A new empirical correlation between pressuremeter modules (EM) and shear wave velocity (Vs) for clay soils

Journal of Applied Geophysics 171 (2019) 103865

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A new empirical correlation between pressuremeter modules (EM) and shear wave velocity (Vs) for clay soils İsmail Akkaya a,⁎, Ali Özvan b, Elif E. Özvan c a b c

Van Yüzüncü Yıl University, Department of Geophysical Engineering, Van, Turkey Van Yüzüncü Yıl University, Department of Geological Engineering, VAN, Turkey Çukurova University, Institute of Natural and Applied Sciences, Adana, Turkey

a r t i c l e

i n f o

Article history: Received 23 March 2019 Received in revised form 28 August 2019 Accepted 3 October 2019 Available online 23 October 2019 Keywords: Pressuremeter test Standard penetration test Shear wave velocity Clay soil Correlation

a b s t r a c t The pressuremeter (PMT) and standard penetration (SPT) tests are the most common in situ tests used for determining the engineering properties of soils and rocks. PMT method can be used to determine the deformation and strength properties of soil or very blocky rock masses. PMT procedure is time-consuming and expensive, and it requires advanced testing equipment. Both SPT and PMT methods also require drilling to be performed in the area. The shear wave velocity (Vs) is a parameter obtained using active and passive seismic methods and provides insight into the strength properties of the soil and rock. Vs is easy to obtain with these methods and can be determined in all kinds of field conditions. Due to the difficulties experienced during many types of in-situ tests, numerous empirical equations for the soil or rock units have been proposed in the literature that are based on Vs. In this paper, correlations of Menard Deformation Modules (EM) with the corrected SPT blow counts (SPT-N60) and shear wave velocity (Vs) data were conducted. For this purpose, parameters of the pressuremeter were defined as a function of two variables. In order to determine the relationship between the results of these field tests and the results obtained from high-consolidated clayey soils with high and low plasticity properties, 10 boreholes with a depth of 15 m were drilled and in-situ tests were carried out at diverse depths. In addition, seismic measurements were performed at the same locations and depth-based Vs velocity data was obtained. It was concluded that EM could be predicted as a function of SPT-N60 and Vs values, and the predictions had relatively high R2 values of 0.77 and 0.75, respectively. This study thereby introduces to the literature empirical equations between EM and Vs for the first time. As soil properties are heterogeneous and anisotropic, it has been shown that it is more appropriate to use the equations produced from logarithmic and exponential relations in both single and multiple statistical analysis. © 2019 Elsevier B.V. All rights reserved.

1. Introduction The Standard Penetration Test (SPT), Pressuremeter test (PMT) and seismic surface wave methods are three of the most commonly used insitu measurement technics during geotechnical site investigations. The parameters obtained using these methods are then used for calculation of liquefaction (Seed and Idriss 1971; Robertson and Wride 1997; Andrus and Stokoe 2000; Uyanık and Taktak 2009; Uyanık et al. 2013), bearing capacity (Imai and Yoshimura 1972; Keçeli, 2000; Tezcan et al. 2006; Uyanık and Ulugergerli 2008; Uyanık and Gördesli 2013; Ghavami et al. 2019) and settlement properties of soils (Terzaghi and Peck 1967; Keçeli, 2000). These methods have various advantages and disadvantages in field applications. SPT test is a standard application used in all kinds of soil exploration projects all around the world due to its low cost. Although PMT test is comparatively expensive ⁎ Corresponding author. E-mail address: [email protected] (İ. Akkaya).

https://doi.org/10.1016/j.jappgeo.2019.103865 0926-9851/© 2019 Elsevier B.V. All rights reserved.

and more complex than SPT, it is a method where various variables can be measured directly. In addition, this test can be applied to both soil and very blocky rocks. SPT method has been used in many field investigations to measure penetration resistance of the soil. It is a field test that is frequently used in the calculation of bearing capacity and liquefaction potential of soil structures. SPT-N value, which is related to the vertical resistance to penetration, is the number of blows that are needed to penetrate the split spoon sampler tube into the ground. After recording the SPT-N value, SPT-N60 value is calculated by revising it in according to the corrections suggested in the literature (Skempton 1986; Bowles 1997; ASTM D1586/D1586M-18, 2018; BS EN ISO 22476-3 2007). The PMT method, which was developed by Louis Menard called as the Menard Pressuremeter, is one of the borehole loading tests that define the strength parameters and the deformation characteristics of the soil or very blocky rocks. The pressuremeters are inserted into the borehole and uniform pressure is applied outwards to the walls of the borehole by means of the inflatable elastic membrane. The applied pressure

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is increased every 60 seconds to determine the deformation of the borehole walls. The pressure is held constant for 30–60 seconds, and the increase in the volume required for maintaining the constant pressure is recorded. At the end of the experiment, Menard Deformation Modules (EM) and Limit Pressure (PL) values are calculated using the loaddeformation diagram (Menard 1957; Baguelin et al. 1978; Mair and Wood 1987; Clarke 1995; ASTM D4719-00). Shear wave velocity (Vs) which is a significant physical parameter such as SPT-N is widely used for determining the dynamic properties of soils depending on relative density, effective stress, and porosity. Vs velocity values can be obtained comparatively quickly and easily compared to other field tests. Vs measurement can be applied both in the field and in the laboratory. Several empirical formulas were developed to determine a correlation between SPT-N and Vs in the previous studies (Imai and Yoshimura 1970; Imai 1977; Ohta and Goto 1978; Seed and Idriss 1981; Sykora and Stokoe 1983; Iyisan 1996; Kayabalı 1996; Jafari et al. 2002; Andrus et al. 2006; Akın et al. 2011; Hasançebi and Ulusay 2007; Ulugergerli and Uyanık 2007; Dikmen 2009). In addition,

several empirical formulas were developed to determine a relationship that uses EM parameter and SPT-N values (Yagiz et al. 2008; Bozbey and Togrol 2010; Kayabaşı 2012; Kayabaşı and Gökceoğlu 2012; Cheshomi and Ghodrati 2015; Anwar 2016; Özvan et al. 2018; Bajaj and Anbazhagan 2019). However, no empirical equation between the Vs and the EM parameters was suggested in the literature. The main purpose of the study is to obtain SPT and EM values statistically by using Vs velocity data, which can be obtained in the field easily from both soil and rock. For this reason, the primary objective of this study is to perform linear and non-linear regression analyses between the SPT-N60, Vs, and PMT parameters. These parameters were obtained from an engineering investigation performed in consolidated clay layers in a study area located towards the eastern side of Lake Van in Turkey. The data used in this study was acquired from a total of 10 different boreholes used as part of the site investigation (Fig. 1). The study area is composed of low (CL) and high (CH) plasticity clayey soils layers. For the measurements, two different boreholes were opened side by side at the same location. PMT, EM, and PL values were then calculated

Fig. 1. Location map of the study area.

İ. Akkaya et al. / Journal of Applied Geophysics 171 (2019) 103865

for 33 different depth levels. In addition, 28-profile seismic measurements (MASW) and 97 different depth levels SPT tests were performed. EM values were compared to both Vs and SPT-N60 values, and high coefficients of determination (denoted by R2) were obtained from these correlations. 2. Geological and seismotectonic properties in the study region The study area is located in the Lake Van region, which is the most seismically active region in eastern Turkey (Fig. 1). Numerous destructive earthquakes have occurred during the last century in the Lake Van area (Fig. 1). The region is under the effects of compression stress in N-S directions due to the continental collision between the Arabian and the Eurasian plates (Koçyiğit 2013). Many tectonic structures occurred due to this compression and shaped the seismicity of the region. There are different types of active faults in the region with the potential to create a major earthquake such as the Van (Everek), Yeniköşk, Alaköy, and Özalp thrust faults, and Çaldıran and Erciş strike-slip faults (Koçyiğit 2013; Selçuk 2016; Sengul et al. 2019). The study area consists of Pliocene and Quaternary age alluvial deposits, and old lake and recent river sediments (Selçuk 2003; Özvan 2004; Akın et al. 2013, 2015; Erdoğan and Özvan 2015; Özvan and Erdoğan 2016; Akkaya et al. 2015, 2017, 2018; Akkaya and Özvan 2019). These units comprise of clay, silt, sand, and gravel grain size, with layers of different thicknesses and usually heterogeneous in both vertical and lateral directions. The groundwater levels in the study area are very shallow (b10 m). The groundwater level is especially shallow close to the Lake Van (Özvan 2004; Özvan et al. 2005; Akkaya et al. 2015). These types of soils are extremely affected by possible destructive earthquakes. Therefore, it is very important to determine the different types of deformations that may occur due to repeated earthquake loads. 3. Field investigations In the study area, a number of boreholes have been made in the recent years, ranging from 15 to 20 m in depth (Selçuk 2003; Akın et al. 2015) (Fig. 2). In these studies, SPT tests were performed in each well and laboratory tests were performed. However, there are not too many data about the pressuremeter and seismic measurements in the same study area. PMT and SPT tests were performed for determining the engineering properties of soils in this study. Two boreholes were opened next to each other for SPT and PMT so that they could be performed in the same borehole location (Fig. 3), and both SPT and PMT measurements were taken at every 1.5 m, and the process was repeated for a total of 10 different locations. In addition, multi-channel analysis of surface wave (MASW) measurements was performed at the same locations, and the Vs velocity data were obtained depending on the depth. The relationship between SPT-N60–Vs and EM–Vs values were then investigated. After obtaining statistically significant relations, the results of 41 boreholes and 28 seismic (refraction and MASW) measurement points were calculated by using these equations, and the zone map in the area was made from the data. The SPT test is a well-known and relatively inexpensive and easy to use in-situ test for determining design parameters of soil properties such as indirectly density, bearing capacity, liquefaction, strength and deformation modulus. After recording raw SPT (SPT-N30) data, which is the number of blows necessary advancing the penetrate the tube into the ground for the last 30 cm, SPT-N60 value is calculated by revising the obtained values (Bowles 1997; ASTM D1586/D1586M-18 2018). SPT was performed for 41 boreholes at different depths with 1.5 m increments (Fig. 2). SPT-N values were found to be particularly high near the fault areas (N50 pulses/30cm). After 50 blow count in the SPT values were obtained using automatic pile driver.

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During the SPT, the blow counts are highly sensitive to the length of rods, hammer energy, sampler type, borehole diameter and overburden stress (Idriss and Boulanger 2008, 2010). Thus, a corrected penetration resistance is obtained using raw SPT data and a number of correction factors as shown in equation, N60 ¼ ðCE CR CB CS CA CBF CC ÞNm

ð1Þ

N1;60 ¼ ðCN Þ N60

ð2Þ

where CN, CE, CR, CB, CS, CA, CBF, and CC are the correction parameters whereas Nm is the SPT blow count obtained in-situ (McGregor and Duncan 1998; Idriss and Boulanger 2008, 2010; ASTM D1586). While all corrections are applied to discrete grained soils, overburden correction factor (CN) and ram impact frequency (CBF) corrections are not practiced on fine-grained soils (McGregor and Duncan 1998). For fine grained soils the equation with general corrections is as follows; N60 ¼ ðCE CR CB CS CA CC ÞNm

ð3Þ

Although PMT is comparatively time-consuming, more complex, and expensive to perform compared to SPT, it is applicable in both soft rocks and soils and in terms of obtaining deformation modulus directly. Certain other variables can also be measured directly with the PMT method. Pressuremeter tests were performed using a Menard Pressuremeter (Menard 1957). ASTM D4719-00 standard was used during this experiment. Constant pressure was applied to the walls of the boreholes by means of the expanding probe. At the end of this experiment, limit pressure (PL) and Menard deformation modules (EM) values were obtained from these pressure volumetric deformation diagrams (Menard 1957; Baguelin et al. 1978; Mair and Wood 1987; Clarke 1995; ASTM D4719-00 2000). PL is the pressure at which the volume of the probe is doubled to the original soil space volume (ASTM 1994). EM is calculated from the slope of the pseudo-elastic part of the corrected pressure-volume curve. These parameters obtained after the experiment are used to calculate the bearing capacity of the soil. Calibration tests like the pressure loss test, volume loss test, and adjusted pressure difference was performed for each well. In the experimental phase, the level difference between the middle level of the Menard pressuremeter and the ground surface was measured as 60 cm. A pressure value of 0.06 bar due to this level difference in the calculations was added to the pressure data. The pressuremeter modulus is determined as follows: ΔP EM ¼ 2ð1 þ γ ÞðV 0 þ V M Þ ΔV

ð4Þ

where EM is pressuremeter modulus (kPa), an arbitrary modulus of deformation as related to the pressuremeter based on data reduction included, γ is Poisson ratio (ASTM D4719-00). These in-situ tests were applied at 10 different boreholes with 1.5 m increments to determine the soil elasticity parameters. The PMT test can be influenced by many factors such as well collapse and groundwater presence. Due to these conditions, some levels of EM and PL values could not be calculated. The PMT tests were completed at a total of 33 different levels of the boreholes (Table 1). EM and PL values were correlated with the SPT-N60 and Vs velocity results in the study. The Atterberg limits are a basic measure of the critical water contents of a fine-grained soils. Casagrande test equipment is used to determine the liquid limit. The Plastic Limit (PL) is determined by rolling out a thread of the fine portion of a soil on a flat, non-porous surface. In the first stage of laboratory experiments, the physical properties of clay levels are determined (Table 1). It is found that the silt and clay grains represent more than 80% of all the soil samples according to sieve and hydrometer analyses (ASTM D7928-17). Passive and active source measurements of surface waves have been widely used in site investigations. Data acquisition in the field is much

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Fig. 2. Geological map of the study area and geological cross-section of NE-SW line.

easy and less time-consuming as compared to the in-situ tests. Methods are based on the determination of Vs velocity values by taking advantage of the dispersion analysis of surface waves (Park et al. 1999; Xia et al. 1998, 2002; Miller et al. 1999; Dikmen et al. 2010a, 2010b; Akkaya and Özvan 2019). Vs velocity for the study area was obtained as a function of the depth that uses the multichannel analysis of surface waves (MASW) technique. The MASW method, which is a widely used, active- source type surface-wave method, was performed at 28 sites

in this study. MASW data was collected with multiple channel seismographs to which the sledgehammer was the impulse source. Low-frequency vertical geophones with 4.5 Hz (Figs. 2–3) were utilized for this purpose as well. Data acquisition parameter was selected with a record length of 1–2 s and a 1 ms sampling rate. The MASW data were acquired as a linear receiver array spacing from 5 m. Some of the MASW measurement results obtained in the study area are shown in Fig. 4.

İ. Akkaya et al. / Journal of Applied Geophysics 171 (2019) 103865

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Fig. 3. View of an SPT and PMT (a), and MASW data collection and processing (b).

4. Statistical evaluation Regression analyses are commonly used for geotechnical investigations. As the first condition for safe regression analysis, the data set

must be interrelated and comparable. The SPT-N60, EM, and Vs values are significant parameters that may change depending on physical and mechanical properties of the soil, and therefore are related to each other (Fig 5; Table 2). However, no empirical equation between

İ. Akkaya et al. / Journal of Applied Geophysics 171 (2019) 103865

6 Table 1 The measured soil parameters in this study No

Soil type

SPT-N60

Liquid limit, LL

Plastic Limit, PL

Plasticity index, PI

Moisture content, w (%)

Density (gr / cm3)

Em (MPa)

PL (MPa)

Vs (m/s)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 min max Average Std

CH CH CL CL CL CH CH CL CH CH CH CH CH CH CH CL CH CH CL CH CH CH CH CH CL CL CL CL CL CL CL CH CL

21.4 43.8 71.3 74.8 77.0 68.3 76.5 24.2 19.8 33.5 21.4 16.9 31.2 51.0 69.1 83.4 58.4 95.3 111.8 47.0 70.5 110.4 127.5 168.0 17.2 71.3 128.3 17.4 24.9 35.6 55.6 141.8 147.8 16.9 168.0 67.0 42.3

66.0 66.0 44.0 44.0 88.0 56.0 60.0 46.0 58.0 72.0 63.0 76.0 80.0 52.0 50.0 51.0 51.0 49.0 41.0 65.0 62.0 56.0 74.0 49.0 26.0 34.0 34.0 48.0 48.0 46.0 53.0 45.0 61.0 26.0 88.0 55.0 13.7

27.0 27.0 20.0 18.0 28.0 26.0 25.0 18.0 20.0 22.0 22.0 26.0 28.0 21.0 20.0 23.0 23.0 19.0 18.0 23.0 22.0 21.0 26.0 18.0 15.0 18.0 21.0 18.0 18.0 20.0 24.0 20.0 21.0 15.0 28.0 21.7 3.4

39.0 39.0 24.0 26.0 60.0 30.0 35.0 29.0 39.0 49.0 41.0 50.0 52.0 31.0 30.0 28.0 28.0 30.0 23.0 42.0 40.0 34.0 48.0 31.0 11.0 16.0 13.0 30.0 30.0 26.0 29.0 25.0 39.0 11.0 60.0 33.2 11.0

16.35 24.40 20.21 12.65 23.48 16.33 21.16 17.12 31.20 29.30 31.10 23.33 23.93 21.60 22.29 22.76 27.45 21.07 23.99 17.43 20.94 20.89 19.75 19.44 19.00 11.60 18.00 26.09 17.80 23.57 27.22 22.63 20.55 11.6 31.2 21.7 4.6

2.11 2.03 2.13 2.10 1.98 2.03 2.06 1.93 1.97 1.82 1.92 1.85 1.92 2.07 2.01 2.02 2.00 2.10 2.02 2.14 2.10 2.09 2.08 2.08 2.05 2.06 2.06 2.06 1.99 2.01 1.96 2.04 2.09 1.8 2.1 2.0 0.1

19.31 31.58 35.43 41.49 38.77 39.06 34.28 14.95 12.64 25.90 23.10 20.10 23.18 32.85 34.56 43.83 39.73 41.08 49.97 28.78 40.66 47.91 59.07 65.89 13.27 51.49 62.00 5.87 9.43 9.67 17.37 49.30 55.21 5.9 65.9 33.9 16.3

0.87 3.25 2.54 3.84 3.83 3.13 2.12 1.78 1.66 3.53 2.68 2.14 2.05 4.22 3.19 3.73 5.26 3.68 3.89 3.10 3.45 4.07 3.14 3.86 1.67 5.53 5.15 0.99 1.07 1.02 2.36 6.71 5.40 0.9 6.7 3.2 1.4

288 292 375 378 382 388 392 252 232 220 202 285 299 309 314 316 319 348 368 258 387 437 473 485 311 398 433 211 233 268 310 425 445 202.0 485.0 334.3 78.4

the Vs and the EM parameters was present in the literature until this study. In this paper, EM values of boreholes were calculated for 33 different pressuremeter test levels, and together with the SPT-N60 values from 33 of 97 SPT data, and 33 of 292 Vs velocity values, they were used as the

comparable data (Table 1). Fistly, statistical analyses were carried out to calculate empirical relations between the SPT blow counts (SPTN60) and Vs velocity data. SPT-N60 and Vs data used in the analysis were calculated from various levels of depths, ranging from 1.5 m to 20 m. The results of the regression analysis as follows;

Fig. 4. Demonstration of some data samples includes the EM, SPT-N60, and Vs variation with depth.

İ. Akkaya et al. / Journal of Applied Geophysics 171 (2019) 103865

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Fig. 5. SPT-N60 - Vs relations obtained from the some literature and from this study (a), comparison of the measured data obtained in this study with some SPT-N60 - Vs relationships derived from the literature (b).

The Vs velocities obtained using Eq. (5) obtained in this study, and some of the earlier recommended formulae, are shown in Table 2, versus the SPT-N60 data that are plotted for high and low clay types of

soils in Fig. 5a. Although the proposed relationships are more suitable for CL-CH type soils like the study area, the proposed formula was also determined to be compatible with certain other equations, such as the

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Table 2 Some available correlations from SPT-N60 for EM and Vs in the literature. Researcher(s) EM

Briaud (1992) Yagiz et al. (2008) Bozbey and Togrol (2010) Kayabaşı (2012) Ağan (2011) Cheshomi and Ghodrati (2015)

Vs (m/s)

Özvan et al. (2018) Kanai (1966) Imai and Yoshimura (1970) Fujiwara (1972) Shibata (1970) Ohsaki and Iwasaki (1973) Imai et al. (1975) Imai (1977) Ohta and Goto (1978) Seed and Idriss (1981) Imai and Tonouchi (1982) Seed et al., 1983 Sykora and Stokoe (1983) Lee (1990) Pitilakis et al. (1999) Athanasopoulos (1995) Sisman (1995) Iyisan (1996) Kayabalı (1996) Jafari et al. (1997) Kiku et al. (2001) Jafari et al. (2002) Hasançebi and Ulusay (2007) Ulugergerli and Uyanık (2007) Dikmen (2009) Akın et al. (2011)

All soils blows

Em ¼ 383N 60 ðkPaÞ 30cm EM = 388N60 + 4554 (kPa) EM = 0.29(N60)1.4 (MPa) Vs = 19N0.6 Vs = 76N0.33 Vs = 92.1N0.337 Vs = 81.4N0.39 Vs = 89.9N0.341 Vs = 91N0.337 VS = 85.35N0.348 Vs = 61.4N0.5 VS = 97N0.314 Vs= 107.6N036 VS = 32.8N051 Vs = 51.5N0-516 VS = 22N0.85 Vs = 68.3 N0.292 Vs = 90N0.309 VsU=23.291*LN(N)+405.61 VsL=52.9e-0.011N VS = 58N0.39 Vs = 121.75N0.101z0.216

ones proposed by Imai and Yoshimura (1970), and Dikmen (2009) in the literature. As can be seen in Fig. 5b, approximately 80 to 90% of the Vs velocities were estimated within a below 20% error margin. These results show that the proposed relationships for the consolidated type of clay soils indicate a better forecast than those from former existing correlations. Regression analysis was performed with the Vs dependent variable and the independent variable SPT-N60. When the difference between the measured and calculated Vs values from the regression analysis was examined, the values were found to be quite close to each other (Fig. 5b).   R2 ¼ 0:75 Vs ¼ 108:49 N 0:281 60

ð5Þ

The equation with the highest determination coefficients (R2) of the regression was obtained by a power function (Fig. 6a). In addition, high determination coefficients were obtained in linear and logarithmic regressions as well (Fig. 6a).   Vs ¼ 1:4629N60 þ 241:82 R2 ¼ 0:78

ð6Þ

  Vs ¼ 93:268 LNðN60 Þ−30:64 R2 ¼ 0:78

ð7Þ

Empirical relations between Vs and SPT-N60 were evaluated by a power function with the effect of the depth (z). Eq. (8) are applicable up to 20 m depth for the study region.   0:272 0:017 z R2 ¼ 0:78 Vs ¼ 109:94 N60

ð8Þ

Sands

Clays

-

-

EPMT(MPa) = 1.33(N60)0.77(MPa) EMPT = 0.922(N60) − 8.1362 (MPa) Vs = 31.7N0.54 Vs = 59.4N0.47 Vs = 80.6N0.331 Vs = 56.4N0.5 Vs = 100.5N0.29 Vs = 57N049 Vs = 162N017 Vs = 175 +(3.75 N) Vs = 90.82N0.319 -

EPMT(MPa) = 1.61(N60)0.71(MPa) EPMT ¼ 10N 60 −26:7 ðMPaÞ Pa EM = 2.611 N60 − 26.03 (MPa) Vs = 80.2N0.292 Vs = 114N031 VS = 27N0.73 Vs = 97.89N0.269 -

VS = 73N0.33 Vs = 52.04N0.359z0.177

VS = 44N0.48 Vs = 78.1N0.116z0.35

Cd is defined as the normalized consistency ratio for measured and calculated parameters. Cd ¼ ðVsM −VsC Þ=SPT−N60

ð9Þ

where VsM is the measured and VsC is the calculated Vs from Eq 5 and SPT-N60 values corresponding to VsM. The closer the Cd values to zero, the better the compatibility in the prediction of Vs value was obtained. In this study, the proposed equations have suitable prediction except for small SPT-N60 values (SPT-N60 b 25) (Fig. 6b). When the obtained data are analyzed, it was seen that SPT-N60 and Vs values increase as the depth increases (Fig. 6c–d). Although there are many studies related to the relationship between SPT-N and Vs values, and the relationship between SPT-N and EM values, no empirical equation was suggested in the literature between the Vs and the EM parameters. The results of the regression analysis as follows;   EM ¼ 0:1819 Vs−26:94 R2 ¼ 0:77

ð10Þ

The equation with the high determination coefficients (R2) of the simple statistical regression analysis between the EM and Vs gives Eq 10 with a linear function (Fig. 7a). In addition, high determination coefficients were obtained in power (Eq 11) and logarithmic (Eq 12) regressions (Fig. 7a). Consequently, it is determined that the EM values obtained from Vs test results can be used to calculate settlement and bearing capacity of the consolidated clayey soils of the high and low plasticity (CH-CL). The obtained relationships are valid in the Vs velocity limit value range from 200–500 m / s.   EM ¼ 0:0002 Vs2:03 R2 ¼ 0:66

ð11Þ

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  EM ¼ 57:687 LNðVsÞ−299:82 R2 ¼ 0:74

ð12Þ

As in the relationship between Vs and SPT-N60, the normalized coefficient ratio (Cd) was also calculated. CdEM ¼ ðEMM −EMC Þ=Vs

ð13Þ

where EMM is measured pressuremeter test, EMC is calculated from equations (10). CdEM values next to zero, which means that the suggested equations have suitable in the prediction of Vs (Fig. 7b). When the obtained data are analyzed, it is seen that EM and Vs values increase as the depth increases (Fig. 7c–d). The statistical analysis indicates that the non-linear multiple regression approach is more suitable than the linear multiple regression. In the nonlinear multiple regression steps of the statistical studies, the relationships between the EM with the SPT-N60 and Vs were evaluated together. First, it was defined as a function of the EM parameters of the SPT-N60 and Vs value. EM ¼ f ðVs ; N60 Þ After this definition, the relationships between the different combinations of Vs and SPT-N60 values were evaluated. A, B, C, and D are the coefficients of the equations. The non-linear multiple regression equations obtained are given as follows; Em ¼ A þ BN 60 þ CVs

EM ¼ −39:32 þ 2:461N60 þ 0:637 Vs

9

ð14Þ

Em ¼ ANB60 þ CVsD EM ¼ 20:076 N0:627 þ 0:00002 Vs2:579 60

ð15Þ

Em ¼ ANB60 VsC 0:0574 EM ¼ 5:29 N 0:38 60 Vs

ð16Þ

Em ¼ AH B NC60 VsD EM ¼ 0:236 H 0:061 N 0:569 Vs0:428 60

ð17Þ

High correlation coefficients between EM(measured) and EM(predicted) from the Formulas 14–17 produced show that the SPT-N60 value has an important and significant effect in Vs velocity prediction. Analysis of statistical suitability was performed for the measured EM, Vs and SPT-N60 values. All results of this analysis are given in Table 3. The suitability of the data set was determined for all equations. Then, regression analyses were performed using package commercial software (SPSS v23, OriginPro, JMP 8). Table 3 shows the results of this study. Especially in multiple regressions, high determination coefficients were obtained. In the case of multiple regression analysis, the adjusted R2 value must be taken into account. If the value of R2 is between 0.84 and 0.66, indicating that the models are highly represented. It shows that 66% to 84% of the change

Fig. 6. Correlations between SPT-N60 and Vs values (a), normalized consistency ratio (b), SPT-N60 values change with depth (c), Vs values change with depth (d).

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Fig. 7. Correlations between EM and Vs values (a), normalized consistency ratio (b), EM values change with depth (c), Vs values change with depth (d).

in the dependent variable (EM) can be explained by independent variables (SPT-N60 and Vs) entering the model. In addition, the ANOVA (Variance Analysis) test provided the results of the F test, indicating the significance of the whole model (Table 3). If the F test value is found to be significant, it can be concluded that our model is statistically significant in its entirety. The significance value for this analysis was b0.0001. This means that our regression model is strongly meaningful. Regression analysis was performed with the EM dependent variable and the independent variable Vs and SPT-N60. When the difference between the measured and calculated EM values from the regression analysis was examined, the values were found to be quite close to each other (Fig. 8).

5. Results and discussions As part of this study, SPT, PMT, and Vs measurements were performed in the study area. Using the obtained statistical relationships between EM-SPT-N60 and EM-Vs values, EM values were calculated and mapped for the study area. The Vs velocity and EM values maps for the first 1.5 m obtained with the data used in the study area is given in Fig. 9, up to a depth of 10 m. When the zone map obtained from the data in the study area is examined, it can be seen that there are different soil characteristics in the old lake deposits. The changes in the mechanical parameters of the ground are especially prominent in areas close to Van Fault in the northern site of the study region (Fig. 9).

Table 3 Statistical results of multiple regression analysis including the EM dependent variable and SPT-N60 and Vs independent variables. Summary of fit

Eq5 Eq6 Eq7 Eq8 Eq10 Eq11 Eq12 Eq14 Eq15 Eq16 Eq17 a

Analysis of variance

R2

R2 Adj

RMSEa

Mean of Response

Observations (or Sum Wgts)

F Ratio

Prob N F Sig.

Sum of Squares

Mean Square

0.75 0.78 0.78 0.78 0.77 0.66 0.74 0.85 0.84 0.84 0.79

0.75 0.77 0.77 0.78 0.76 0.65 0.73 0.84 0.84 0.83 0.79

33.58 35.59 27.01 84.76 79.24 77.74 84.65 63.97 62.26 62.87 62.40

338 338.2 338.2 338.2 338.69 338.69 338.69 338.69 338.69 338.69 338.69

63 63 36 63 33 33 33 33 33 33 33

112.8 110.17 77.75 112.53 103.65 121.8 118.09 88.32 87.25 144,3 189.4

b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001

68853.6 69793.5 69374.6 474189.7 650907.8 187374.6 222181.3 722809.01 112408.8 118406.48 112948.2

1128.7 1368.5 1444.2 7184.6 650908 6044.3 7176.1 361405 3876.2 3946.8 3894.76

Root mean square error.

İ. Akkaya et al. / Journal of Applied Geophysics 171 (2019) 103865

Fig. 8. Relationship between the calculated EM from Eq 10 to Eq 17 and the measured EM.

Fig. 9. Vs (a) and EM (b) distribution maps of the study area (upper panel: up to 1.5 m, lower panel: up to 10 m).

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The Van (Everek) thrust fault, which is one of the active faults in the east of Lake Van, caused a destructive earthquake (M w=7.1) on 23 October 2011. This fault, which has an approximately eastwest direction and is dipped to the north, also affected the old lake deposits in the study area. This fault lies to the north of the study area and extends from the southwest of the study area towards the Lake Van (Figs. 1 and 2). During this compression period, stresses along the fault zone have caused orientations on the soil layers. These stresses are the reason for the different engineering parameters measured in the old lake sediments. Stresses along the Van Fault effect zone also caused deformations on the ground. It has been determined that these deformations especially influence the results obtained towards the thrust fault in the hanging wall. Fig. 9a–b shows that higher EM and Vs values were calculated close to the Van Fault zone. The E M values are reduced as they move away from the fault, with the exception of some local points (Fig 9b). As the depth increases, the EM values increase, particularly in the hanging wall area within the fault zone (Fig 9blower panel). Fig. 10 shows that the variations of the EM and Vs resulting from the depth along the cross-section of the NE-SW line with the A-B profile given in Fig. 2. There was a significant change in both EM and Vs values in the fault zone in these sections (Fig. 10).

6. Conclusion A new empirical equation between EM and Vs and between Vs and SPT-N60 were developed in this study. Experimental relationships that can be used for practical purposes have been obtained with these important parameters, which are commonly utilized in soil characterization. The equations obtained as part of this study have high determination coefficients (R2) in both linear and nonlinear multiple statistical analyses. This is indicative that the empirical equations developed in this study are within statistically acceptable limits. Consequently, these equations can prove useful for the calculation of soil parameters in geotechnical engineering projects involving consolidated clayey soils of high and low plasticities (CH-CL). Since the soil characteristics are heterogeneous and anisotropic, it was not possible to make a linear correlation between the in-situ data regressions in statistical analysis in this study. Therefore, it is more appropriate to use the equations produced from logarithmic and exponential relations in the regressions. The proposed equations have suitable prediction capabilities except for small SPTN 60 values (SPT-N 60 b 25). The developed correlations can be used for medium and stiff soils, especially for those of CL-CH type. The obtained relationships are valid in the Vs velocity limit value ranging from 200–500 m/s.

Fig. 10. Variations of EM (a) and Vs (b) values with the depth along the cross-section of NE-SW line.

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