clean, medium, uncemented, unaged quartz sands about 1000 years old. This constant may vary between 300 and 400 for fine-to-coarse sands, respectively. They also suggested Eq. (8) (Table 1) as a simplified formula for most young uncemented sands based on the updated normalized cone resistance associated with the SBTn chart, Qtn, which can be estimated as (Robertson, 2016)

0.50

(5)

v

Kulhawy and Mayne (1990) expressed a simpler relationship for estimating the DR from a CPT that accounted for the additional effects of aging and overconsolidation. Mayne (2006) presented a modified form of the relation with the normalized cone resistance corrected for water effects, qt1N, as shown in Eq. (6) (Table 1). Also, a number of researchers (Lunne et al., 1986; Karray and Hussien, 2017) agreed that qt can be estimated as:

qt = (qc + u2 (1

a))

Qt =

Fr =

qt

where qt, qc, and ui are in similar units; a is the ratio between shoulder area (cone base) unaffected by the pore water pressure to total shoulder

,

fs (qt

Ic = [(3.47

(7)

v

(9)

v

v)

100%,

log Qt )2 + (log Fr + 1.22)2]0.50 ,

n = 0.381(Ic ) + 0.05

14

(10)

v

Pa

0.15,

(11)

(12)

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Fig. 3. Comparison between semi-infinite FDM simulation and laboratory CPT tests under different boundary stiffness conditions; (a) Development of lateral stresses with variation of the applied effective overburden pressures during consolidation, (b) Effect of 300 (mm) penetration of the CPT cone and sleeve on the development of vertical stresses under σ'v = 40 (kPa), (c) Effect of 300 (mm) penetration of the CPT cone and sleeve on the development of lateral stresses after under σ'v = 40 (kPa). (d) Examples of tested soil classification based on SBT chart of Jefferies and Davies (1991) modified by Robertson and Wride (1998).

Qtn =

qt

v

Pa

Pa v

n. A number of researchers (Robertson, 2016) have indicated that n is < 1.0 for coarse-grained soils. Jamiolkowski et al. (2001) gathered 456 experimental data pairs of calibration chamber testing corrected to the calibration chamber size

n

.

(13)

Note that the updated normalized SBT chart uses Qtn instead of Qt. Ic is also calculated using Qtn, which is dependent on the stress exponent, 15

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to investigate the real D50, Cu, and A2D of all tested clean sands. The principal advantage of these techniques was the separation of the effect of particle shape on real volume. The Malvern Mastersizer 2000 apparatus utilized for laser scanning was ideal for developing the gradation curves of sand having a maximum particle size of 2.0 mm. Six 15-g samples were randomly chosen from each sand soil tested and three specimens were used for the experiment from each sample. A light stereomicroscope, Leica MZFL-III fluorescence stereo-zoom microscope, was employed for the image analysis to develop grading curves of sand with particle diameters > 2.0 mm. In addition, the AiD of all the natural sand samples tested in the current work was predicted using the recorded two-dimensional images. Tables 2 and 3 present a summary of particle characterizations for tested glass beads and natural sands. Fig. 1a and b show examples of the conventional and corrected soil gradations, respectively. Fig. 1c shows images for tested sands, and Fig. 1d shows the technique of predicting A2D compared to the proposed chart modified after Lees (1964a, 1964b).

Table 4 Assumed Uni values with relevant DR values. DR (%)

Uni

0–15 15–35 35–65 65–85 85–100

12–15 9–12 6–9 3–6 0–3

and proposed Eq. (14) (Table 1). They also proposed a standard deviation, σ = 7.9%, which leads to a variation in the DR values from [DR % (Eq. (14)) – 2σ%] for low compressibility sands to [DR % (Eq. (14)) + 2σ%] for high compressibility sands. It is evident from the above-mentioned correlations that the soil constants in each correlation vary considerably with the physical parameters reflecting the various compressibility conditions of different sands. Therefore, the primary purpose of this study was to experimentally investigate the effects of physical parameters that represent the compressibility conditions of uncemented, unaged silica and quartz sands on CPT resistances.

3.2. CPT laboratory simulations Simulating real field conditions is a significant task because of the limitations of calibration chamber size and surrounding boundary conditions. These considerations lead to a disparity of results between chamber test results and the corresponding field test results. Such an inquiry may decrease as the ratio of chamber/cone diameter increases (Salgado et al., 1998). In addition, the scale effect, which represents the influence of the penetration device diameter (d) to the D50 of the soil, is highly significant. Many researchers (Damavandi-Monfared and Sadrekarimi, 2015; Huang and Hsu, 2005; Bolton et al., 1999; Hsu and Huang, 1999) have indicated that with an increasing d/D50 ratio, the scale effect decreases and may be considered negligible if d/D50 ≥ 20. Also, researchers have introduced remarkable attempts to simulate field conditions by controlling the variation of the applied lateral stresses in accord with the field conditions. For instance, Ghionna and Jamiolkowski (1991) and Foray (1991) allowed the lateral stress to vary throughout the lateral boundary of the calibration chamber. Hsu and Huang (1999) and Huang and Hsu (2005) introduced the pioneering idea of allowing the lateral stress to vary with the height of the tested sample by using a stack of 20 rings to replace the single rubber membrane typically used in a conventional calibration chamber. They controlled the lateral stiffness conditions using a servo-controlled boundary according to a constitutive model that emulated soil from the physical boundary to infinity. In this study, the axisymmetric simulator consisted of a large-scale oedometer and a guide frame to fix the penetration devices over the top center of the tested sample. A linear actuator with an adjustable speed

3. Experimental program A series of experiments was performed on glass beads having specific gravity and damping behavior close to silica sands and natural clean dry silica/quartz sands with the objective of performing laboratory parametric studies. Modern techniques and methods and conventional geotechnical laboratory experiments were utilized to predict the gradation of natural cohesionless sands. Laboratory CPT simulations were performed under several particular DRs, loading conditions, and stress–strain-controlled boundaries using different boundary stiffness and elasticity conditions. The results obtained from the series of experiments were stored in digital format for further processing and analysis. 3.1. Soil characterization The ASTM specification guidelines (ASTM D854-14, 2014; ASTM D4253-14, 2014; ASTM D4254-14, 2014; and ASTM D2487-11, 2011) were followed for the geotechnical testing program in this study. The primary purpose of the conventional geotechnical tests (sieve analyses, minimum dry density, and maximum dry density) was to determine the specific gravity, maximum and minimum void ratios, D50, and Cu of all the samples tested in the current program. Laser scanning and image analysis techniques were then applied according to Ghali et al. (2018a) Table 5 Summary of CPT laboratory simulations. Sample Code

σ'v kPa

DRa %

D50 (mm)

Cu

A2D

qt1 (MPa)

fs1 (kPa)

Qtn

Fr %

Sample Code

σ'v kPa

DRa %

D50 (mm)

Cu

A2D

qt1 (MPa)

fs1 (kPa)

Qtn

Fr %

GB-1 GB-2 GB-2b GB-3 GB-4 GB-5 E-1 E-2 E-3 F-1 F-2 G-1 G-2

100 100 100 100 100 100 100 100 100 100 100 100 100

45.40 51.17 50.86 62.18 72.18 76.64 49.82 59.48 66.42 53.45 61.52 35.28 37.59

0.35 0.50 0.50 1.00 2.00 3.00 0.85 1.15 1.60 0.85 1.30 0.30 0.50

1.00 1.00 1.00 1.00 1.00 1.00 1.59 2.62 3.66 1.25 2.25 2.50 3.00

– – – – – – 490 490 490 600 600 650 650

7.74 9.87 9.73 14.26 20.03 22.33 6.89 11.26 15.44 6.71 9.90 3.45 4.68

69.84 71.05 70.99 78.82 116.71 120.58 57.18 64.91 109.83 58.11 63.26 38.80 51.21

76.40 97.70 96.30 141.60 199.30 222.30 67.90 111.60 153.40 66.10 98.00 33.50 45.80

0.91 0.73 0.74 0.56 0.59 0.54 0.84 0.58 0.72 0.88 0.65 1.16 1.12

G-2b H-1 H-2 H-2b S-1 S-2 PS-1 PS-2 PS-3 PS-3b PS-4 PS-5 PS-6

100 100 100 100 100 100 100 100 100 100 100 100 100

37.84 52.64 57.69 57.86 28.65 24.53 27.69 33.47 37.94 38.75 43.65 43.57 47.10

0.50 1.85 2.10 2.10 0.25 0.18 0.30 0.80 1.10 1.10 1.60 1.80 2.20

3.00 6.36 6.50 6.50 2.40 2.40 2.00 2.00 2.00 2.00 2.00 2.00 2.00

650 780 780 780 450 450 490 490 490 490 490 490 490

4.69 9.76 11.23 11.24 2.81 2.02 2.41 3.72 4.76 4.75 5.81 5.99 6.80

51.23 71.66 94.86 95.01 27.69 22.14 28.35 36.37 37.72 37.61 48.25 48.98 54.13

45.90 96.60 111.30 111.40 27.10 19.20 23.10 36.20 46.60 46.50 57.10 58.90 67.00

1.12 0.74 0.85 0.85 1.02 1.15 1.23 1.00 0.81 0.81 0.85 0.83 0.81

a b

After normal consolidation. Repeated experiments. 16

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Fig. 4. a) The standardized tip resistance to a reference pressure of 100 kPa as a function of DR b) The standardized sleeve friction to a reference pressure of 100 kPa as a function of DR.

earlier stated attempts by allowing the lateral as well as the vertical strains to vary in accordance with the desired field conditions. A semiinfinite simulation using finite difference method (FDM) software was initially performed for the consolidation phase and the CPT penetration phase, and then the elasticities of the rubber rings and bottom liners were chosen to satisfy the resulting stress–strain behavior at locations corresponding to the calibration chamber edges. In other words, the simulator did not apply lateral stress but varied according to the variation of the applied vertical and penetration stresses and the variation of the elasticity grades of the employed liners. The resulting physical stresses and strains around the sample edges of the experimental simulations were then reviewed with a finite difference method-based software under the desired field conditions. Fig. 3a–c show the ability of the simulator to represent a range of different site conditions by reducing, if not eliminating, the boundary and scale effects. Several repetitive tests were performed under identical conditions and DR surrounded by different rubber liners, and the results were compared to a corresponding finite difference method

of 1–50 mm/s and rigid outer cell of inner diameter 360 mm and internal height of 600 mm was utilized. Flexible, oil-lubricated, changeable rubber liners having elasticities ranging from 186 to 1048 kPa were installed inside the testing cell to eliminate calibration chamber size and rigid boundary effects. Liners of 10-mm thickness were utilized to provide a sample diameter of 340 mm. The chamber was equipped with several flexible lateral- and vertical-strip tactile pressure sensors (piezoelectric film sensors) to measure and record the development of stresses around the sample edges. A pressure compressor unit was used to develop the applied vertical pressure at the top surface of the tested sample. Strain gauges, calibration and acquisition devices, and a computer-controlled system were also employed. A standard cone with a diameter of 35.7 mm and a penetration rate of 20 mm/s were used in the calibration chamber during the tests for a maximum penetration depth of 300 mm. The main components of the simulator are illustrated in Fig. 2a, and a digital photo of a running CPT simulation is presented in Fig. 2b. The axisymmetric simulator used had a slight advantage over the 17

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Fig. 5. fI and fII values respectively for: a) & d) Glass bead samples (Cu = 1.0), and reconstituted c) lean sand samples (Cu ≈ 2.0 & A2D ≈ 490); b) & e) Glass bead samples (D50 = 1.0 mm), and graded clean sands (D50 ≈ 0.5–1.0 mm & A2D ≈ 500 ± 10); c) & f) Glass beads & clean dry sands (Cu ≈ 1.0, D50 ≈ 0.85–1.00 mm).

numerical simulation. The current experimental program was performed on several samples of uniform grade to well-graded glass beads and reconstituted samples of uniform grade to well-graded clean sands. Samples were carefully selected to pursue parametric studies on the concerned geotechnical parameters of this study. Tests were performed for each sample under several desired initial values of DRs following the

procedures of Ghali et al. (2018a) and based on the under-compaction technique by Ladd (1978). The tested specimens were divided into six layers of equal initial weight. The under-consolidation percent for the first layer, Uni, was assumed as shown in Table 4. Then, 5-kg and 7.5-kg compaction rods with a free drop height of approximately 20–25 cm were used for the compaction process. These sets of experiments were performed on samples having a D50 range of 0.18–2.0 mm. Additional 18

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Fig. 6. Comparison between the proposed Eq. (16) and literature empirical correlations.

Fig. 7. Coefficients of correlation between the proposed equations and some experimental results: (a) the stress normalized qt1, (b) the stress normalized fs1.

experiments were conducted on samples having a D50 range of 2.0–4.0 mm, and the results were analyzed not only to study the effect of the increase of D5i but also that of the variation of flexible boundaries on the scale effect d/D5i. The recorded data for the developed threedimensional deformations were used to estimate the overall DR of the sample during the consolidation and penetration phases. The developments of qc and fs values with increasing applied surcharge loads were also documented. Table 5 and Fig. 3d show examples of the results.

easily realized functional empirical correlations between CPT resistances and various physical parameters, Dii correlations were backadjusted to the sieve analysis diameters according to the modified comparative empirical relationship proposed by Ghali et al. (2018a) as illustrated in Eq. (15). This relation is suitable for spherical, ellipsoidal, and roller-shaped particles but overestimates the diameters of equivalent spheres for bladed or thinly flattened particles.

4. analysis and proposed correlations

+ D50 =1 D50

Most worldwide laboratory and field results reported in the current literature depend on sieve analysis results for estimating soil gradation. However, because the principal purpose of this study was to develop

where D5i+ is the mean particle diameter determined by laser scanning in the same units of Dii, which is the corresponding mean particle diameter estimated from sieve analysis. 19

0.65 A2D , 1200

(15)

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Fig. 8. Database of Péribonka Main Dam site and Post Judith-Jasmin site: (a) Geological province, (b) SBT classification chart of Jefferies and Davies (1991) modified by Robertson and Wride (1998). Table 6 Database from Péribonka dam site and Judith-Jasmin site. Site

Test Code

D50 (mm)

Cu

A2D

Péribonka dam site

TF-80-05 TF-82-05 TF-83-05 TF-85-05 TF-86-05 TF-87-05 TF-89-05 TF-90-05 TF-91-05 TF-92-05 TF-93-05 F3-CF3 F4-CF4 F4-CF5 F5-CF3 F5-CF5 F6-CF4 F7-CF3

0.47 (0.01) 0.51 (0.13) 3.08 (4.39) 5.50 (0.03) 0.47 (0.01) 1.59 (1.34) 1.53 (1.01) 3.20 (3.96) 3.85 (0.16) 3.31 (2.44) 2.75 (2.05) 0.20 0.20 0.22 0.19 0.205 0.20 0.22

4.5 (0.5) 5.5 (0.7) ˃8 ˃8 3.3 (0.6) ˃8 ˃8 5.0 (1.4) ˃8 ˃8 ˃8 2.33 2.47 1.73 2.53 2.05 2.71 2.00

420 510 600 510 410 600 380 510 600 590 550 760 760 780 760 780 760 780

Judith-Jasmin site

DR % (30) (55) (80) (50) (30) (60) (120) (20) (40) (50) (120) (31) (22) (18) (24) (24) (26) (23)

92 68 66 95 84 74 96 63 67 51 69 49 53 49 56 49 48 52

(4) (11) (9) (2) (13) (9) (2) (20) (3) (21) (28) (18) (11) (11) (11) (14) (9) (21)

qt1 (MPa)

qt1a (MPa)

qt1b (MPa)

qt1c (MPa)

fs1 (kPa)

fs1d (kPa)

29.9 17.2 16.1 30.7 26.2 20.6 48.1 16.1 16.8 11.2 32.0 5.25 6.82 4.52 8.09 5.04 5.74 5.49

30.4 16.9 16.1 33.2 23.5 20.9 41.7 15.1 17.2 12.2 28.4 5.39 6.16 4.37 7.42 4.93 5.82 5.46

41.2 16.4 15.3 42.6 31.6 20.6 51.1 14.9 20.1 10.9 31.2 7.12 7.98 7.49 9.82 7.33 6.85 7.75

26.9 (2.6) 14.3 (4.6) 13.6 (3.5) 28.1 (1.1) 21.9 (7.8) 16.9 (4.3) 30.3 (0.4) 12.8 (7.7) 18.2 (2.0) 9.1 (7.2) 20.3 (14.5) 7.35 (2.4) 8.18 (2.5) 7.08 (2.4) 9.58 (2.9) 7.19 (2.1) 7.45 (1.3) 8.31 (2.5)

118.1 (1.2) 67.1 (4.6) 73.6 (13.6) 117.8 (1.9) 106.2 (34.5) 94.7 (26.2) 155.7 (22.3) 73.5 (26.1) 60.2 (0.4) 64.2 (35.2) 89.7 (35.8) 36.1 (6.1) 39.9 (8.5) 36.2 (7.1) 46.2 (15.6) 38.9 (7.6) 37.0 (12.8) 36.6 (6.4)

109.8 (1.4) 81.5 (11.7) 79.6 (9.5) 123.1 (1.7) 95.9 (17.7) 85.2 (20.9) 129.0 (9.5) 76.7 (15.6) 84.3 (3.8) 65.9 (25.1) 101.9 (43.6) 39.3 (7.6) 43.3 (9.1) 38.1 (14.2) 45.9 (12.0) 38.3 (11.1) 41.8 (9.8) 40.2 (11.8)

(2.1) (4.4) (3.5) (0.6) (10.1) (5.0) (12.2) (9.3) (1.3) (8.8) (29.0) (1.25) (0.9) (0.7) (3.1) (1.0) (1.4) (1.3)

(2.6) (4.7) (3.6) (1.7) (8.7) (3.9) (6.2) (6.0) (2.4) (9.1) (22.1) (0.5) (1.0) (0.9) (2.2) (0.6) (1.7) (2.2)

(3.3) (6.6) (4.6) (2.3) (17.9) (6.9) (1.1) (10.3) (2.2) (9.1) (29.2) (1.8) (2.5) (2.4) (3.8) (2.5) (1.9) (2.4)

The numbers given in the table are overall mean values (with standard deviations in parentheses). a Predicted after current correlation (Eq. (16)). b Predicted after Jamiolkowski et al. (2001) (Eq. (14)). c Predicted after Kulhawy and Mayne (1990) & Mayne (2006) (Eq. (6)). d Predicted after current correlation (Eq. (17)).

The standardized CPT resistances to a reference pressure of 100 kPa were calculated as qti = qt (Pa/σ'v)0.5 and fs1 = fs (Pa/σ'v)0.5, where (qt1 and qt), (fsi and fs), and (Pa and σ'v) are in the same units (e.g., qt1 & qt are in MPa; and fs1 & fs in kPa). Then the best fit trends of the resistances obtained were correlated to DR, as illustrated in Fig. 4a and b. From these figures, correlations of (qt1 = fI DR1.76) and (fs1 = fII DR0.89) were concluded, where fI is the physical parameters factor for the CPT tip resistance while fII is the physical parameters factor for the CPT sleeve friction. Formulas in Fig. 4a and b show that the values of fI and

fII are varying considerably with the variation of D50, Cu and A2D values. The best fit trends of fI and fII were found to be slightly positively related to D500.05 and D500.025, respectively, as shown in Fig. 5a and d. In addition, fI and fII trends were found to be positively related to Cu0.32 and Cu0.16, respectively, as shown in Fig. 5b and e. Eventually, as illustrated in Fig. 5c and f and corresponding to the above-mentioned glass bead samples (same D50 and Cu), several reconstituted samples of cliean sand having different A2D values were tested to include the effect of particle shape. Trends of fI and fII were found to be related to exp. 20

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Fig. 9. Comparative study on CPT resistances from different geological provinces: (a) qt1 from Prébonka Main Dam site, (b) fs1 from Prébonka Main Dam site, (c) qt1 from Poste Judith-Jasmin site, (d) fs1 from Poste Judith-Jasmin site.

(−A2D/1000) and exp.(−A2D/2000), respectively. Based on the above-mentioned derivations, the authors proposed the use of amplitude multiplication factors to combine the physical parameters and the DR to the standardized qt1 and fs1 of normally consolidated, uncemented, unaged, clean sand as

qt1 DR1.76 fI = fs1 DR 0.89

= fI ,

1

A2D

2

A2D

0.025 C 0.16 exp 2000 D50 u

(17b)

where α1 and αi are amplitude factors estimated by regression analysis in ranges of 32–34 and 112–119, respectively. In this study, α1 = 33 and αi = 115 were utilized, qti was measured in MPa, fs1 in kPa, and D5i in mm. In this study, sand and glass beads having Cu ≥ 8 did not show any significant variance in trend; therefore, it was acceptable to substitute Cu = 8 into Eqs. (16) and (17) for such granular materials. To validate Eq. (16), performance trends were compared to existing empirical correlations from the literature, as shown in Fig. 6. All patterns showed a high coincidence for normally consolidated, uncemented, unaged, clean sands with moderate compressibility, particularly for the DR range of 30–80%. The current proposals extend the trend range by

(16a)

0.05 C 0.32 exp1000 D50 u

= fII ,

fII =

(16b)

(17a) 21

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Table 7 Database from Holocene age sand deposits. Site Name USA SRS, B35-S30

Canada Syncrude, Mildred Lake Fraser River Delta, Massey Fraser River Delta, Kidd Syncrude, J-Pit HVC Mine, LL Dam HVC Mine, Highmont Dam Korea NRD site, NRD site, NRD site, NRD site, NRD site, NRD site,

MD1P-2 MD1P-2 MD1P-2 MD1P-5 MD1P-5 MD1P-5

Taiwan CHCIP site, CHCIP site, CHCIP site, CHCIP site,

S1 S2 S3 S4

Dep. (m)

Fc (%)

D50 (mm)

Cu

Particle Shape

A2D min.

A2D max.

qt1 (MPa)

fs1 (kPa)

DR %

qt1max. (MPa)

qt1min. (MPa)

fs1max. (MPa)

fs1min. (MPa)

A2D#

10.0 12.5 15.0 17.5 20.0

5 5 5 5 5

0.50 0.50 0.50 0.50 0.50

4.44 4.44 4.44 4.44 4.44

SA SA SA SA SA

475 475 475 475 475

750 750 750 750 750

4.6 6.2 5.0 3.7 2.4

42.43 49.33 42.72 37.95 31.00

36⁎ 41⁎ 37⁎ 32⁎ 25⁎

5.3 6.8 5.6 4.2 2.8

4.0 5.1 4.2 3.2 2.1

45.41 51.61 46.74 40.61 33.03

39.58 44.98 40.73 35.39 28.78

605 567 620 609 615

a

27–37 8–13

10 < 5

0.16 0.20

2.22 1.57

SR-SA SR

200 200

750 475

7.38 6.9

51.81 47.29

46⁎ 44⁎

8.09 6.90

4.67 5.24

56.49 52.16

42.91 45.46

332 298

a

12–17 3–7 6–10 8–12

< 5 15 8 10

0.20 0.17 0.20 0.25

1.78 2.50 2.78 4.00

SR SR-SA A A

200 200 750 750

475 750 1000 1000

10 2.8 2.6 5.5

58.98 32.40 24.74 37.51

53⁎ 28⁎ 27⁎ 40⁎

9.96 3.59 2.02 4.45

7.56 2.07 1.58 3.46

62.77 37.46 28.12 41.83

54.71 28.45 24.81 36.91

260 470 753 753

a

33.5 37.5 41.5 36.0 38.0 39.5

< < < < < <

0.35 0.22 0.72 0.42 0.35 0.20

2.24 1.77 4.84 2.88 2.92 2.2

SR SR SA SR SR SR

200 200 200 200 200 200

750 750 750 750 750 750

19.12 8.94 15.81 11.55 8.32 13.56

86.93 58.42 78.10 67.08 58.04 72.94

73⁎ 50⁎ 67⁎ 57⁎ 48⁎ 62⁎

19.3 8.8 21.5 13.4 9.9 13.7

11.1 5.1 12.4 7.7 5.7 7.9

87.58 58.98 92.50 72.87 62.54 73.67

66.53 44.80 70.26 55.35 47.50 55.96

215 219 538 366 349 220

a

0.55–1 3.55–4 5.55–6 9.55–10

2 7 2 6

0.2 0.15 0.23 0.16

3.14 7.39 2 4.72

SR-SA SR-SA SR-SA SR-SA

200 200 200 200

750 750 750 750

16 4 2.5 6.5

– – – –

68⁎ 34⁎ 27⁎ 43⁎

18.1 6.9 3.1 9.2

10.4 4.0 1.8 5.3

– – – –

– – – –

321 747 406 548

SR SA SR SA

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32 0.32

2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5 2.5

SA-A SA-A SA-A SA-A SA-A SA-A SA-A SA-A SA-A SA-A SA-A SA-A SA-A SA-A SA-A SA-A

475 475 475 475 475 475 475 475 475 475 475 475 475 475 475 475

1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000

4.1 4.1 3.8 4.2 4.3 4.9 7.5 9.5 9.5 8 17.5 17.5 16.5 15.5 17 25

– – – – – – – – – – – – – – – –

42 43 43 44 46 48 61 62 62.5 63 78 79 79 80 82 85

5.6 5.9 5.9 6.1 6.6 7.1 10.9 11.2 11.4 11.5 16.8 17.2 17.2 17.5 18.3 19.5

3.3 3.5 3.5 3.6 3.9 4.2 6.4 6.6 6.7 6.8 9.9 10.2 10.2 10.4 10.8 11.6

– – – – – – – – – – – – – – – –

– – – – – – – – – – – – – – – –

795 836 912 853 907 852 848 640 654 840 433 456 515 599 550 228

A A A A A A A SA SA A SR SR SA SA SA SR

Korea (Laboratory results) Sample 1 – Sample 2 – Sample 3 – Sample 4 – Sample 5 – Sample 6 – Sample 7 – Sample 8 – Sample 9 – Sample 10 – Sample 11 – Sample 12 – Sample 13 – Sample 14 – Sample 15 – Sample 16 –

4 4 4 4 4 4

+ + + + + +

a a a a

a

a a a

a a a a a

Particle Shape# SA SA SA SA SA SR SR SR SR-SA A A

SR SR SA SR SR SR

SR = Sub-rounded, SA = Sub-angular, A = Angular. ⁎ Predicted after Robertson and Cabal (2010) (Eq. (8)). + Evaluated from image analyses, in accordance with the original visual description. # Reevaluated from the in-situ CPT records and the Proposed Eqs. (16) and (17). a Average values evaluated from the recorded qt1 & fs1 values using Eqs. (16) and (17) respectively.

including high compressibility conditions of clean sands resulting from increasing the angularity of particles to low compressibility conditions at a low void-ratio range by increasing Di0 and Cu. In other words, the compressibility conditions of clean sands were positively related to the void-ratio range (emax–emin). In addition, the graphical presentations of Ghali et al. (2018a) illustrate that uniform, angular, fine clean sands have a higher emax–emin range than that of rounded, well-graded, coarse clean sands. Therefore, the theoretical boundary for high compressibility conditions in clean sand sizes was assumed at D50 = 0.075 mm, Cu = 1, and A2D = 800, while the theoretical boundary for low compressibility conditions was assumed at D50 = 5.0 mm, Cu ≥ 8, and A2D = 0.

5. Verification studies 5.1. Experimental CPT results Table 5 and Fig. 7a and b show the experimental results for normally consolidated clean sand and spherical glass beads compared to the predicted values fromi Eqs. (16) and (17). In addition, some predicted qt1 values from the actual correlations stated in Table 1 were compared to the experimental results. Comparisons showed a high coincidence between most correlations. The superiority of the current proposals was demonstrated by coefficients of correlation (R2) of 99% and 95% for Eqs. (16) and (17), respectively. 5.2. Applicability on several geological provinces Sands from two different geological provinces in Quebec (Grenville Province and Saint Lawrence Platform), Canada, as shown in Fig. 8a, 22

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Fig. 10. Comparative case study on database from literature: (a) Development of qt1 with relative density, (b) Development of fs1 with relative density.

of metasedimentary and metamorphic rocks of the Precambrian Age, the highland surface is covered with a variety of deposits of the Cenozoic Age with a blocky landscape of steep slopes. Hill slopes are mantled with sandy tills whose depth over the bedrock varies from a few centimeters to > 12 m; these deposits have considerably softened the rugged rock knob landscape. The sand deposits are generally made up of angular to very angular poorly graded sand and gravelly sand with a fine particle content < 5%. The selected data were collected from highly accurate testing points representing ideal normally consolidated layers as presented in Fig. 8b. The DR was initially estimated in accord with Robertson and Cabal (2010) from Eq. (8), while the soil physical parameters were evaluated using the image analysis technique and conventional sieve analysis on disturbed samples extracted from the split spoon sampler during standard penetration tests performed adjacent to the CPT points. A summary of the verification study is presented in Table 6 and Fig. 9. Results show a high coincidence between all compared correlations. Moreover, the results demonstrate that the proposed Eqs. (16) and (17) accurately predicted the qc corrected for water pressure immediately behind the

were investigated based on the database gathered from the main dam site of Peribonka and the Judith-Jasmin substation site. Karray et al. (2011) provided the database from CPTs in the Peribonka main dam site for normally consolidated, uncemented, coarse-grained materials of quartz minerals with feldspar. The dam is built on sedimentation deposits that appear to be fluvioglacial deposits formed during the last ice age, 7800 to 9800 years ago (Bernatchez, 1997). These deposits are also found in the riverbed and are generally made up of subrounded to subangular well-graded sand, gravelly sand, and gravel with a fine particle content < 2%. Karray et al. (2016) provided the database from CPTs in the JudithJasmin substation site located at the center of the city of Terrebonne, Quebec, Canada, which two of the major physiographic provinces of North America straddle (Saint Lawrence Lowland and Laurentian Upland). The general geological formation of the lowland zone is a bed of flat-lying Ordovician limestone and dolomites, and a thick mantle of till, clay, and alluvium (deposited by the postglacial Champlain Sea) blankets the bedrock. In many areas, thick sand and gravel deposits of marine origin overlie the clays. While the upland underlay is a complex 23

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cone tip as well as the fs, respectively.

b) The proposed Eqs. (16) and (17) show that D50 ranges from 0.075 to 5.0 mm may affect the qt1 values by a factor ranging from 0.88 to 1.08 and the fs1 by a factor ranging from 0.94 to 1.04. c) A Cu ranging from 1.0 to ≥8.0 may affect the qt1 values by a factor ranging from 1.00 to 1.95 and the fs1 by a factor ranging from 1.00 to 1.39. Notably, the tested samples of Cu ≥ 8 in the current experiment showed no significant variation in results. d) Similarly, A2D ranging from 300 to 800 may affect the qt1 values by a factor ranging from 0.74 to 0.45 and the fs1 by a factor ranging from 0.86 to 0.67. e) As the present study was carried out on natural disturbed clean sands, glass beads, and premixed clean sands, the proposed Eqs. (16) and (17) overestimated the CPT resistances of sands having Fc% > 5%.

5.3. Worldwide literature CPT results Worldwide CPT resistances were collected for several sands to validate the applicability of the proposed Eqs. (16) and (17). The sands examined were from the Savannah River Site in South Carolina, USA (Ku et al., 2016); the CANLEX project in Canada (Robertson et al., 2000); the Changhwa Coastal Industrial Park in Taiwan (Shen et al., 2018); the Nakdong River Delta in Korea (Singh and Chung, 2013); and the calibration chamber testing results of South Sea sands in Korea (Lee et al., 2011). Table 7 summarizes the comparative study on the collected database of fine-to-coarse sands having Fc ≤ 15% and Cus ranging from 1.57 to 7.39. The observed sands had particle shapes ranging from subround to angular. Fig. 10 illustrates the ability of the proposed Eqs. (16) and (17) to predict the Standardized CPT resistances efficiently. All the results of sands with Fc ≤ 5% fell in the proposed range of Eqs. (16) and (17). Eventually, the average two-dimensional angularity of particles was reevaluated from the in-situ qt1 and fs1 records and found to be in general accordance with the original visual description.

Acknowledgments The writers are grateful to Hydro-Quebec and the Natural Sciences and Engineering Research Council of Canada for their financial support (Grant ID: CRSNG RDC HQ - 451301-13). The authors also extend sincere thanks to the soil mechanics laboratory team, in particular Alexandre Sevigny and Valérie Dumoulin who were instrumental in the laboratory work.

6. Functionality and limitations

References

The efficiency and accuracy of the methods utilized and the newly proposed correlations were investigated by statistical regression of data presented in comparative studies for three main cases. A random 162 field and laboratory CPT results were examined from various highly accurate tests, in which the proposed correlations were compared to the most widely utilized relevant empirical relationships in the geotechnical domain. The verification studies showed a remarkable advantage of the new correlations over all other compared relations. It was found that 93.16% of the predicted results fell within the assumed range of ± 20% deviation, while the best case for other relations was only 73%. The present study was carried out on glass beads and disturbed samples of premixed clean sands, which means that the developed correlations may only be applicable for normally consolidated, uncemented, unaged, coarse-grained soils with a fine particle content < 5%. In addition, the two-dimensional angularity was found to be sufficient to represent particle form size as well as particle corner conditions but did not take into consideration the surface texture roughness of coarse-grained particles (Ghali et al., 2018a). Certain test assumptions were employed. For example, the effect of the variation of specific gravity ranging from 2.71 to 2.74 in reconstituted sand samples and 2.59 in glass beads was not considered in the current study, and samples of A2D ± 10 were considered to be similar in angularity.

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7. Conclusions The proposed Eqs. (16) and (17) included the effect of physical parameters on the CPT measurements separately. This is a novelty in the field of engineering geology because the main physical variations in sands of different geological provinces are the shape, size, and uniformity of particles. In addition, the DR, which is the essential geotechnical parameter representing the in-situ consistency and compaction conditions, can be easily estimated from the CPT measurements and easily extracts disturbed sand samples to evaluate their physical properties without the necessity of extracting undisturbed samples. We also presented a range of high compressibility conditions of clean sands by increasing the angularity of particles to low compressibility conditions at a low void-ratio range by increasing the D50 and Cu. Other conclusions are as follows. a) D50, Cu, and DR were found to be positively related to qt1 and fs1, while A2D negatively affected the CPT measurements. 24

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