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Evaluation of CPT-based characterization methods for loose to medium-dense sands
Soils and Foundations 2016;56(3):460–472
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The Japanese Geotechnical Society
Soils and Foundations www.sciencedirect.com journal homepage: www.elsevier.com/locate/sandf
Technical Paper
Evaluation of CPT-based characterization methods for loose to medium-dense sands Abouzar Sadrekarimi Assistant Professor, Department of Civil and Environmental Engineering, Western University, London, Ontario, Canada Received 27 April 2015; received in revised form 28 January 2016; accepted 27 February 2016 Available online 20 May 2016
Abstract As a result of the difficulties related to obtaining undisturbed samples of cohesionless soils, CPT-based empirical correlations, often developed from calibration chamber experiments, are widely used for determining many soil parameters for geotechnical investigation. This paper describes the application of 19 reduced-scale calibration chamber cone penetration tests to evaluate empirical correlations for predicting the relative density, the unit weight, the constrained modulus, and the soil identification of loose to medium-dense sands. A subtraction cone, 6 mm in diameter with an apex angle of 601 and a net area ratio of 0.75, is used in the laboratory tests. Due to the fine gradation of the quartz sand used in the experiments, some of the CPT results are located within the silty sand range of the soil identification charts. An extensive evaluation is also presented for the stress normalization process of the CPT data. It is determined that a relative density-based overburden stress normalization method provided the best estimates for correcting the cone tip resistance for effective overburden stress. & 2016 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.
Keywords: Cone penetration test; Calibration chamber test; Sand; Relative density; Modulus; Critical state; Stress normalization; Soil identification
1. Introduction Geotechnical engineering analyses and designs require accurate identification and characterization of soil layers, as well as an assessment of soil stratigraphy at the site. However, due to the difficulties in obtaining undisturbed samples of cohesionless soils, geotechnical engineers often rely on field tests to obtain the insitu soil characteristics. Owing to relatively lower costs, simplicity, continuous measurement with depth, and excellent repeatability and accuracy, the electronic cone penetration test (CPT) has emerged as one of the most popular tools for ground investigation in geotechnical engineering. CPTs are particularly instrumental for characterizing saturated loose to medium-dense cohesionless soils due to the susceptibility of these soils to static E-mail address: [email protected] Peer review under responsibility of The Japanese Geotechnical Society.
or cyclic liquefaction and their potential for liquefaction flow failure. As CPT does not directly measure any particular soil properties, extensive research has been conducted to develop empirical correlations of CPT measurements with soil type and engineering properties (including unit weight, relative density, and modulus) using laboratory calibration chamber experiments (Schmertmann, 1978; Villet and Mitchell, 1981; Baldi et al., 1986; Jamiolkowski et al., 1988, 2001; Huang and Hsu, 2005). These experiments can provide the most reliable and precise experimental data for developing CPT-based correlations and calibration as the entire procedure (including sample preparation, consolidation, and cone penetration) is conducted in the laboratory and can be readily monitored and controlled. Carrying out controlled CPT calibration chamber tests with a standard cone (with a diameter of 35.7 mm) requires a largediameter (typically more than 1.2 m) chamber. Such an experiment can be expensive and time-consuming, as sample preparation
http://dx.doi.org/10.1016/j.sandf.2016.04.012 0038-0806/& 2016 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.
A. Sadrekarimi / Soils and Foundations 56 (2016) 460–472
involves placing a large volume of sand in the testing chamber at a controlled density. The control of sample uniformity and external stress can also become difficult (Parkin and Lunne, 1982). Due to these challenges, several studies have employed miniature cones and reduced-scale calibration chamber devices (Abedin, 1995; Huang and Hsu, 2005; Kumar and Raju, 2009; Kokusho et al., 2012; Franzen, 2006; Pournaghiazar et al., 2011) frequently on dense sands, with little experimental data on medium-dense to loose sands. This is often because of the collapsible fabric of loose sands which results in initially loose calibration chamber samples collapsing into a denser state during sample saturation and flushing (Been et al., 1987b). This study presents the results of miniature CPT calibration chamber experiments (Damavandi and Sadrekarimi, 2015) carried out at Western University. The results
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are employed to evaluate a number of existing empirical correlations for determining some of the geotechnical properties of loose to medium-dense sands. 2. Experimental procedure 2.1. Miniature CPT system The largest cell that could be accommodated in an existing uniaxial loading frame is manufactured as a CPT calibration chamber in this study. The large custom-made cell contains cylindrical specimens of 150 mm in diameter and 195 mm high. The major components of the CPT calibration chamber are schematically illustrated in Fig. 1. A stainless steel cone,
Fig. 1. Illustration of calibration chamber testing components.
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with a diameter of 6 mm, an apex angle of 601, and a net area ratio of 0.75 (i.e., ratio of the cone base area unaffected by pore water pressure to total projected cone area), is employed in the calibration chamber tests. The miniature cone, developed at Western University, is a subtraction-type penetrometer in which both the cone tip resistance (qc) and the sleeve friction (fs) are measured. Similar to a type 2 cone (Lunne et al., 1997), sample pore water pressure, including any excess pore pressure developing during cone penetration (u2), is measured behind the cone's shoulder above its tip by a pressure transducer with a capacity of 1380 kPa. A thin plastic collar with small notches is used above the cone tip to allow the passage of water while blocking the intrusion of sand particles. A servo-controlled triaxial loading frame, with a uniaxial loading capacity of 10 kN, is used to drive the cone. The loading frame is equipped with a digital encoder which records its travel distance, and therefore, the amount of cone penetration. The encoder was calibrated with a high resolution LVDT. Two electromechanical pressure pumps with capacities of 75 and 170 mL are used to measure and control the fluid volume changes of the soil sample and the cell. Each pressure pump is equipped with electrical pressure transducers, with a capacity of 2070 kPa, to measure and control the specimen and the cell fluid pressures. A data logger with a maximum sampling frequency of 1 Hz, included with the triaxial loading frame, is used for data acquisition and for the real-time monitoring of the experiments. Damavandi and Sadrekarimi (2015) provide further details of the miniature CPT equipment, data analysis, verification, and the repeatability of the miniature CPT results. 2.2. Tested Material Reconstituted specimens of fine Ottawa sand were prepared and tested in this experimental program. The Ottawa sand used in this study was a uniformly graded clean sand (with no fines) – classified as SP according to the Unified Soil Classification System (Astm, 2011) – composed of white-colored quartz particles with round to sub-rounded particle shapes. Sand particles had a specific gravity (Gs) of 2.65, a mean diameter (D50) of 0.193 mm, and coefficients of uniformity (CU) and curvature (CC) of 1.71 and 1.07, respectively. Fig. 2 presents the particle size distribution of this sand. Maximum (emax) and minimum (emin) void ratios, 0.821 and 0.490, respectively, were determined following the ASTM standard procedures (Astm, 2006a; Astm, 2006b). Loose specimens of this sand exhibited non-linear isotropic compressive behavior in triaxial compression tests with compression indices (Cc) of 0.032– 0.050 at effective confining pressures of 7–700 kPa, while a more-or-less constant recompression index (Cr) of 0.005 was determined. A critical state friction angle ϕ0 cs of 30.71 was also measured for this sand in triaxial compression tests (Omar and Sadrekarimi, 2015). 2.3. Specimen preparation For the calibration chamber CPT experiments, cylindrical soil samples were prepared using the moist tamping method, which
Fig. 2. Average particle size distribution of Ottawa sand used in this study.
produces minimum particle segregation (Yang, 2005; Chen, 2000). Moist tamping often replicates the soil fabric developed by hydraulically transported sand fills (Sladen et al., 1985) or in nature as loose sand layers (Schlosser, 1985). In order to improve specimen uniformity, the under-compaction moist tamping method, suggested by Ladd (1978), was employed. This method involves the compaction of moist sand in layers slightly different than the target global density, with the bottom layer compacted the least and the top layer compacted the most, so that the final density of each layer would be equal to the target global density even with the effects of compacting the successive overlaying layers. Sand with a moisture content of 5%, required for each layer, was weighed, poured into the mold, and tamped into 13 layers of 15 mm thick in a circular pattern using a scaled tamper. This moisture developed a capillary force among the sand particles that produced a stable sand fabric and kept the specimen shape once the split mold was removed. This was necessary during specimen preparation before filling the cell and applying a seating confining pressure of 10 kPa. A latex membrane enclosed and sealed the specimen, thereby creating a flexible boundary via which a uniform axisymmetric confining pressure could be applied. The diameter and the height of the specimen were carefully measured after preparation to ensure the accuracy of the initial relative density (Dri) determination of the sample. The miniature cone was then mounted on the external rod and the cell was subsequently assembled on the specimen. Specimen uniformity was evaluated for a number of specimens by taking plug samples from the top, middle, and bottom of each specimen prepared by following the same procedure. Void ratio variations of about 70.006 (corresponding to a change in relative density of 71.5%) and 70.004 (corresponding to a change in relative density of 71.0%) were obtained from the top to the bottom of the specimen for sample relative densities of 10% and 26.8%, respectively. Despite improved specimen uniformity, small fluctuations were still observed in some of the experiments (e.g., test No. 16 in Fig. 3) reflecting the remaining specimen non-uniformity. A particular limitation of reduced-scale cones can result from the scale of the cone diameter (dc) compared to the diameter of the soil particles (e.g., D50). Several studies have
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consolidation pressure (p0 c) using two electromechanical pressure pumps. The change in sample volume during consolidation was measured by pressure pumps to determine the precise void ratio of the sample after consolidation (ec) as well as the consolidation relative density (Drc). 2.5. Cone penetration
Fig. 3. Cone penetration resistance mobilized in Tests No. 9, 11, 13, and 16: (a) qc, (b) fs..
investigated the scale effect on cone penetration tests (Schmertmann, 1978; Canou et al., 1988; Jacobs and Coutts, 1992; Salgado, 2013; Gui et al., 1998; Baldi and O'neill, 1995; Huntsman, 1985; Huang and Hsu, 2005; Lee, 1990; Balachowski, 2007; Sharp et al., 2010). For example, Canou et al. (1988) carried out reduced-scale cone penetration tests in several sands with D50 ¼ 0.3–0.7 mm (corresponding to dc/ D50 ¼ 32–18) and observed no difference between their results and those from a standard-size CPT, suggesting no scale effect. Lee (1990) carried out a series of centrifuge CPT model experiments on several gradations of Leighton Buzzard sand using three different miniature cones (with dc ¼ 19.05 mm, 10 mm, and 6.35 mm). They observed that the scale effect became appreciable only for dc/D50 o 16. Based on centrifuge model experiments, Balachowski (2007) also observed no scale effect for dc/D50 4 20. More recently, Sharp et al. (2010) performed miniature cone penetration tests on fine Nevada sand (with D50 ¼ 0.13 mm) using centrifuge testing and found no grain size effect for the dc/D50 ¼ 30.7. These results suggest that particle size and scale effect are negligible for the combination of cone diameter (dc ¼ 6 mm) and D50 (¼ 0.193 mm) – corresponding to dc/D50 ¼ 31 – used in this study. 2.4. Specimen saturation and consolidation Although previous studies have shown similar cone penetration resistance in dry and saturated clean sands (Bellotti et al., 1988; Schmertmann, 1976; Bonita, 2000; Jamiolkowski et al., 2001; Villet and Mitchell, 1981), moist tamped samples of this study were saturated in order to remove the effects of soil suction on cone resistance and to allow for the precise measurement of the change in sample volume during consolidation. This was accomplished by flushing the soil specimen with CO2 and then de-aired water to remove air and to dissolve the CO2. A back-pressure saturation procedure was subsequently followed until a pore pressure coefficient of at least 0.96 was achieved (Skempton, 1954). After specimen saturation, the samples were subjected to an isotropic
Following consolidation, a uniaxial loading frame (originally designed for triaxial testing) was used to push the miniature cone into the sample up to a penetration depth of 60 mm, while qc and fs were simultaneously measured. During cone penetration, the sample was kept globally drained through the top and bottom drainage ports. Table 1 summarizes the characteristics of the miniature cone penetration tests conducted in this study. The chamber boundary effect can be a major limitation in the comparison of CPT calibration chamber results with in-situ field tests. However, several studies (Parkin and Lunne, 1982, Baldi et al., 1982, Jamiolkowski et al., 1985, Been et al., 1987a, Mayne and Kulhawy, 1991, Salgado, 1993) have found this effect to be insignificant for loose to medium-dense sands. For example, Parkin and Lunne (1982) investigated the effect of flexible boundary conditions (similar to the samples of this study) on CPT resistance using different cone (dc) and chamber (Dc) diameters. They found that the effect of chamber boundary was negligible in loose sands (Drc r 30%) for Dc/ dc Z 20. While for very dense sands (with Drc E90%), Dc/ dc Z 50 was required to minimize chamber size effect. Similarly, Jamiolkowski et al. (2003) studied calibration chamber CPT data on Ticino and Hokksund sands, and suggested correcting the CPT resistance for chamber boundary effects only for Drc Z 40%. More recently, using 3D discrete element analyses, Butlanska et al. (2010) found no specimen size or boundary effects in sands at Drc o 45%. Based on the Table 1 Summary of miniature CPT tests performed in this study. Test no.
Drc (%)
p0 c (kPa)
qc (MPa)
fs (kPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
22.0 24.5 25.9 29.8 36.6 38.6 42.5 33.7 33.7 33.7 33.3 33.7 33.1 33.7 30.8 33.1 30.3 25.0 27.4
100 100 100 100 100 100 100 100 45 75 150 200 300 450 500 600 700 200 300
3.96 3.99 4.08 4.73 5.10 5.26 5.78 4.80 2.52 4.18 6.02 7.09 10.40 13.75 10.29 13.73 13.93 5.20 6.55
38.54 32.32 38.54 64.04 50.43 52.70 63.19 49.82 14.40 30.36 47.85 49.50 51.80 63.10 42.00 69.94 76.55 56.41 51.30
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findings of these studies, the effects of specimen size and boundary conditions on cone resistance are expected to be negligible for the experiments of this study which were carried out on sand samples with Dc/dc ¼ 25 at Drc o 43%. Therefore, corrections for boundary conditions are not applied in the comparisons and analyses presented here. 3. Experimental results Fig. 3 presents cone penetration resistances (qc, fs) for the series of miniature CPT tests of this study. According to these plots, for the relatively uniform specimens of this study, the cone tip resistance increased with penetration depth as soil resistance to the insertion of the cone was fully mobilized. After about 20 mm, qc approached a more-or-less uniform plateau. Note that fs is plotted for penetration depths of greater than 10 mm where the friction sleeve was effectively inserted into the soil away from the specimen's top cap. Average magnitudes of qc and fs, determined after a cone penetration of 20 mm, are also summarized in Table 1. Due to the high hydraulic conductivity and free-draining nature of the tested Ottawa sand, cone penetration occurred under a primarily drained condition with no excess pore water pressure being generated adjacent to the cone tip (u2). Accordingly, correction for the effect of unequal end areas was not needed (Robertson and Cabal, 2015).
Fig. 4. Comparison of CPT data of this study with soil identification zones of Mayne (2006).
4. Comparison with existing empirical correlations In the following paragraphs, the experimental results of this study (summarized in Table 1) are compared with some of the existing methods for CPT-based soil classification, stress normalization, predicting sand relative density, unit weight, and constrained modulus. 4.1. Evaluation of soil classification methods
Fig. 5. Comparison of CPT data of this study with soil type zones of Eslami and Fellenius (1997).
One of the useful applications of CPT is to identify the soil type. Several studies have proposed empirical soil behavioral charts or correlations for soil classification based on CPT measurements. Figs. 4–6 compare the CPT data of this study with the soil type boundaries or zones proposed by some of these methods (Mayne, 2006; Eslami and Fellenius, 1997; Robertson, 2009). In these plots, s0 vc and svc are the initial effective and total vertical stresses, respectively, which correspond to p0 c for the CPT experiments of this study, Pa ¼ 100 kPa is a reference pressure, and qc,net ¼ qc svc. Regarding Fig. 6, Qtn ¼ qc,net/Pa (Pa/s0 vc)n and FR¼ fs/qc,net 100 are the normalized cone parameter and the friction ratio, respectively, and n is a stress normalization exponent which depends on the soil behavior (Robertson, 2009). According to Figs. 4 and 5, the soil type identification charts of Mayne (2006) and Eslami and Fellenius (1997) provide reasonable predictions of the clean Ottawa sand used in this study. A few data points plot between the sands and silts or within the silt zones of these charts. This is likely to be because of the fine gradation (D50 ¼ 0.19 mm) of the Ottawa sand used here compared to that used for developing the
Fig. 6. Comparison of CPT data of this study with soil identification zones of Robertson (2009). Numbered zones correspond to 1: sensitive fine-grained soil, 2: organic soil, 3: silty clay to clay, 4: clayey silt to silty clay, 5: silty sand to sandy silt, 6: sand, 7: gravelly sand to dense sand, 8: very stiff sand to clayey sand, and 9: very stiff fine-grained soil.
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soil identification charts of Mayne (2006) and Eslami and Fellenius (1997). However, the experimental data plot entirely as silty sands to sandy silts (zone 5) in Fig. 6, suggesting that the empirical chart of Robertson (2009) might be less accurate for identifying quartz fine sands. A few field samples from each soil stratum are recommended to confirm the predictions of soil classification techniques.
4.2. Evaluation of overburden stress normalization methods In order to compare soil behavior from different depths, the cone resistance is often normalized (or corrected) to a common effective overburden stress of 100 kPa (Wroth, 1984). As summarized in Table 2, a number of techniques (Wroth, 1984; Robertson, 2009; Olsen and Mitchell, 1995; Kayen et al., 1992; Moss et al., 2006; Liao and Whitman, 1986; Cetin and Isik, 2007; Idriss and Boulanger, 2006) are suggested for converting the total (qc) or the net (qc, net ¼ qc sv) cone tip resistances and sleeve friction to those that would have been measured if CPT had been carried out at Table 2 CPT overburden stress normalization methods. Normalized parametera Cone tip resistance 0:5 qc1;net ¼ qc;net sP0a vc 0:5 Pa qc1 ¼ qc s0
Reference Sleeve friction –
Wroth (1984)
–
Liao and Whitman (1986)
vc
qc1 ¼
1:8 0:8 þ s0vc =Pa
qc c
–
c
Kayen et al. (1992)
qc1;net ¼ qc;net sP0a vc
f s1 ¼ f s sP0a vc
Olsen and Mitchell (1995)
qc1;net ¼ qc;net
–
Cetin and Isik (2007); Robertson (2009) Idriss and Boulanger (2006)
qc1 ¼ qc qc1 ¼ qc
c Pa s0vc
0:784 0:521Drc Pa s0
vc c Pa s0vc
– f s1 ¼ f s
c Pa s0vc
Moss et al. (2006)
a svc and s0 vc are total and effective initial vertical stresses, respectively; Pa: atmospheric pressure ( E100 kPa); c: stress normalization exponent.
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s0 vc ¼ 100 kPa. These methods are briefly described and compared with the CPT experiments of this study. An ideal stress normalization method should produce an equal normalized cone resistance from different depths or s0 vc in the same soil at the same Drc. As tests Nos. 8–17 were conducted at close Drc (¼ 30.3–33.7%), they provide an exceptional opportunity to evaluate the stress normalization techniques of Table 2. Fig. 7a compares the stress normalization methods for qc. In this figure, the qc measured in test No. 8 (carried out at p0 c ¼ 100 kPa) is normalized by qc at other p0 c in order to obtain stress normalization factors (qc1/qc). Note that for the isotropically consolidated experiments of this study, s0 vc ¼ p0 c. According to Fig. 7, the widely used stress normalization factor of Liao and Whitman (1986) somewhat overestimates the experimental data at s0 vc 4 100 kPa, which could lead to unconservative values for normalized qc (qc1) at s0 vc 4 100 kPa. Based on a combination of theory and empirical observations, Moss et al. (2006) suggested a stress normalization exponent for normalizing both qc and fs, as follows: c ¼ 0:78qc ðMPaÞ
0:33
f s ðMPaÞ qc ðMPaÞ
100
! ð 0:32qc ðMPaÞ 0:35 þ 0:49Þ
1:21 abs log 10 þ qc ðMPaÞ
ð1Þ The above equation results in c E 0.5, which is the same as that suggested by Liao and Whitman (1986); and therefore, the resulting qc1 becomes relatively larger than those of this study at s0 vc 4 100 kPa. As shown in Fig. 7a, while the stress normalization method suggested by Kayen et al. (1992) predicts slightly smaller qc1 than those of this study, the Drcbased normalization profile proposed by Idriss and Boulanger (2006) provides the best estimates for qc1/qc from the CPT experiments. Nevertheless, the choice of the overburden stress correction method seems to have a negligible impact on qc1 for s0 vc/Pa ¼ 0.5 2.0 in Fig. 7a. Similar to Fig. 7a, Fig. 7b compares the stress normalization methods based on qc,net with the laboratory CPT data of this study. According to this figure, these methods provide different normalized net cone resistance (qc1,net), indicating a
Fig. 7. Comparison of existing stress normalization techniques with (a) qc1/qc and (b) qc1,net/qc,net from CPT experiments of this study.
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lack of consensus in stress normalization methods which could lead to very different CPT interpretations. The overburden stress correction of Wroth (1984) largely underestimates the qc1,net measured in the CPT experiments at s0 vc 4 100 kPa. Olsen and Mitchell (1995) collected over 2 decades of field data and an extensive database of CPT calibration chamber tests conducted by other researchers in order to deduce a CPT tip normalization factor. They suggested the following relationship for the stress normalization exponent: c ¼ 1 ðDrc 10%Þ 0:007
ð2Þ
The above equation yields c ¼ 0.86 0.83 for Drc ¼ 30.3– 33.7% in this study and the resulting stress normalization factors tend to underestimate the qc1,net measured in the CPT experiments at s0 vc 4 100 kPa. Cetin and Isik (2007) used a Bayesian probabilistic analysis for the compilation of a database of field tests, CPT calibration chamber tests, and finite element numerical analysis data. They developed an iterative procedure based on the following equations for estimating a range of stress normalization exponents, as follows: R 272:38 7 0:085; 272:38o R o 275:19 ð3Þ 275:19 272:38 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2ffi qc1;net fs R¼ log 100 þ 243:91 þ log 126:24 qc Pa c¼
ð4Þ According to Fig. 7b, the qc1,net from the CPT experiments in this study tend to be smaller than the ranges of those produced by Eq. (3) at s'vc 4 100 kPa. More recently, Robertson (2009) suggested another iterative procedure for determining a variable stress normalization exponent based on a soil behavior type (SBT) index, Ic, as seen below: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð5Þ I c ¼ ð3:47 logQÞ2 þ ðlogF R þ 1:22Þ2 The iteration starts with c¼ 1.0 in order to calculate the first trial of Ic. If Ic r 1.64, then c¼ 0.5; otherwise, it is calculated from the equation given below: 0
s c ¼ 0:381I c þ 0:05 v 0:15 r 1:0 Pa
ð6Þ
As demonstrated in Fig. 7b, this method is found to be conservatively biased by underestimating qc1,net as a result of the relatively large normalization exponents (0.67–1.0) produced by Eq. (6). As shown in the plots of Fig. 7, the CPT experiments suggest c¼ 0.612 for the quartz Ottawa sand used in this study. This produces the same normalization factors as those provided by Idriss and Boulanger (2006). Although many studies have developed stress normalization methods for cone tip resistance, according to Table 2, very few (Olsen and Mitchell, 1995; Moss et al., 2006) consider correcting fs by merely extending the same factors (used for qc) to fs1. Fig. 8 compares the normalization factors of these studies with the fs1/fs from the CPT experiments in this study. Similar to qc1, fs1 is measured in test No. 8 at p0 c ¼ 100 kPa.
Fig. 8. Comparison of existing stress normalization techniques with fs1/fs from the CPT experiments of this study.
According to Fig. 8, the existing methods largely overestimate the effect of the overburden stress on fs. The experiments of this study suggest a bilinear trend (see Fig. 8) with much larger stress normalization factors for fs. As displayed in Fig. 8, fs1/fs decreases sharply with an increase in s0 vc up to about 100 kPa. However, with further increases in s0 vc, the effect of s0 vc on fs1 is significantly reduced. The physical mechanism underlying this trend is investigated below. The sleeve friction (fs) measured during a cone penetration test is essentially a function of the radial stress (s0 rf) and the interface friction angle (δf) between the soil and the cone sleeve (Huntsman, 1985). Based on observations made in the driving of small-scale instrumented steel piles (Lehane et al., 1993), the magnitude of s0 rf depends on the dilatancy of the sand adjacent to the cone sleeve (Lehane and White, 2005). Since neither δf nor s0 rf were directly measured in the CPT experiments of this study, s0 rf is approximately computed in Fig. 9 as s0 rf ¼ fs/tan(δf) for Drc ¼ 30.3–33.7%. A cone penetration of about 2–3 mm is often sufficient to mobilize a constant-volume interface sleeve friction corresponding to the critical state of the sand adjacent to the cone sleeve (Lehane and White, 2005). Accordingly, δf ¼ 1/2ϕ0 cs ¼ 15.41 (ϕ0 cs ¼ 30.71 for the Ottawa sand of this study) is assumed in this analysis (Tejchman and Wu, 1995). According to Fig. 9, the computed s0 rf is greater than the imposed horizontal boundary stress, s0 hc (which is the same as s0 vc and p0 c in this study) at s0 vc r 150 kPa, where sand dilatancy is strong. However, s0 rf drops sharply with an increase in s'vc beyond 150 kPa as the dilantancy of the sand is suppressed and its contractive tendency improves with increasing s0 vc. The observed pattern is analogous to those measured in skin friction on reduced-scale instrumented piles (Boulon and
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Fig. 9. Effect of s0 vc on radial stress amplification (s0 rf/s0 hc) on cone sleeve based on computations of this study and measurements made in other calibration chamber tests (Boulon and Foray 1986; Balachowski 2006).
467
Fig. 10. Comparison of dry unit weights (γd) predicted by Mayne (2007) with those from experiments of this study for tests Nos. 1–8.
Foray, 1986) as well as in rigid-wall calibration chamber experiments on clean quartz sands (Balachowski, 2006). The wide difference between the radial stress amplification factors (s0 rf/s0 hc) of loose and dense sands in Fig. 9 emerges from the greater dilatancy of the denser samples. Similar observations have also been reported in several other experimental investigations (Baldi et al., 1981) as well as in in-situ tests on piles with different lengths (Coyle and Castello, 1981). The trend of fs1/fs with s0 vc/Pa observed in Fig. 9 reflects the changes in (s0 rf/s0 hc), and thus, reduced sand dilatancy and increased contractiveness with an increasing s'vc.
4.3. Evaluation of soil unit weight Soil unit weight is a critical information for calculating the initial geostatic and overburden stresses for CPT data processing and for interpreting many other geotechnical parameters. The soil unit weight can be measured directly from undisturbed samples collected by thin-wall tube samples or ground freezing techniques. However, such techniques can often be expensive, difficult, and onerous in saturated clean sands or gravels and they require costly equipment. Therefore, indirect empirical correlations with CPT measurements are developed and regularly used for quicker processing of cone penetration data and preliminary geotechnical analyses. From the regression analysis of a large database of calibration chamber cone penetration tests in clays, silts, and sands, Mayne et al. (2010) and Mayne (2007) suggested the following correlations for predicting dry (γd) and total (γt) unit weights from the cone tip resistance: ! q =P a c γ d kN=m3 ¼ 1:89log 0 ð7Þ 0:5 þ 11:8 svc =Pa
Fig. 11. Comparison of total unit weights (γt) predicted by Mayne et al. (2010) with those from experiments of this study for tests Nos. 1–8.
γ t ¼ 1:81γ w
0 0:05
svc q svc 0:017 f s 0:073 : c : : Pa Pa Pa
Bq þ 1
0:16 ð8Þ
in which Bq ¼ Δu2/qc,net is the normalized pore water pressure parameter. Figs. 10 and 11 compare these correlations with γd and γt of test Nos. 1–8, conducted at p0 c ¼ 100 kPa. According to these figures, Eq. (7) provides close estimates of γd as Eq. (7) is derived based on calibration chamber tests on silica sands (Mayne, 2007). However, the predictions of Eq. (8) are on average about 1 kN/m3 lower than those from the CPT experiments of this study. This probably stems from the original development of Eq. (8) as an average correlation based on regression analysis of CPT in different soil types, including clays, silts, sands, tills, and largely dominated by clayey soils. Based on the CPT tests in this study (Figs. 10 and 11), the following relationships are suggested for estimating γd and γt for clean silica sands (similar to the Ottawa
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sand used here):
!
q =Pa γ d kN=m3 ¼ 3:00log 0 c 0:5 þ 9:44 svc =Pa
ð9Þ
!
q =Pa γ t kN=m3 ¼ 2:00log 0 c 0:5 þ 15:69 svc =Pa
ð10Þ
A particular difference between Eqs. (8) and (10) is the consideration of fs in Eq. (8). The nearly perfect relationship between γt and qc, provided by Eq. (10), implies a weaker connection between fs and γt (compared to qc), and that fs could be excluded for estimating γt.
Table 3 Summary of correlation parameters suggested by earlier studies for fitting Eq. (11) based on s0 vc. No. Sand
C0
C1
C2
Reference
a b c d e
0.050 0.157 0.086 0.140 0.175
0.700 0.550 0.530 0.550 0.500
2.91 2.41 3.29 2.90 3.10
Schmertmann (1978) Baldi et al. (1986)
Several NC sands Ticino Hokksund Ticino Ticino, Toyoura, Hokksund
Jamiolkowski et al. (2001)
Table 4 Summary of correlation parameters suggested by earlier studies for fitting Eq. (11) based on p0 c.
4.4. Evaluation of sand relative density In addition to the soil unit weight, the relative density is extensively used in geotechnical engineering as an index parameter for characterizing the shearing response of granular soils and it is often used in ground improvement projects for compaction quality control. Considering the difficulties in obtaining undisturbed samples, CPT is a viable tool for estimating the Drc of in-situ sands. The experimental data from this study are used here to evaluate some of the existing predictive correlations for Drc. For normally consolidated and unaged fine to medium clean sands, Schmertmann (1976) suggested the following correlation between qc and Drc: ! 100 qc ðMPaÞ Drc ð%Þ ¼ ln ð11Þ C C2 C 0 s0 1
No. Sand
C0
f g h
Ticino Hokksund Ticino
i j
Ticino Ticino, Toyoura, Hokksund Da Nang (Vietnam)
0.181 0.550 2.61 Baldi et al. (1986) 0.153 0.550 2.88 0.205 0.510 2.93 Jamiolkowski et al. (1988) 0.174 0.560 2.97 Jamiolkowski et al. 0.297 0.460 2.96 (2001)
k
C1
C2
Reference
0.369 0.500 2.34 Huang and Hsu (2005)
vc
in which C0, C1, and C2 are empirical fitting parameters and s0 vc is the initial effective vertical stress. Since the pioneering work of Schmertmann (1976), several investigators (Baldi et al., 1986; Villet and Mitchell, 1981; Jamiolkowski et al., 2001; Schmertmann, 1978) have fitted Eq. (11) to CPT calibration chamber tests on many sands. However, some studies indicate that the qc measured in calibration chamber tests is largely influenced by the horizontal effective stress, s0 hc (Baldi et al., 1986; Houlsby and Hitchman, 1988; Jamiolkowski et al., 2001; Holden, 1971). Accordingly, Eq. (11) has also been expressed (Baldi et al., 1986; Jamiolkowski et al., 2001; Huang and Hsu, 2005; Jamiolkowski et al., 1988) as a function of the mean consolidation pressure, p0 c, in order to include the effects of both s0 vc and s0 hc. For field applications, p0 c can be determined by assuming Ko ¼ 1 sin (ϕ0 ) for normally consolidated young sand deposits in which ϕ' is the sand's effective stress friction angle. Tables 3 and 4 summarize the fitting parameters of Eq. (11) suggested by these studies. Figs. 12 and 13 compare the predictions made in these studies with the CPT experiments based on s0 vc and p0 c, respectively. For the isotropically-consolidated samples in this study, s0 vc ¼ p0 c. Except for the s0 vc-based correlations proposed by Baldi et al. (1986) (for Hokksund sand) and by Schmertmann (1978), the remaining methods underestimate the Drc values in this study. The overall amount of underestimation seems to be greater for the p0 c-based methods,
Fig. 12. Comparison of Drc from CPT experiments of this study with those predicted by other studies based on s0 vc. Line labels are a: Schmertmann (1978), b: Baldi et al. (1986) based on Ticino sand, c: Baldi et al. (1986) based on Hokksund sand, d: Jamiolkowski et al. (2001) based on Ticino sand, e: Jamiolkowski et al. (2001) based on Ticino, Toyoura and Hokksund sands, and l: Kulhawy and Mayne (1990).
suggesting a greater effect of s0 vc than that incorporated through p0 c. The s0 vc-based correlation of Baldi et al. (1986), from calibration chamber CPT tests on Hokksund sand, provides the closest estimates to the Drc in this study, while those of Schmertmann (1978) largely overestimate Drc. In summary, the correlations proposed by different studies predict a very wide range of Drc because of the different types of sands used in their databases. Therefore, a unique form of Eq. (11) cannot be determined for all sands, and particularly
A. Sadrekarimi / Soils and Foundations 56 (2016) 460–472
469
Fig. 13. Comparison of Drc from CPT experiments of this study with those predicted by other studies based on p0 c. Line labels are f: Baldi et al. (1986) based on Ticino sand, g: Baldi et al. (1986) based on Hokksund sand, h: Jamiolkowski et al. (1988), i: Jamiolkowski et al. (2001) based on Ticino sand, j: Jamiolkowski et al. (2001) based on Ticino, Toyoura and Hokksund sands, and k: Huang and Hsu (2005).
Fig. 14. Comparison of Drc from CPT experiments of this study with ranges of those predicted by Eq. (13).
for variable soil deposits. In other words, different sands will not necessarily behave the same at the same Drc and p0 c. For the CPT experiments in this study, fitting parameters of C0 ¼ 0.119, C1 ¼ 0.612, and C2 ¼ 2.55 are found following an optimization process by minimizing the standard deviation between the calculated and the measured qc. However, the values for Drc predicted with these parameters in Eq. (11), are still within 7 6.5% of the actual values. This indicates the limited accuracy of Eq. (11) which merely uses p0 c and qc (Sladen, 1989; Huang and Hsu, 2005; Hamidi et al., 2013). Accordingly, Kulhawy and Mayne (1990) and Jamiolkowski et al. (2001) have proposed empirical relationships for estimating Drc with additional consideration regarding the effect of sand compressibility. Kulhawy and Mayne (1990) compiled the results of 24 sets of calibration chamber tests on fine to medium sands and suggested the following relationship:
4.5. Evaluation of soil stiffness
D2rc ¼
1 q =Pa : c 0:5 305Qc s0 =Pa
ð12Þ
vc
in which Qc is a compressibility factor equal to 0.91, 1.00, and 1.09 for high, medium, and low compressibility sands, respectively. According to Fig. 12, Eq. (12) (labeled “l”) provides close estimates of Drc for qc/(s0 vc)0.5 ¼ 200–327, while underestimating at greater qc/(s0 vc)0.5 values. From a review of the calibration chamber tests data, Jamiolkowski et al. (2001) suggested a modified form of Eq. (11) as below: ! qc =Pa ð13Þ Drc ð%Þ ¼ 26:8ln C bx s0vc =Pa 1 in which C1 is a stress normalization exponent (¼ 0.50) similar to Eq. (11), and bx ¼ 52.5, 67.5, 82.5 are for high, medium, and low compressibility sands, respectively. As illustrated in Fig. 14, the experiments of this study plot within the medium to low compressibility range (bx ¼ 70.2) using C1 ¼ 0.612, which
is consistent with the stress normalization exponent determined in Fig. 7.
Soil stiffness describes the soil deformation behavior under an increment in confining stress or shear stress. Several investigators have attempted to relate soil stiffness to cone penetration resistance (Schmertmann, 1978; Tanaka and Tanaka, 1998; Mayne, 2006; Tonni et al., 2010). Here, the bulk moduli (K) of the samples were determined from the isotropic consolidation stages of the CPT experiments as the incremental change in effective confining pressure (∂p0 ) divided by the volumetric strain (εv). These were then converted to constrained moduli (M) using the following relationship for each experiment: M¼
3K ð1 νÞ ð1 þ νÞ
ð14Þ
A Poisson's ratio ν (¼ εr/εa) of 0.36 was also determined based on the measurements of axial strain (εa) and volumetric strain (εv ¼ εa þ 2εr) of the same sand in consolidated drained triaxial compression shear tests. In these experiments, the sand specimen was loaded in axial compression while maintaining a constant radial confining pressure. In practice, M is often related by a constant coefficient to qc,net or qc (Schmertmann, 1978). As illustrated in Fig. 15a, constrained moduli from the experiments of this study are very close to the empirical relationship (M¼ 5qc,net) suggested by Mayne (2006) for normally consolidated clean sands. The ranges of M are also close and within the lower bound of those determined by Veismanis (1974) and Lunne and Christoffersen (1983), as seen in Fig. 15b. 4.6. Effect of lateral stress ratio (Kc) Vast experimental evidences (Huntsman, 1985; Jamiolkowski et al., 1985; Baldi et al., 1986; Houlsby and Hitchman, 1988;
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A. Sadrekarimi / Soils and Foundations 56 (2016) 460–472
Fig. 15. Comparison of constrained moduli for CPT samples with empirical correlations based on (a) qc,net and (b) qc u2..
Mayne and Kulhawy, 1991; Salgado, 1993; Ahmadi et al., 2005), as well as theoretical analyses of cone penetration tests using bearing capacity, cavity expansion, strain path, and finite element or a combination of these techniques (Vesic, 1975; Teh and Houlsby, 1991; Salgado et al., 1997b; Yu et al., 2000), indicate that both qc and fs are strongly correlated with the horizontal effective stress (s0 hc), rather than s0 vc, whereas the relative density, the unit weight, and the modulus of cohesionless soil are controlled by both s'hc and s'vc. Despite the primary effect of s0 hc on qc, CPT interpretation methods are predominantly based on s0 vc, as s0 vc is easily calculated with reasonable certainty from the soil unit weight and a knowledge of the location of the groundwater table. Thus, these methods are compared based on s0 vc with the CPT experiments of this study for which s0 vc ¼ s0 hc, whereas field stress conditions are seldom isotropic. This could have produced some unknown bias in the comparisons of Figs. 10–12. Note that both the normalized penetration resistances (qc1, fs1, or qc1,net) and the original penetration resistances (qc, fs, or qc,net) are similarly affected by changes in Kc; and therefore, the stress normalization factors (qc1/qc, fs1/fs, or qc1,net/qc,net) of Figs. 7 and 8 are unaffected by the lateral stress ratio, Kc ¼ s0 hc/ s0 vc. This is further supported by cavity expansion analysis (Salgado et al., 1997a; Moss et al., 2006), in which the stress normalization exponent is found to vary by less than 1% with a change in Kc from 0.5 to 1.0 for loose sands with Drc o 45%. The effect of the change in Kc on the constrained moduli comparison in Fig. 15 is also small because of the much larger magnitude of qc compared to s0 vc (in qc,net).
5. Summary and conclusions A series of 19 miniature cone penetration tests was described in this study. The tests were used to evaluate some of the existing empirical methods for soil type identification and to determine the relative density, the unit weight, the stress normalization, and the modulus of loose to medium-dense sands. Due to the fine gradation (Dmax ¼ 0.85 mm) of the Ottawa sand used in the CPT experiments in this study, the results were plotted within
or around the boundaries for sand and silty sand of the soil type identification plots. The experimental results suggested an overburden stress normalization exponent of 0.612 for the quartz sand used in this study for Drc ¼ 30.3–33.7%. Different overburden stress normalization techniques were then evaluated by comparison with the cone resistance measured in this study. The Drcbased stress normalization scheme of Idriss and Boulanger (2006) provided the closest estimates to qc1/qc from the CPT experiments. On the other hand, the existing overburden stress correction methods largely underestimated the normalized sleeve friction resistance (fs1). Hence, a bilinear relationship was proposed for normalizing sleeve friction based on the experiments of this study. The relationship indicates a sharply reducing normalization factor with increasing effective stress up to about 100 kPa and a significantly reduced gradient with further increases in effective stress (4100 kPa). Specific CPT-based correlations were suggested for estimating the dry and saturated unit weights of quartz sands from the CPT experiments in this study. Several empirical correlations for predicting relative density from CPT resistance were also reviewed in this study. The existing correlations exhibited very wide ranges in relative density predictions. These relationships are not universally applicable to all sand types, and therefore, cannot be used as reliable ground improvement acceptance criteria. The constrained moduli of the CPT samples also agreed very well with an empirical correlation proposed by Mayne (2006) for clean sands. Acknowledgments The research described in this study was carried out with funding provided to the author by the Natural Sciences and Engineering Research Council of Canada (NSERC: Discovery Grant). The author is also grateful to Mr. Erol Tas, a technician at Western University's Soil Mechanics Laboratory, and to graduate student Ms. Sepideh Damavandi for their assistance in performing the CPT experiments. References Abedin, M.Z., 1995. The characterization of unsaturated soil behaviour from penetrometer performance and the critical state concept. In: Department of
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Evaluation of CPT-based characterization methods for loose to medium-dense sands Abouzar Sadrekarimi Assistant Professor, Department of Civil and Environmental Engineering, Western University, London, Ontario, Canada Received 27 April 2015; received in revised form 28 January 2016; accepted 27 February 2016 Available online 20 May 2016
Abstract As a result of the difficulties related to obtaining undisturbed samples of cohesionless soils, CPT-based empirical correlations, often developed from calibration chamber experiments, are widely used for determining many soil parameters for geotechnical investigation. This paper describes the application of 19 reduced-scale calibration chamber cone penetration tests to evaluate empirical correlations for predicting the relative density, the unit weight, the constrained modulus, and the soil identification of loose to medium-dense sands. A subtraction cone, 6 mm in diameter with an apex angle of 601 and a net area ratio of 0.75, is used in the laboratory tests. Due to the fine gradation of the quartz sand used in the experiments, some of the CPT results are located within the silty sand range of the soil identification charts. An extensive evaluation is also presented for the stress normalization process of the CPT data. It is determined that a relative density-based overburden stress normalization method provided the best estimates for correcting the cone tip resistance for effective overburden stress. & 2016 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.
Keywords: Cone penetration test; Calibration chamber test; Sand; Relative density; Modulus; Critical state; Stress normalization; Soil identification
1. Introduction Geotechnical engineering analyses and designs require accurate identification and characterization of soil layers, as well as an assessment of soil stratigraphy at the site. However, due to the difficulties in obtaining undisturbed samples of cohesionless soils, geotechnical engineers often rely on field tests to obtain the insitu soil characteristics. Owing to relatively lower costs, simplicity, continuous measurement with depth, and excellent repeatability and accuracy, the electronic cone penetration test (CPT) has emerged as one of the most popular tools for ground investigation in geotechnical engineering. CPTs are particularly instrumental for characterizing saturated loose to medium-dense cohesionless soils due to the susceptibility of these soils to static E-mail address: [email protected] Peer review under responsibility of The Japanese Geotechnical Society.
or cyclic liquefaction and their potential for liquefaction flow failure. As CPT does not directly measure any particular soil properties, extensive research has been conducted to develop empirical correlations of CPT measurements with soil type and engineering properties (including unit weight, relative density, and modulus) using laboratory calibration chamber experiments (Schmertmann, 1978; Villet and Mitchell, 1981; Baldi et al., 1986; Jamiolkowski et al., 1988, 2001; Huang and Hsu, 2005). These experiments can provide the most reliable and precise experimental data for developing CPT-based correlations and calibration as the entire procedure (including sample preparation, consolidation, and cone penetration) is conducted in the laboratory and can be readily monitored and controlled. Carrying out controlled CPT calibration chamber tests with a standard cone (with a diameter of 35.7 mm) requires a largediameter (typically more than 1.2 m) chamber. Such an experiment can be expensive and time-consuming, as sample preparation
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involves placing a large volume of sand in the testing chamber at a controlled density. The control of sample uniformity and external stress can also become difficult (Parkin and Lunne, 1982). Due to these challenges, several studies have employed miniature cones and reduced-scale calibration chamber devices (Abedin, 1995; Huang and Hsu, 2005; Kumar and Raju, 2009; Kokusho et al., 2012; Franzen, 2006; Pournaghiazar et al., 2011) frequently on dense sands, with little experimental data on medium-dense to loose sands. This is often because of the collapsible fabric of loose sands which results in initially loose calibration chamber samples collapsing into a denser state during sample saturation and flushing (Been et al., 1987b). This study presents the results of miniature CPT calibration chamber experiments (Damavandi and Sadrekarimi, 2015) carried out at Western University. The results
461
are employed to evaluate a number of existing empirical correlations for determining some of the geotechnical properties of loose to medium-dense sands. 2. Experimental procedure 2.1. Miniature CPT system The largest cell that could be accommodated in an existing uniaxial loading frame is manufactured as a CPT calibration chamber in this study. The large custom-made cell contains cylindrical specimens of 150 mm in diameter and 195 mm high. The major components of the CPT calibration chamber are schematically illustrated in Fig. 1. A stainless steel cone,
Fig. 1. Illustration of calibration chamber testing components.
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with a diameter of 6 mm, an apex angle of 601, and a net area ratio of 0.75 (i.e., ratio of the cone base area unaffected by pore water pressure to total projected cone area), is employed in the calibration chamber tests. The miniature cone, developed at Western University, is a subtraction-type penetrometer in which both the cone tip resistance (qc) and the sleeve friction (fs) are measured. Similar to a type 2 cone (Lunne et al., 1997), sample pore water pressure, including any excess pore pressure developing during cone penetration (u2), is measured behind the cone's shoulder above its tip by a pressure transducer with a capacity of 1380 kPa. A thin plastic collar with small notches is used above the cone tip to allow the passage of water while blocking the intrusion of sand particles. A servo-controlled triaxial loading frame, with a uniaxial loading capacity of 10 kN, is used to drive the cone. The loading frame is equipped with a digital encoder which records its travel distance, and therefore, the amount of cone penetration. The encoder was calibrated with a high resolution LVDT. Two electromechanical pressure pumps with capacities of 75 and 170 mL are used to measure and control the fluid volume changes of the soil sample and the cell. Each pressure pump is equipped with electrical pressure transducers, with a capacity of 2070 kPa, to measure and control the specimen and the cell fluid pressures. A data logger with a maximum sampling frequency of 1 Hz, included with the triaxial loading frame, is used for data acquisition and for the real-time monitoring of the experiments. Damavandi and Sadrekarimi (2015) provide further details of the miniature CPT equipment, data analysis, verification, and the repeatability of the miniature CPT results. 2.2. Tested Material Reconstituted specimens of fine Ottawa sand were prepared and tested in this experimental program. The Ottawa sand used in this study was a uniformly graded clean sand (with no fines) – classified as SP according to the Unified Soil Classification System (Astm, 2011) – composed of white-colored quartz particles with round to sub-rounded particle shapes. Sand particles had a specific gravity (Gs) of 2.65, a mean diameter (D50) of 0.193 mm, and coefficients of uniformity (CU) and curvature (CC) of 1.71 and 1.07, respectively. Fig. 2 presents the particle size distribution of this sand. Maximum (emax) and minimum (emin) void ratios, 0.821 and 0.490, respectively, were determined following the ASTM standard procedures (Astm, 2006a; Astm, 2006b). Loose specimens of this sand exhibited non-linear isotropic compressive behavior in triaxial compression tests with compression indices (Cc) of 0.032– 0.050 at effective confining pressures of 7–700 kPa, while a more-or-less constant recompression index (Cr) of 0.005 was determined. A critical state friction angle ϕ0 cs of 30.71 was also measured for this sand in triaxial compression tests (Omar and Sadrekarimi, 2015). 2.3. Specimen preparation For the calibration chamber CPT experiments, cylindrical soil samples were prepared using the moist tamping method, which
Fig. 2. Average particle size distribution of Ottawa sand used in this study.
produces minimum particle segregation (Yang, 2005; Chen, 2000). Moist tamping often replicates the soil fabric developed by hydraulically transported sand fills (Sladen et al., 1985) or in nature as loose sand layers (Schlosser, 1985). In order to improve specimen uniformity, the under-compaction moist tamping method, suggested by Ladd (1978), was employed. This method involves the compaction of moist sand in layers slightly different than the target global density, with the bottom layer compacted the least and the top layer compacted the most, so that the final density of each layer would be equal to the target global density even with the effects of compacting the successive overlaying layers. Sand with a moisture content of 5%, required for each layer, was weighed, poured into the mold, and tamped into 13 layers of 15 mm thick in a circular pattern using a scaled tamper. This moisture developed a capillary force among the sand particles that produced a stable sand fabric and kept the specimen shape once the split mold was removed. This was necessary during specimen preparation before filling the cell and applying a seating confining pressure of 10 kPa. A latex membrane enclosed and sealed the specimen, thereby creating a flexible boundary via which a uniform axisymmetric confining pressure could be applied. The diameter and the height of the specimen were carefully measured after preparation to ensure the accuracy of the initial relative density (Dri) determination of the sample. The miniature cone was then mounted on the external rod and the cell was subsequently assembled on the specimen. Specimen uniformity was evaluated for a number of specimens by taking plug samples from the top, middle, and bottom of each specimen prepared by following the same procedure. Void ratio variations of about 70.006 (corresponding to a change in relative density of 71.5%) and 70.004 (corresponding to a change in relative density of 71.0%) were obtained from the top to the bottom of the specimen for sample relative densities of 10% and 26.8%, respectively. Despite improved specimen uniformity, small fluctuations were still observed in some of the experiments (e.g., test No. 16 in Fig. 3) reflecting the remaining specimen non-uniformity. A particular limitation of reduced-scale cones can result from the scale of the cone diameter (dc) compared to the diameter of the soil particles (e.g., D50). Several studies have
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consolidation pressure (p0 c) using two electromechanical pressure pumps. The change in sample volume during consolidation was measured by pressure pumps to determine the precise void ratio of the sample after consolidation (ec) as well as the consolidation relative density (Drc). 2.5. Cone penetration
Fig. 3. Cone penetration resistance mobilized in Tests No. 9, 11, 13, and 16: (a) qc, (b) fs..
investigated the scale effect on cone penetration tests (Schmertmann, 1978; Canou et al., 1988; Jacobs and Coutts, 1992; Salgado, 2013; Gui et al., 1998; Baldi and O'neill, 1995; Huntsman, 1985; Huang and Hsu, 2005; Lee, 1990; Balachowski, 2007; Sharp et al., 2010). For example, Canou et al. (1988) carried out reduced-scale cone penetration tests in several sands with D50 ¼ 0.3–0.7 mm (corresponding to dc/ D50 ¼ 32–18) and observed no difference between their results and those from a standard-size CPT, suggesting no scale effect. Lee (1990) carried out a series of centrifuge CPT model experiments on several gradations of Leighton Buzzard sand using three different miniature cones (with dc ¼ 19.05 mm, 10 mm, and 6.35 mm). They observed that the scale effect became appreciable only for dc/D50 o 16. Based on centrifuge model experiments, Balachowski (2007) also observed no scale effect for dc/D50 4 20. More recently, Sharp et al. (2010) performed miniature cone penetration tests on fine Nevada sand (with D50 ¼ 0.13 mm) using centrifuge testing and found no grain size effect for the dc/D50 ¼ 30.7. These results suggest that particle size and scale effect are negligible for the combination of cone diameter (dc ¼ 6 mm) and D50 (¼ 0.193 mm) – corresponding to dc/D50 ¼ 31 – used in this study. 2.4. Specimen saturation and consolidation Although previous studies have shown similar cone penetration resistance in dry and saturated clean sands (Bellotti et al., 1988; Schmertmann, 1976; Bonita, 2000; Jamiolkowski et al., 2001; Villet and Mitchell, 1981), moist tamped samples of this study were saturated in order to remove the effects of soil suction on cone resistance and to allow for the precise measurement of the change in sample volume during consolidation. This was accomplished by flushing the soil specimen with CO2 and then de-aired water to remove air and to dissolve the CO2. A back-pressure saturation procedure was subsequently followed until a pore pressure coefficient of at least 0.96 was achieved (Skempton, 1954). After specimen saturation, the samples were subjected to an isotropic
Following consolidation, a uniaxial loading frame (originally designed for triaxial testing) was used to push the miniature cone into the sample up to a penetration depth of 60 mm, while qc and fs were simultaneously measured. During cone penetration, the sample was kept globally drained through the top and bottom drainage ports. Table 1 summarizes the characteristics of the miniature cone penetration tests conducted in this study. The chamber boundary effect can be a major limitation in the comparison of CPT calibration chamber results with in-situ field tests. However, several studies (Parkin and Lunne, 1982, Baldi et al., 1982, Jamiolkowski et al., 1985, Been et al., 1987a, Mayne and Kulhawy, 1991, Salgado, 1993) have found this effect to be insignificant for loose to medium-dense sands. For example, Parkin and Lunne (1982) investigated the effect of flexible boundary conditions (similar to the samples of this study) on CPT resistance using different cone (dc) and chamber (Dc) diameters. They found that the effect of chamber boundary was negligible in loose sands (Drc r 30%) for Dc/ dc Z 20. While for very dense sands (with Drc E90%), Dc/ dc Z 50 was required to minimize chamber size effect. Similarly, Jamiolkowski et al. (2003) studied calibration chamber CPT data on Ticino and Hokksund sands, and suggested correcting the CPT resistance for chamber boundary effects only for Drc Z 40%. More recently, using 3D discrete element analyses, Butlanska et al. (2010) found no specimen size or boundary effects in sands at Drc o 45%. Based on the Table 1 Summary of miniature CPT tests performed in this study. Test no.
Drc (%)
p0 c (kPa)
qc (MPa)
fs (kPa)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
22.0 24.5 25.9 29.8 36.6 38.6 42.5 33.7 33.7 33.7 33.3 33.7 33.1 33.7 30.8 33.1 30.3 25.0 27.4
100 100 100 100 100 100 100 100 45 75 150 200 300 450 500 600 700 200 300
3.96 3.99 4.08 4.73 5.10 5.26 5.78 4.80 2.52 4.18 6.02 7.09 10.40 13.75 10.29 13.73 13.93 5.20 6.55
38.54 32.32 38.54 64.04 50.43 52.70 63.19 49.82 14.40 30.36 47.85 49.50 51.80 63.10 42.00 69.94 76.55 56.41 51.30
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findings of these studies, the effects of specimen size and boundary conditions on cone resistance are expected to be negligible for the experiments of this study which were carried out on sand samples with Dc/dc ¼ 25 at Drc o 43%. Therefore, corrections for boundary conditions are not applied in the comparisons and analyses presented here. 3. Experimental results Fig. 3 presents cone penetration resistances (qc, fs) for the series of miniature CPT tests of this study. According to these plots, for the relatively uniform specimens of this study, the cone tip resistance increased with penetration depth as soil resistance to the insertion of the cone was fully mobilized. After about 20 mm, qc approached a more-or-less uniform plateau. Note that fs is plotted for penetration depths of greater than 10 mm where the friction sleeve was effectively inserted into the soil away from the specimen's top cap. Average magnitudes of qc and fs, determined after a cone penetration of 20 mm, are also summarized in Table 1. Due to the high hydraulic conductivity and free-draining nature of the tested Ottawa sand, cone penetration occurred under a primarily drained condition with no excess pore water pressure being generated adjacent to the cone tip (u2). Accordingly, correction for the effect of unequal end areas was not needed (Robertson and Cabal, 2015).
Fig. 4. Comparison of CPT data of this study with soil identification zones of Mayne (2006).
4. Comparison with existing empirical correlations In the following paragraphs, the experimental results of this study (summarized in Table 1) are compared with some of the existing methods for CPT-based soil classification, stress normalization, predicting sand relative density, unit weight, and constrained modulus. 4.1. Evaluation of soil classification methods
Fig. 5. Comparison of CPT data of this study with soil type zones of Eslami and Fellenius (1997).
One of the useful applications of CPT is to identify the soil type. Several studies have proposed empirical soil behavioral charts or correlations for soil classification based on CPT measurements. Figs. 4–6 compare the CPT data of this study with the soil type boundaries or zones proposed by some of these methods (Mayne, 2006; Eslami and Fellenius, 1997; Robertson, 2009). In these plots, s0 vc and svc are the initial effective and total vertical stresses, respectively, which correspond to p0 c for the CPT experiments of this study, Pa ¼ 100 kPa is a reference pressure, and qc,net ¼ qc svc. Regarding Fig. 6, Qtn ¼ qc,net/Pa (Pa/s0 vc)n and FR¼ fs/qc,net 100 are the normalized cone parameter and the friction ratio, respectively, and n is a stress normalization exponent which depends on the soil behavior (Robertson, 2009). According to Figs. 4 and 5, the soil type identification charts of Mayne (2006) and Eslami and Fellenius (1997) provide reasonable predictions of the clean Ottawa sand used in this study. A few data points plot between the sands and silts or within the silt zones of these charts. This is likely to be because of the fine gradation (D50 ¼ 0.19 mm) of the Ottawa sand used here compared to that used for developing the
Fig. 6. Comparison of CPT data of this study with soil identification zones of Robertson (2009). Numbered zones correspond to 1: sensitive fine-grained soil, 2: organic soil, 3: silty clay to clay, 4: clayey silt to silty clay, 5: silty sand to sandy silt, 6: sand, 7: gravelly sand to dense sand, 8: very stiff sand to clayey sand, and 9: very stiff fine-grained soil.
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soil identification charts of Mayne (2006) and Eslami and Fellenius (1997). However, the experimental data plot entirely as silty sands to sandy silts (zone 5) in Fig. 6, suggesting that the empirical chart of Robertson (2009) might be less accurate for identifying quartz fine sands. A few field samples from each soil stratum are recommended to confirm the predictions of soil classification techniques.
4.2. Evaluation of overburden stress normalization methods In order to compare soil behavior from different depths, the cone resistance is often normalized (or corrected) to a common effective overburden stress of 100 kPa (Wroth, 1984). As summarized in Table 2, a number of techniques (Wroth, 1984; Robertson, 2009; Olsen and Mitchell, 1995; Kayen et al., 1992; Moss et al., 2006; Liao and Whitman, 1986; Cetin and Isik, 2007; Idriss and Boulanger, 2006) are suggested for converting the total (qc) or the net (qc, net ¼ qc sv) cone tip resistances and sleeve friction to those that would have been measured if CPT had been carried out at Table 2 CPT overburden stress normalization methods. Normalized parametera Cone tip resistance 0:5 qc1;net ¼ qc;net sP0a vc 0:5 Pa qc1 ¼ qc s0
Reference Sleeve friction –
Wroth (1984)
–
Liao and Whitman (1986)
vc
qc1 ¼
1:8 0:8 þ s0vc =Pa
qc c
–
c
Kayen et al. (1992)
qc1;net ¼ qc;net sP0a vc
f s1 ¼ f s sP0a vc
Olsen and Mitchell (1995)
qc1;net ¼ qc;net
–
Cetin and Isik (2007); Robertson (2009) Idriss and Boulanger (2006)
qc1 ¼ qc qc1 ¼ qc
c Pa s0vc
0:784 0:521Drc Pa s0
vc c Pa s0vc
– f s1 ¼ f s
c Pa s0vc
Moss et al. (2006)
a svc and s0 vc are total and effective initial vertical stresses, respectively; Pa: atmospheric pressure ( E100 kPa); c: stress normalization exponent.
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s0 vc ¼ 100 kPa. These methods are briefly described and compared with the CPT experiments of this study. An ideal stress normalization method should produce an equal normalized cone resistance from different depths or s0 vc in the same soil at the same Drc. As tests Nos. 8–17 were conducted at close Drc (¼ 30.3–33.7%), they provide an exceptional opportunity to evaluate the stress normalization techniques of Table 2. Fig. 7a compares the stress normalization methods for qc. In this figure, the qc measured in test No. 8 (carried out at p0 c ¼ 100 kPa) is normalized by qc at other p0 c in order to obtain stress normalization factors (qc1/qc). Note that for the isotropically consolidated experiments of this study, s0 vc ¼ p0 c. According to Fig. 7, the widely used stress normalization factor of Liao and Whitman (1986) somewhat overestimates the experimental data at s0 vc 4 100 kPa, which could lead to unconservative values for normalized qc (qc1) at s0 vc 4 100 kPa. Based on a combination of theory and empirical observations, Moss et al. (2006) suggested a stress normalization exponent for normalizing both qc and fs, as follows: c ¼ 0:78qc ðMPaÞ
0:33
f s ðMPaÞ qc ðMPaÞ
100
! ð 0:32qc ðMPaÞ 0:35 þ 0:49Þ
1:21 abs log 10 þ qc ðMPaÞ
ð1Þ The above equation results in c E 0.5, which is the same as that suggested by Liao and Whitman (1986); and therefore, the resulting qc1 becomes relatively larger than those of this study at s0 vc 4 100 kPa. As shown in Fig. 7a, while the stress normalization method suggested by Kayen et al. (1992) predicts slightly smaller qc1 than those of this study, the Drcbased normalization profile proposed by Idriss and Boulanger (2006) provides the best estimates for qc1/qc from the CPT experiments. Nevertheless, the choice of the overburden stress correction method seems to have a negligible impact on qc1 for s0 vc/Pa ¼ 0.5 2.0 in Fig. 7a. Similar to Fig. 7a, Fig. 7b compares the stress normalization methods based on qc,net with the laboratory CPT data of this study. According to this figure, these methods provide different normalized net cone resistance (qc1,net), indicating a
Fig. 7. Comparison of existing stress normalization techniques with (a) qc1/qc and (b) qc1,net/qc,net from CPT experiments of this study.
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lack of consensus in stress normalization methods which could lead to very different CPT interpretations. The overburden stress correction of Wroth (1984) largely underestimates the qc1,net measured in the CPT experiments at s0 vc 4 100 kPa. Olsen and Mitchell (1995) collected over 2 decades of field data and an extensive database of CPT calibration chamber tests conducted by other researchers in order to deduce a CPT tip normalization factor. They suggested the following relationship for the stress normalization exponent: c ¼ 1 ðDrc 10%Þ 0:007
ð2Þ
The above equation yields c ¼ 0.86 0.83 for Drc ¼ 30.3– 33.7% in this study and the resulting stress normalization factors tend to underestimate the qc1,net measured in the CPT experiments at s0 vc 4 100 kPa. Cetin and Isik (2007) used a Bayesian probabilistic analysis for the compilation of a database of field tests, CPT calibration chamber tests, and finite element numerical analysis data. They developed an iterative procedure based on the following equations for estimating a range of stress normalization exponents, as follows: R 272:38 7 0:085; 272:38o R o 275:19 ð3Þ 275:19 272:38 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2ffi qc1;net fs R¼ log 100 þ 243:91 þ log 126:24 qc Pa c¼
ð4Þ According to Fig. 7b, the qc1,net from the CPT experiments in this study tend to be smaller than the ranges of those produced by Eq. (3) at s'vc 4 100 kPa. More recently, Robertson (2009) suggested another iterative procedure for determining a variable stress normalization exponent based on a soil behavior type (SBT) index, Ic, as seen below: qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð5Þ I c ¼ ð3:47 logQÞ2 þ ðlogF R þ 1:22Þ2 The iteration starts with c¼ 1.0 in order to calculate the first trial of Ic. If Ic r 1.64, then c¼ 0.5; otherwise, it is calculated from the equation given below: 0
s c ¼ 0:381I c þ 0:05 v 0:15 r 1:0 Pa
ð6Þ
As demonstrated in Fig. 7b, this method is found to be conservatively biased by underestimating qc1,net as a result of the relatively large normalization exponents (0.67–1.0) produced by Eq. (6). As shown in the plots of Fig. 7, the CPT experiments suggest c¼ 0.612 for the quartz Ottawa sand used in this study. This produces the same normalization factors as those provided by Idriss and Boulanger (2006). Although many studies have developed stress normalization methods for cone tip resistance, according to Table 2, very few (Olsen and Mitchell, 1995; Moss et al., 2006) consider correcting fs by merely extending the same factors (used for qc) to fs1. Fig. 8 compares the normalization factors of these studies with the fs1/fs from the CPT experiments in this study. Similar to qc1, fs1 is measured in test No. 8 at p0 c ¼ 100 kPa.
Fig. 8. Comparison of existing stress normalization techniques with fs1/fs from the CPT experiments of this study.
According to Fig. 8, the existing methods largely overestimate the effect of the overburden stress on fs. The experiments of this study suggest a bilinear trend (see Fig. 8) with much larger stress normalization factors for fs. As displayed in Fig. 8, fs1/fs decreases sharply with an increase in s0 vc up to about 100 kPa. However, with further increases in s0 vc, the effect of s0 vc on fs1 is significantly reduced. The physical mechanism underlying this trend is investigated below. The sleeve friction (fs) measured during a cone penetration test is essentially a function of the radial stress (s0 rf) and the interface friction angle (δf) between the soil and the cone sleeve (Huntsman, 1985). Based on observations made in the driving of small-scale instrumented steel piles (Lehane et al., 1993), the magnitude of s0 rf depends on the dilatancy of the sand adjacent to the cone sleeve (Lehane and White, 2005). Since neither δf nor s0 rf were directly measured in the CPT experiments of this study, s0 rf is approximately computed in Fig. 9 as s0 rf ¼ fs/tan(δf) for Drc ¼ 30.3–33.7%. A cone penetration of about 2–3 mm is often sufficient to mobilize a constant-volume interface sleeve friction corresponding to the critical state of the sand adjacent to the cone sleeve (Lehane and White, 2005). Accordingly, δf ¼ 1/2ϕ0 cs ¼ 15.41 (ϕ0 cs ¼ 30.71 for the Ottawa sand of this study) is assumed in this analysis (Tejchman and Wu, 1995). According to Fig. 9, the computed s0 rf is greater than the imposed horizontal boundary stress, s0 hc (which is the same as s0 vc and p0 c in this study) at s0 vc r 150 kPa, where sand dilatancy is strong. However, s0 rf drops sharply with an increase in s'vc beyond 150 kPa as the dilantancy of the sand is suppressed and its contractive tendency improves with increasing s0 vc. The observed pattern is analogous to those measured in skin friction on reduced-scale instrumented piles (Boulon and
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Fig. 9. Effect of s0 vc on radial stress amplification (s0 rf/s0 hc) on cone sleeve based on computations of this study and measurements made in other calibration chamber tests (Boulon and Foray 1986; Balachowski 2006).
467
Fig. 10. Comparison of dry unit weights (γd) predicted by Mayne (2007) with those from experiments of this study for tests Nos. 1–8.
Foray, 1986) as well as in rigid-wall calibration chamber experiments on clean quartz sands (Balachowski, 2006). The wide difference between the radial stress amplification factors (s0 rf/s0 hc) of loose and dense sands in Fig. 9 emerges from the greater dilatancy of the denser samples. Similar observations have also been reported in several other experimental investigations (Baldi et al., 1981) as well as in in-situ tests on piles with different lengths (Coyle and Castello, 1981). The trend of fs1/fs with s0 vc/Pa observed in Fig. 9 reflects the changes in (s0 rf/s0 hc), and thus, reduced sand dilatancy and increased contractiveness with an increasing s'vc.
4.3. Evaluation of soil unit weight Soil unit weight is a critical information for calculating the initial geostatic and overburden stresses for CPT data processing and for interpreting many other geotechnical parameters. The soil unit weight can be measured directly from undisturbed samples collected by thin-wall tube samples or ground freezing techniques. However, such techniques can often be expensive, difficult, and onerous in saturated clean sands or gravels and they require costly equipment. Therefore, indirect empirical correlations with CPT measurements are developed and regularly used for quicker processing of cone penetration data and preliminary geotechnical analyses. From the regression analysis of a large database of calibration chamber cone penetration tests in clays, silts, and sands, Mayne et al. (2010) and Mayne (2007) suggested the following correlations for predicting dry (γd) and total (γt) unit weights from the cone tip resistance: ! q =P a c γ d kN=m3 ¼ 1:89log 0 ð7Þ 0:5 þ 11:8 svc =Pa
Fig. 11. Comparison of total unit weights (γt) predicted by Mayne et al. (2010) with those from experiments of this study for tests Nos. 1–8.
γ t ¼ 1:81γ w
0 0:05
svc q svc 0:017 f s 0:073 : c : : Pa Pa Pa
Bq þ 1
0:16 ð8Þ
in which Bq ¼ Δu2/qc,net is the normalized pore water pressure parameter. Figs. 10 and 11 compare these correlations with γd and γt of test Nos. 1–8, conducted at p0 c ¼ 100 kPa. According to these figures, Eq. (7) provides close estimates of γd as Eq. (7) is derived based on calibration chamber tests on silica sands (Mayne, 2007). However, the predictions of Eq. (8) are on average about 1 kN/m3 lower than those from the CPT experiments of this study. This probably stems from the original development of Eq. (8) as an average correlation based on regression analysis of CPT in different soil types, including clays, silts, sands, tills, and largely dominated by clayey soils. Based on the CPT tests in this study (Figs. 10 and 11), the following relationships are suggested for estimating γd and γt for clean silica sands (similar to the Ottawa
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sand used here):
!
q =Pa γ d kN=m3 ¼ 3:00log 0 c 0:5 þ 9:44 svc =Pa
ð9Þ
!
q =Pa γ t kN=m3 ¼ 2:00log 0 c 0:5 þ 15:69 svc =Pa
ð10Þ
A particular difference between Eqs. (8) and (10) is the consideration of fs in Eq. (8). The nearly perfect relationship between γt and qc, provided by Eq. (10), implies a weaker connection between fs and γt (compared to qc), and that fs could be excluded for estimating γt.
Table 3 Summary of correlation parameters suggested by earlier studies for fitting Eq. (11) based on s0 vc. No. Sand
C0
C1
C2
Reference
a b c d e
0.050 0.157 0.086 0.140 0.175
0.700 0.550 0.530 0.550 0.500
2.91 2.41 3.29 2.90 3.10
Schmertmann (1978) Baldi et al. (1986)
Several NC sands Ticino Hokksund Ticino Ticino, Toyoura, Hokksund
Jamiolkowski et al. (2001)
Table 4 Summary of correlation parameters suggested by earlier studies for fitting Eq. (11) based on p0 c.
4.4. Evaluation of sand relative density In addition to the soil unit weight, the relative density is extensively used in geotechnical engineering as an index parameter for characterizing the shearing response of granular soils and it is often used in ground improvement projects for compaction quality control. Considering the difficulties in obtaining undisturbed samples, CPT is a viable tool for estimating the Drc of in-situ sands. The experimental data from this study are used here to evaluate some of the existing predictive correlations for Drc. For normally consolidated and unaged fine to medium clean sands, Schmertmann (1976) suggested the following correlation between qc and Drc: ! 100 qc ðMPaÞ Drc ð%Þ ¼ ln ð11Þ C C2 C 0 s0 1
No. Sand
C0
f g h
Ticino Hokksund Ticino
i j
Ticino Ticino, Toyoura, Hokksund Da Nang (Vietnam)
0.181 0.550 2.61 Baldi et al. (1986) 0.153 0.550 2.88 0.205 0.510 2.93 Jamiolkowski et al. (1988) 0.174 0.560 2.97 Jamiolkowski et al. 0.297 0.460 2.96 (2001)
k
C1
C2
Reference
0.369 0.500 2.34 Huang and Hsu (2005)
vc
in which C0, C1, and C2 are empirical fitting parameters and s0 vc is the initial effective vertical stress. Since the pioneering work of Schmertmann (1976), several investigators (Baldi et al., 1986; Villet and Mitchell, 1981; Jamiolkowski et al., 2001; Schmertmann, 1978) have fitted Eq. (11) to CPT calibration chamber tests on many sands. However, some studies indicate that the qc measured in calibration chamber tests is largely influenced by the horizontal effective stress, s0 hc (Baldi et al., 1986; Houlsby and Hitchman, 1988; Jamiolkowski et al., 2001; Holden, 1971). Accordingly, Eq. (11) has also been expressed (Baldi et al., 1986; Jamiolkowski et al., 2001; Huang and Hsu, 2005; Jamiolkowski et al., 1988) as a function of the mean consolidation pressure, p0 c, in order to include the effects of both s0 vc and s0 hc. For field applications, p0 c can be determined by assuming Ko ¼ 1 sin (ϕ0 ) for normally consolidated young sand deposits in which ϕ' is the sand's effective stress friction angle. Tables 3 and 4 summarize the fitting parameters of Eq. (11) suggested by these studies. Figs. 12 and 13 compare the predictions made in these studies with the CPT experiments based on s0 vc and p0 c, respectively. For the isotropically-consolidated samples in this study, s0 vc ¼ p0 c. Except for the s0 vc-based correlations proposed by Baldi et al. (1986) (for Hokksund sand) and by Schmertmann (1978), the remaining methods underestimate the Drc values in this study. The overall amount of underestimation seems to be greater for the p0 c-based methods,
Fig. 12. Comparison of Drc from CPT experiments of this study with those predicted by other studies based on s0 vc. Line labels are a: Schmertmann (1978), b: Baldi et al. (1986) based on Ticino sand, c: Baldi et al. (1986) based on Hokksund sand, d: Jamiolkowski et al. (2001) based on Ticino sand, e: Jamiolkowski et al. (2001) based on Ticino, Toyoura and Hokksund sands, and l: Kulhawy and Mayne (1990).
suggesting a greater effect of s0 vc than that incorporated through p0 c. The s0 vc-based correlation of Baldi et al. (1986), from calibration chamber CPT tests on Hokksund sand, provides the closest estimates to the Drc in this study, while those of Schmertmann (1978) largely overestimate Drc. In summary, the correlations proposed by different studies predict a very wide range of Drc because of the different types of sands used in their databases. Therefore, a unique form of Eq. (11) cannot be determined for all sands, and particularly
A. Sadrekarimi / Soils and Foundations 56 (2016) 460–472
469
Fig. 13. Comparison of Drc from CPT experiments of this study with those predicted by other studies based on p0 c. Line labels are f: Baldi et al. (1986) based on Ticino sand, g: Baldi et al. (1986) based on Hokksund sand, h: Jamiolkowski et al. (1988), i: Jamiolkowski et al. (2001) based on Ticino sand, j: Jamiolkowski et al. (2001) based on Ticino, Toyoura and Hokksund sands, and k: Huang and Hsu (2005).
Fig. 14. Comparison of Drc from CPT experiments of this study with ranges of those predicted by Eq. (13).
for variable soil deposits. In other words, different sands will not necessarily behave the same at the same Drc and p0 c. For the CPT experiments in this study, fitting parameters of C0 ¼ 0.119, C1 ¼ 0.612, and C2 ¼ 2.55 are found following an optimization process by minimizing the standard deviation between the calculated and the measured qc. However, the values for Drc predicted with these parameters in Eq. (11), are still within 7 6.5% of the actual values. This indicates the limited accuracy of Eq. (11) which merely uses p0 c and qc (Sladen, 1989; Huang and Hsu, 2005; Hamidi et al., 2013). Accordingly, Kulhawy and Mayne (1990) and Jamiolkowski et al. (2001) have proposed empirical relationships for estimating Drc with additional consideration regarding the effect of sand compressibility. Kulhawy and Mayne (1990) compiled the results of 24 sets of calibration chamber tests on fine to medium sands and suggested the following relationship:
4.5. Evaluation of soil stiffness
D2rc ¼
1 q =Pa : c 0:5 305Qc s0 =Pa
ð12Þ
vc
in which Qc is a compressibility factor equal to 0.91, 1.00, and 1.09 for high, medium, and low compressibility sands, respectively. According to Fig. 12, Eq. (12) (labeled “l”) provides close estimates of Drc for qc/(s0 vc)0.5 ¼ 200–327, while underestimating at greater qc/(s0 vc)0.5 values. From a review of the calibration chamber tests data, Jamiolkowski et al. (2001) suggested a modified form of Eq. (11) as below: ! qc =Pa ð13Þ Drc ð%Þ ¼ 26:8ln C bx s0vc =Pa 1 in which C1 is a stress normalization exponent (¼ 0.50) similar to Eq. (11), and bx ¼ 52.5, 67.5, 82.5 are for high, medium, and low compressibility sands, respectively. As illustrated in Fig. 14, the experiments of this study plot within the medium to low compressibility range (bx ¼ 70.2) using C1 ¼ 0.612, which
is consistent with the stress normalization exponent determined in Fig. 7.
Soil stiffness describes the soil deformation behavior under an increment in confining stress or shear stress. Several investigators have attempted to relate soil stiffness to cone penetration resistance (Schmertmann, 1978; Tanaka and Tanaka, 1998; Mayne, 2006; Tonni et al., 2010). Here, the bulk moduli (K) of the samples were determined from the isotropic consolidation stages of the CPT experiments as the incremental change in effective confining pressure (∂p0 ) divided by the volumetric strain (εv). These were then converted to constrained moduli (M) using the following relationship for each experiment: M¼
3K ð1 νÞ ð1 þ νÞ
ð14Þ
A Poisson's ratio ν (¼ εr/εa) of 0.36 was also determined based on the measurements of axial strain (εa) and volumetric strain (εv ¼ εa þ 2εr) of the same sand in consolidated drained triaxial compression shear tests. In these experiments, the sand specimen was loaded in axial compression while maintaining a constant radial confining pressure. In practice, M is often related by a constant coefficient to qc,net or qc (Schmertmann, 1978). As illustrated in Fig. 15a, constrained moduli from the experiments of this study are very close to the empirical relationship (M¼ 5qc,net) suggested by Mayne (2006) for normally consolidated clean sands. The ranges of M are also close and within the lower bound of those determined by Veismanis (1974) and Lunne and Christoffersen (1983), as seen in Fig. 15b. 4.6. Effect of lateral stress ratio (Kc) Vast experimental evidences (Huntsman, 1985; Jamiolkowski et al., 1985; Baldi et al., 1986; Houlsby and Hitchman, 1988;
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Fig. 15. Comparison of constrained moduli for CPT samples with empirical correlations based on (a) qc,net and (b) qc u2..
Mayne and Kulhawy, 1991; Salgado, 1993; Ahmadi et al., 2005), as well as theoretical analyses of cone penetration tests using bearing capacity, cavity expansion, strain path, and finite element or a combination of these techniques (Vesic, 1975; Teh and Houlsby, 1991; Salgado et al., 1997b; Yu et al., 2000), indicate that both qc and fs are strongly correlated with the horizontal effective stress (s0 hc), rather than s0 vc, whereas the relative density, the unit weight, and the modulus of cohesionless soil are controlled by both s'hc and s'vc. Despite the primary effect of s0 hc on qc, CPT interpretation methods are predominantly based on s0 vc, as s0 vc is easily calculated with reasonable certainty from the soil unit weight and a knowledge of the location of the groundwater table. Thus, these methods are compared based on s0 vc with the CPT experiments of this study for which s0 vc ¼ s0 hc, whereas field stress conditions are seldom isotropic. This could have produced some unknown bias in the comparisons of Figs. 10–12. Note that both the normalized penetration resistances (qc1, fs1, or qc1,net) and the original penetration resistances (qc, fs, or qc,net) are similarly affected by changes in Kc; and therefore, the stress normalization factors (qc1/qc, fs1/fs, or qc1,net/qc,net) of Figs. 7 and 8 are unaffected by the lateral stress ratio, Kc ¼ s0 hc/ s0 vc. This is further supported by cavity expansion analysis (Salgado et al., 1997a; Moss et al., 2006), in which the stress normalization exponent is found to vary by less than 1% with a change in Kc from 0.5 to 1.0 for loose sands with Drc o 45%. The effect of the change in Kc on the constrained moduli comparison in Fig. 15 is also small because of the much larger magnitude of qc compared to s0 vc (in qc,net).
5. Summary and conclusions A series of 19 miniature cone penetration tests was described in this study. The tests were used to evaluate some of the existing empirical methods for soil type identification and to determine the relative density, the unit weight, the stress normalization, and the modulus of loose to medium-dense sands. Due to the fine gradation (Dmax ¼ 0.85 mm) of the Ottawa sand used in the CPT experiments in this study, the results were plotted within
or around the boundaries for sand and silty sand of the soil type identification plots. The experimental results suggested an overburden stress normalization exponent of 0.612 for the quartz sand used in this study for Drc ¼ 30.3–33.7%. Different overburden stress normalization techniques were then evaluated by comparison with the cone resistance measured in this study. The Drcbased stress normalization scheme of Idriss and Boulanger (2006) provided the closest estimates to qc1/qc from the CPT experiments. On the other hand, the existing overburden stress correction methods largely underestimated the normalized sleeve friction resistance (fs1). Hence, a bilinear relationship was proposed for normalizing sleeve friction based on the experiments of this study. The relationship indicates a sharply reducing normalization factor with increasing effective stress up to about 100 kPa and a significantly reduced gradient with further increases in effective stress (4100 kPa). Specific CPT-based correlations were suggested for estimating the dry and saturated unit weights of quartz sands from the CPT experiments in this study. Several empirical correlations for predicting relative density from CPT resistance were also reviewed in this study. The existing correlations exhibited very wide ranges in relative density predictions. These relationships are not universally applicable to all sand types, and therefore, cannot be used as reliable ground improvement acceptance criteria. The constrained moduli of the CPT samples also agreed very well with an empirical correlation proposed by Mayne (2006) for clean sands. Acknowledgments The research described in this study was carried out with funding provided to the author by the Natural Sciences and Engineering Research Council of Canada (NSERC: Discovery Grant). The author is also grateful to Mr. Erol Tas, a technician at Western University's Soil Mechanics Laboratory, and to graduate student Ms. Sepideh Damavandi for their assistance in performing the CPT experiments. References Abedin, M.Z., 1995. The characterization of unsaturated soil behaviour from penetrometer performance and the critical state concept. In: Department of
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