Introduction

In addition to the structural quality, surface deformations (liquefaction, lateral spreading, etc.) which occur due to adverse soil properties, have a significant role in the loss of life and property during earthquakes. Liquefaction occurs as a result of earthquakes in loose sandy, silty soils and areas with shallow groundwater level. Pore water pressure between the soil particles increases due to earthquake waves during liquefaction. Once, the pore water pressure and the total stress are equal, the frictional force between the soil particles, in other words, the effective stress reaches to zero. Thus, bearing capacity and sudden settlement problems occur in the foundation ground and there may be significant structural problems such as overturning of structures. Liquefaction is mostly observed after moderate to high magnitude earthquakes. It is very important to determine the liquefaction potential of the ground under dynamic loads to prevent damage due to liquefaction.

Following the 1964 earthquake in Japan, lots of studies have been carried out to explain soil liquefaction. Shear wave velocity measurements, CPT and SPT, have been used by many researchers for determining the liquefaction potential of soils (Seed and Idriss 1971; Dobry et al. 1982; Iwasaki et al. 1982; Tokimatsu and Yoshimi 1983; Ishihara 1996; Kramer 1996; Robertson and Wride 1998; Juang et al. 2003; Cetin et al. 2004; Idriss and Boulanger 2006, 2008; Yi 2010). In addition, Andrus and Stokoe (2000), Uyanık (2002), Uyanik and Taktak (2009), Uyanik et al. (2013a) developed liquefaction analysis methods that depend upon the S wave velocity. Several empirical formulas were developed to determine the liquefaction potential using SPT-N values and V s data using Seed and Idriss (1971) method (Dikmen 2009; Akın et al. 2011; Hasançebi and Ulusay 2007). V s which is an important parameter used in earthquake engineering, is mainly used for determining the dynamic properties and liquefaction potential of soils (Karastathis et al. 2002; Soupios et al. 2005; Uyanık et al. 2006; Tezcan et al. 2006; Bozcu et al. 2007; Dadashpour et al. 2009; Uyanık and Ulugergerli 2008; Uyanik 2010, 2011; Uyanik et al. 2013b).

The SPT-N and V s values are important physical parameters that may vary depending on porosity, effective stress, and relative density. V s velocity is considered to be an easy and fast method as it can be applied both in the field and in the laboratory. In particular, liquefaction analysis based on V s data, which can be easily obtained in environments where the SPT and CPT measurements cannot be performed, has been frequently used in recent years (Dobry et al. 1981b; Seed et al. 1983; Tokimatsu and Uchida 1990; Kayen et al. 1992; Andrus and Stokoe 2000; Uyanık 2002, 2006; Uyanik and Taktak 2009; Uyanik et al. 2013a; Duman and Ikizler 2014; Pekkan et al. 2015).

The liquefaction analysis methods based on SPT and laboratory data are frequently used. The studies in which liquefaction analysis methods based on SPT and V s wave velocities coexist are limited.

In this study, Erciş (Van, Turkey) settlement area, which is under the effect of three different major fault zones, is selected as the study location. Erciş residential area is the largest district of the region located at the north of Lake Van, with more than 150,000 inhabitants (Fig. 1). A catastrophic earthquake of 7.1(M w) shook the study area on 23rd October, 2011 at 13:41 local time (KOERI 2011). As a result of this earthquake, lateral spreading and liquefaction occured in the Erciş settlement area and in the close vicinity (Akın et al. 2013, 2015a, b; Aydan et al. 2012, 2013). The earthquake heavily damaged hundreds of buildings in Van and Erciş city, rendering them unusable. The Erciş settlement is classified in the first-degree seismic hazard zone of Turkey (ABYYHY 1997).

Fig. 1
figure 1

Location map of the study area

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In this study, the grain size distribution of recent loose sediments and the presence of groundwater as well as the seismicity of the region were jointly investigated to determine the liquefaction potential of the subsurface soil. Liquefaction analysis was conducted using the V s velocities and SPT-N values. Moreover, the advantages and disadvantages of these methods were highlighted by performing liquefaction analyses using both SPT and V s data in a model area. Four different methodologies (SPT-based LPI and LSI, V s-based threshold acceleration and safety factor) used for the assessment of liquefaction potential were taken into consideration. Moreover, the results of both methods were compared. Additionally, the liquefaction potential of the study area was determined on the basis of different magnitude earthquakes using the seismic data complied from 21 different sites along with the SPT values collected from a total of 165 different boreholes (Fig. 1). Finally, maps presenting the liquefaction potential were prepared and the results of the analyses were discussed. Different earthquake scenarios for three different active faults that can produce large earthquakes in the selected area were considered in these analyses.

Geology of the study area

The Lake Van basin, involving the Erciş settlement, consists of Late Cretaceous ophiolites and Tertiary marine sediments (Fig. 2a). A number of dissimilar rock masses and alluvium are traced in some locations of the Lake Van as shown in the geological map illustrated in Fig. 2b.

Fig. 2
figure 2

The general geological map of Lake Van basin (modified from MTA, 2007) (a), geological map of Erciş (b) (Picture 1, 2, 3 and 4 refers to Quaternary aged alluvium units)

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The Erciş province and its surroundings consist of three main geological units which are the basement rocks of the Erciş region. The limestone unit which is also known as the Lower Miocene aged Adilcevaz limestone, Pliocene–Pleistocene aged volcanics and volcano-sedimentary clasts and Quaternary–Holocene aged recent, and old alluviums and old lake sediments are the major geological units in the study area (Fig. 2). Volcanism occurred in various stages from Pliocene to Quaternary with different volcanic units in the region (Özdemir et al. 2006, 2016; Özdemir and Güleç 2014; Oyan et al. 2016). Erciş settlement is covered by old alluvial deposits of Quaternary age and the recent alluvium around Zilan Creek with Holocene age. This unit is comprised of loose and soft clay, sand, silt and gravels.

The groundwater level is shallow particularly around the Lake Van considering the borehole data (Fig. 3). While the groundwater level in the study area is generally observed after 5 m in old lake sediments, it is shallower than 5 m in the coastal sections of Lake Van and around Zilan Creek in recent alluvial deposits (Özvan et al. 2008; Akın et al. 2015a, b) (Fig. 3).

Fig. 3
figure 3

Depth to groundwater level map of the study area

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Seismic characteristics of the region

Erciş and its surroundings is located in the Lake Van basin at the Eastern Anatolian Plateau, that was formed due to the collision of Arabian and Eurasian Plates in Late Miocene (Şengör and Yılmaz 1981; Şengör and Kidd 1979; Koçyiğit et al. 2001). Attributable to these crustal movements, north–south direction compression in the region, east–west trending reverse faults and main folding axis and northeast–southwest left-lateral and northwest–southeast right-lateral strike-slip faults and north–south trending normal faults were developed (Şaroğlu and Yılmaz 1986; Koçyiğit et al. 2001; Bozkurt 2001; Koçyiğit 2013). The activity of all these tectonic structures supports the ongoing seismic activity in the region (Fig. 4, Table 1).

Fig. 4
figure 4

a Tectonic map of Turkey. b Simplified tectonic map of Eastern Anatolia (AFZ Aşkale fault zone, BFZ Başkale fault zone, ÇFZ Çobandede fault zone, ÇAFZ Çaldıran fault zone, EAFS East Anatolian fault zone, EKFZ Erciş–Kocapınar fault zone, NAFS North Anatolian fault zone, KF Kağızman fault zone, MGFZ Muş–Gevaş thrust to reverse fault zone, TF Tutak fault, VTF Van thrust fault, VFZ: Varto fault zone) (modified from Koçyiğit, 2013) c the distribution of earthquakes (M > 4.0) around the Lake Van

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Table 1 Major Earthquakes (M ≥ 5) around the Lake Van between 1900 and 2017 (KOERI http://www.koeri.boun.edu.tr/sismo/2/en/ )
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The Lake Van basin and its surrounding area has a very complex seismotectonic setting and active fault zones, such as Çaldiran fault zone, Çolpan fault, Erciş–Kocapınar fault zone, Süphan fault, Everek fault, Alaköy fault, Özalp fault, Gürpınar fault zone and Van thrust fault (Koçyiğit 2013; Selçuk 2016) (Fig. 4). Numerous devastating earthquakes have been documented around the Lake Van basin in the last century, such as 1941 Erciş (M s = 5.9); 1945 Van (M s = 5.8); 1966 Varto (M s = 6.8); 1903 Malazgirt (M s = 6.3); 1976 Çaldıran (M s = 7.3); 2011 Van (M w = 7.1) and 2011 Van (M w = 5.6) earthquakes (Ambraseys 2001; Koçyiğit 2013). Erciş–Kocapınar Fault, Çaldıran Fault and Van Fault are important fault zones that can adversely affect the study area.

Liquefaction analyses

In the study area, liquefaction analyses were carried out according to different liquefaction analysis methods as well as dissimilar magnitude and acceleration values that can be produced by three different active faults. Experimental data of 165 boreholes drilled in the study area were used to evaluate Liquefaction Potential (LPI) and Liquefaction Severity (LSI) Index (Table 2). LPI (Iwasaki et al. 1982) and LSI (Sonmez and Gokceoglu 2005) values were calculated using the liquefaction safety factor of every geotechnical borehole. Idriss and Boulanger (2008) method, which depends on the ratio between cyclic stress ratio (CSR) and cyclic resistance ratio (CRR), was utilized for the determination of safety factor against liquefaction.

Table 2 The utilized data of the geotechnical boreholes within the study area
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It is inevitable to use V s as a parameter for the determination of liquefaction resistance. In this sense, seismic surface wave measurements (MASW) were performed at 21 points in the study area (Table 3). In this study, liquefaction analyses based on calculated V s values and geotechnical data were performed.

Table 3 Seismic measurement points in Erciş settlement area
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Calculated LPI, LSI, \(V_{{{\text{s}}_{30} }}\) distribution, liquefaction potential according to threshold acceleration criteria, and safety factor liquefaction potential maps obtained according to V s velocities were prepared using ArcMap10 Geographic Information Systems software. Inverse Distance Weighting (IDW) statistical method was utilized during the preparation of the maps. IDW interpolation designates cell values using weighted combination of sample points (Watson and Philip 1985).

Attenuation relationship for the determination of peak ground acceleration (a max)

In this study, scenario earthquakes were initially designed, and then liquefaction analyses were performed. Equations of liquefaction analyses are highly dependent on the peak ground acceleration (a max) which is an important parameter for the scenario earthquakes.

In the liquefaction analyses based on SPT and V s, active faults that may affect and/or affected the Erciş settlement area and the largest earthquakes that occurred in the region were considered. As a result of these analyses, magnitude (M), distance (R) and acceleration calculations were performed for three different active faults (Erciş–Kocapınar, Çaldıran and Van fault) that can adversely affect the study area (Table 4, Fig. 5). Major earthquakes that hit the region were gathered from the Kandilli Observatory and Earthquake Research Institute (KOERI) earthquake data. Each earthquake was expressed in terms of M w using the magnitude conversion relations suggested by Kadirioğlu and Kartal (2016) after determining the largest earthquakes that occurred on three active faults (Table 4). Kadirioğlu and Kartal (2016) proposed M S to M w conversion as follows;

Table 4 Scenario earthquake parameters used in liquefaction analyses
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Fig. 5
figure 5

Peak ground accelerations of Erciş, Çaldıran and Van faults that may affect the study area

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$$\begin{aligned} M_{\text{w}} = \,0.5716\,( \pm 0.024927)\,M_{\text{s}} \, + \,\,2.4980\,( \pm 0.117197)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,3.4\, \le \,M_{s} \, \le 5.4 \hfill \\ M_{\text{w}} = \,0.8126\,( \pm 0.034602)\,M_{\text{s}} \, + \,\,1.1723\,( \pm 0.208173)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,M_{\text{s}} \, \ge 5.5. \hfill \\ \end{aligned}$$
(1)

Using the magnitude and distance parameters obtained from the analyses, accelerations were calculated with the ground motion prediction model proposed by Graizer and Kalkan (2015). The obtained data were used as scenario earthquakes in SPT and V s-based liquefaction analyses. Ground motion prediction equation (GMPE) developed by Graizer and Kalkan (2015) is as follows;

$${ \ln }(Y) = { \ln }(G_{1} ) + { \ln }(G_{2} ) + { \ln }(G_{3} ) + { \ln }(G_{4} ) + { \ln }(G_{5} ) + \sigma_{{{ \ln }\left( {\text{PGA}} \right)}} ,$$
(2)

where \(\sigma_{{{ \ln }\left( {\text{PGA}} \right)}}\) is the random variability and Y is the PGA. The formulations of G 1, G 2, G 3, G 4, and G 5 are given,

$$\begin{aligned} \ln (G_{1} ) & = \ln [(c_{1} \cdot \arctan (M + c_{2} ) + c_{3} ) \cdot F] \\ \ln (G_{2} ) & = - \,0.5\, \cdot \ln \left[ {\left( {1 - R/(c_{4} .M\, + \,c_{5} )} \right)^{2} \, + \,4.\left( {c_{6} \, \cdot \cos \left[ {c_{7} \cdot (M + c_{8} )} \right]\, + \,c_{9} } \right)^{2} \, \cdot \left( {R/(c_{4} \cdot M\, + \,c_{5} )} \right)} \right] \\ \ln (G_{3} ) & = \, - c_{{10}} \cdot R/Q_{0} \\ \ln (G_{4} ) & = \,\,b_{v} \cdot \ln (V_{{{\text{s}}_{{30}} }} /V_{{\text{A}}} ) \\ \ln (G_{5} ) & = \,\ln \left[ {1\, + \,A_{{{\text{Bdist}}}} \cdot A_{{{\text{Bdepth}}}} } \right]\, \\ A_{{B{\text{depth}}}} & = \,\,1.077/\sqrt {\left[ {1 - (1.5/(B_{{{\text{depth}}}} + 0.1))^{2} } \right]^{2} + \,\,4 \cdot 0.7^{2} \cdot (1.5/(B_{{{\text{depth}}}} + 0.1))^{2} } \\ A_{{B{\text{dist}}}} & = \,\,1/\sqrt {\left[ {1 - (40/(R + 0.1))^{2} } \right]^{2} + \,\,4 \cdot 0.7^{2} \cdot (40/(R + 0.1))^{2} } \\ \end{aligned}$$
(3)

where M is moment magnitude, F is the style of faulting, and R is the nearest distance to fault rupture plane (km). Q 0 is regional quality factor, and B depth basin depth under the site (km). c 1–10, b v and V A are coefficients. The model established by Graizer and Kalkan (2015) may be employed for the earthquakes with moment magnitudes of 5.0–8.0, distances from 0 to 250 km, spectral periods of 0.01–5 s and average V s from 200 to 1300 m/s.

SPT-based liquefaction analyses

Liquefaction analyses were carried out according to the cyclic stress approach. The method proposed by Idriss and Boulanger (2006, 2008) and based on SPT was used in the present research. The liquefaction safety factor is explained as the ratio of the CRR that results in liquefaction for a certain cycle number, to the CSR, generated in the soil as a result of earthquake motion.

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,

$$\left( {N1} \right)_{60} = \, C_{\text{N}} C_{\text{E}} C_{\text{R}} C_{\text{B}} C_{\text{S}} N_{\text{m}} ,$$
(4)

where C N, C E, C R, C B, and C S are the correction parameters whereas N m is the SPT blow count obtained in situ (Idriss and Boulanger 2008, 2010).

The safety factor (FS) against liquefaction is determined considering the influence of the magnitude scaling factor (MSF). The corrected SPT-(N 1)60 values are taken into consideration in the factor of safety analysis as suggested by Youd et al. (2001) and Idriss and Boulanger (2008).

$${\text{FS = }}\frac{\text{CRR}}{\text{CSR}}\,{\text{MSF,}}$$
(5)

FS is the ratio of CRR to CSR, which is an indication of the shear resistance of the soil deposit to liquefaction (CRR) under the influence of the maximum shear stress (CSR) generated by an earthquake. Since the Eq. 5 is appropriate for the magnitude 7.5 earthquakes; a MSF developed by Seed and Idriss (1982) for the earthquakes of diverse magnitudes are used in this study. The soils are assumed to be liquefiable if the safety factor ≤ 1; potentially liquefiable between 1 and 1.2 and non-liquefiable if the safety factor > 1.2 (Seed and Idriss 1982).

The liquefaction resistance of soils is represented by the CRR following some essential corrections. The CRR of a soil is affected by the duration time of earthquake as well as the effective overburden stress which is expressed by a K σ factor. The K σ is commonly small for shallow ground conditions (Idriss and Boulanger 2008, 2010).

CRR is required to determine the liquefaction safety factor and is calculated as a function of SPT values (Seed and Idriss 1982; Seed et al. 1983; Idriss and Boulanger 2008). Idriss and Boulanger (2008, 2010) expressed the subsequent formula for the determination of CRR, corrected for overburden pressure and magnitude.

$$\begin{aligned} {\text{CRR}}_{{\sigma = 1}} & = \exp \left( {\left( {\frac{{\left( {N_{1} } \right)_{{60_{{{\text{CS}}}} }} }}{{14.1}}} \right) + \left( {\frac{{\left( {N_{1} } \right)_{{60_{{{\text{CS}}}} }} }}{{126}}} \right)^{2} - \left( {\frac{{\left( {N_{1} } \right)_{{60_{{{\text{CS}}}} }} }}{{23.6}}} \right)^{3} + \left( {\frac{{\left( {N_{1} } \right)_{{60_{{{\text{CS}}}} }} }}{{25.4}}} \right)^{4} - 2.8} \right)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,(N1)_{{60_{{{\text{CS}}}} }} {\text{ }} < {\text{ }}37.5{\text{ }} \\ {\text{CRR}}_{{\sigma = 1,M = 7.5}} & = 2\,\,\,\,\,\,\,\,\,\,\,\,(N1)_{{60_{{{\text{CS}}}} }} {\text{ }} > {\text{ }}37.5{\text{ }}{\text{.}} \\ \end{aligned}$$
(6)

The following methods for the calculation of CRR are for CRR7.5 and K σ correction factors should still be applied.

$${\text{CRR}} = {\text{CRR}}_{7.5} \, K_{\sigma } \,$$
(7)

Several expressions using different correction factors have been proposed by various researchers. The most recent one is the work by Idriss and Boulanger (2008). It suggests that the value of K σ should be less than 1.0 for loose and shallow sediments, and greater than 1.0 for tight grounds (Seed and Harder 1990). Idriss and Boulanger (2006) suggest the following relation for the K σ and C σ correction factors.

$$\begin{gathered} K_{\sigma } = 1\, - C_{\sigma } \ln (\frac{{\sigma _{{vo}}^{'} }}{{P_{a} }}) \hfill \\ C_{\sigma } = \frac{1}{{18.9\, - \,2.55\sqrt {\left( {N1} \right)_{{60}} } }} \hfill \\ \end{gathered}$$
(8)

Idriss and Boulanger (2008, 2010) introduced a new and up-to-date analytical approach to cyclic resistance ratio by creating a large database of liquefaction analyses. Details of this approach are listed below.

$$\begin{aligned} (N1)_{{60{\text{CS}}}} = (N1)_{60} + \Delta (N1)_{{60{\text{CS}}}} \hfill \\ \Delta (N1)_{{60{\text{CS}}}} = \exp \left[ {1.63\, + \,\left( {\frac{9.7}{{{\text{FC}}\, + \,0.01}}} \right)\, - \left( {\frac{15.7}{{{\text{FC}}\, + \,0.01}}} \right)^{2} \,} \right] \hfill \\ \end{aligned}$$
(9)
$${\text{CRR}}_{ 7. 5} {\text{ = exp}}\left[ {\frac{{\left( {N1} \right)_{{60{\text{CS}}}} }}{14.1}\, + \,\,\left( {\frac{{\left( {N1} \right)_{{60{\text{CS}}}} }}{ 1 2 6}} \right)^{2} \, - \left( {\frac{{\left( {N1} \right)_{{60{\text{CS}}}} }}{ 2 3. 6}} \right)^{3} + \,\left( {\frac{{\left( {N1} \right)_{{60{\text{CS}}}} }}{ 2 3. 6}} \right)^{4} \, - \,2.8} \right].$$
(10)

The CSR under earthquake loads is usually explained as a characteristic rate corresponding to 65% of the maximum cyclic shear stress at a certain depth, z. The CSR is calculated by an equation that considers acceleration, total and effective stresses at various depths, non-rigidity of the deposit, and several assumptions. Seed and Idriss (1971) presented an equation for the calculation of CSR as follows.

$${\text{CSR}} = \frac{{\tau_{\text{av}} }}{{\sigma_{vo}^{\imath } }}\, = \,\,0.65\left( {\frac{{a_{\hbox{max} } }}{g}} \right)\left( {\frac{{\sigma_{vo} }}{{\sigma_{vo}^{\imath } }}} \right)r_{d}$$
(11)

where τ av is the mean cyclic shear stress triggered by earthquake and is accepted to be 65% of the maximum induced stress, g is the acceleration of gravity, a max is the peak ground acceleration (g), σ v0 and σ’ v0 are total and effective stresses at depth z, respectively, and r d is a stress reduction coefficient.

MSF and reduction factor (r d) were determined by means of the formulations suggested by Golesorkhi (1989) and Idriss (1999), respectively.

$$\begin{aligned} {\text{Ln}}\left( {r_{\text{d}} } \right) & = \alpha (z) + \beta (z)M_{\text{w}} \\ \alpha (z) & = - 1.012 - 1.126\sin \left( {\left( {\frac{z}{11.73}} \right) + 5.133} \right) \\ \beta (z) & = 0.106 + 0.118\sin \left( {\left( {\frac{z}{11.28}} \right) + 5.142} \right), \\ \end{aligned}$$
(12)
$${\text{MSF}} = 6.9\exp \left( {\frac{{ - M_{\text{w}} }}{4}} \right) - 0.058\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,M_{\text{w}} > 5.2$$
(13)

where; M w is the earthquake moment magnitude, z is the depth (m).

LPI and LSI calculations

The LPI method was first introduced by Iwasaki et al. (1978, 1982). LPI depends upon the thickness, depth and liquefaction safety factor of the liquefiable and non-liquefiable layers. LPI provides values for evaluating the liquefaction potentials of liquefiable layers. The equation of LPI is presented in Eq. (14).

$${\text{LPI}} = \int_{0}^{z} {F\left( z \right)W\left( z \right){\text{d}}z}$$
(14)
$$W\left( z \right) = 10 - 0.5z\,\,\,\,\,\,\,\,\,\,{\text{z < 20 m,}}$$
(15)

where F(z) is the liquefaction safety factor that points out the degree of severity whereas W(z) signifies the depth-based weighting factor. Severity factor [F(z)] is designated by the quantitative FS (Sonmez 2003) as follows:

$$F\left( z \right) = \left\{ \begin{aligned} {\text{FS}}\, \le \,0.95\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,F\left( z \right) = \,\,1\, - \,{\text{FS}} \hfill \\ 0.95 \, < {\text{ FS }} < \,1.2\,\,\,\,\,\,\,\,F\left( z \right) = \,2.106\,e^{{ - 18.427\,{\text{FS}}}} \hfill \\ {\text{FS}} \ge \,1.2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\text{non - liquefaction}} \hfill \\ \end{aligned} \right\}\,.$$
(16)

In a sequence with different ground levels, the LPI value is calculated separately for each level. The total LPI value found for each soil level is the sum of the LPI values of the other levels above this level. The total LPI value, in other words the liquefaction potential index of the investigated location specifies the liquefaction risk of the ground (Table 5) (Iwasaki et al. 1982).

Table 5 Degrees of LPI (Iwasaki et al. 1982)
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The LSI approach has quite different boundary values compared to the LPI method. The maximum value of liquefaction is assumed to be 1.411 in this method (Sonmez and Gokceoglu 2005). According to Sonmez and Gokceoglu (2005), the equation required for the calculation of LSI is presented below.

$${\text{LSI}} = \int_{0}^{x} {P\left( L \right)W(z){\text{d}}z}$$
(17)

The liquefaction probability (P L) given in the above equation is calculated as follows.

$$\begin{aligned} P_{\text{L}} & = \frac{1}{{1 + \left( {F_{\text{L}} /0.96} \right)^{4.5} }}{\kern 1pt} \quad {\text{FL }} \le { 1} . 4 1 1 { } \\ \, P_{\text{L}} (z) & = 0\quad {\text{FL > 1}} . 4 1 1\\ \end{aligned}$$
(18)

On the other hand, W (z) is calculated as in the LPI method. Liquefaction potential classes for the LSI method are given in Table 6.

Table 6 Degrees of LSI (Sonmez and Gokceoglu 2005)
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V s-based liquefaction analyses

In this study, seismic wave velocity was revealed using seismic refraction and Multichannel Analysis of Surface Waves (MASW) techniques developed by Park et al. (1999). The seismic data can be gathered by this technique and the V s of soil deposits can be determined using multichannel receivers (Foti 2000; Dikmen et al. 2010a, b). Active source seismograph (12 channels) and 4.5 Hz geophones were employed to acquire data from 21 recording locations in Erciş. Geophone ranges were 3 m, sampling range was 1 ms, as well as record lengths were selected to be 2 s during measurements.

In addition, the V s values were also calculated for each borehole location depending on the SPT values using the Eq. 19 proposed by Akın et al. (2011) considering the SPT blow counts (N) and depth (z).

$$V_{\text{s}} = \,121.75\,N^{ - 0.101} \,z^{0.216} \,\,\,\,\,r = \,0.94.$$
(19)

In the V s-based liquefaction analyses, liquefaction potential is determined using acceleration with V s (Dobry et al. 1981a). The liquefaction potential is defined to be high if the acceleration experienced during an earthquake is greater than 60% of the acceleration that the earth can withstand without being subjected to deformation.

The factor of safety F a account for the threshold acceleration criteria is as follows:

$$F_{\text{a}} = \,1.6\,\left( {\frac{{a_{t} }}{{a_{\hbox{max} } }}} \right)$$
(20)

where F a is the safety factor in threshold acceleration criteria, a t is the threshold acceleration required to start liquefaction, a max is peak ground acceleration of the earthquake. From calculated F a values obtained using the above mentioned equation, F a < 1 is considered as high liquefaction potential and liquefaction potential is classified as low when F a ≥ 1 (Dobry et al. 1981a).

For the calculation of the threshold acceleration value, γt = 0.0001 is adopted and the following formula is used by taking into account the corresponding G/G max value as 0.8 (Hardin and Drnevich 1972).

$$\begin{aligned} \left( {\frac{{a_{t} }}{g}} \right) = \,\frac{{\left[ {\gamma t\,\,\left( {\frac{G}{{G_{\hbox{max} } }}} \right)t\,\,V_{\text{s}}^{2} } \right]}}{{g\,z\,r_{d} }}\, \hfill \\ r_{d} = \,1\,\, - \,\,0.015\,z\,, \hfill \\ \end{aligned}$$
(21)

where, G max refers to shear modulus, γ is the density of soil, g is the gravity and z is the depth (m).

Andrus and Stokoe (1997, 2000), Uyanık (2002), Uyanık and Taktak (2009) and Uyanik et al. (2013a) suggested several V s-based liquefaction analyses. FS is generally used for the determination of liquefaction potential using both SPT and V s data. Seed and Idriss (1971), Uyanık and Taktak (2009) and Uyanik et al. (2013a) formulated the following equation for the calculation of safety factor.

$${\text{FS}}_{{V_{\text{s}} }} { = }\frac{{{\text{CRR}}_{{V_{\text{s}} }} }}{{{\text{CSR}}_{{V_{\text{s}} }} }}{ = }\frac{\text{SRR}}{\text{SSR}}.$$
(22)

Shear resistance ratio (SRR) is determined as a function of V s. The SRR and corrected V s were formulated by Andrus and Stokoe (1997, 2000), Youd et al. (2001), Uyanık (2006) and Uyanık and Taktak (2009).

$${\text{SRR}} = \left[ {a\,\left( {\frac{{Vs_{c} }}{100}} \right)^{2} \, + b\,\left( {\frac{1}{{Vs_{\hbox{max} } - Vs_{c} }}\, - \,\frac{1}{{Vs_{\hbox{max} } }}} \right)} \right]\,{\text{MSF}}$$
(23)
$$\begin{aligned} V_{{s_{\hbox{max} } }} = \,250\,\,{\text{m/s}}\quad {\text{FC}}\, \le \,\% 5 \hfill \\ V_{{s_{\hbox{max} } }} = \,250\, - ({\text{FC}}\, - \,5)\,\,{\text{m/s}}\quad \,\% 5{\text{ < FC}}\,{ < }\% 35 \hfill \\ V_{{s_{\hbox{max} } }} = \,220\,\,{\text{m/s}}\quad {\text{FC}}\, \ge \,\% 35, \hfill \\ \end{aligned}$$
(24)

where \(V_{{{\text{s}}_{\text{c}} }}\) is the corrected V s; \(V_{{s_{\hbox{max} } }}\) is the upper limit of the \(V_{{{\text{s}}_{\text{c}} }}\) and FC is fine content of the soil (Uyanık and Taktak 2009; Uyanik et al. 2013a). MSF is the magnitude scaling factor. a and b are regression coefficients.

Andrus and Stokoe (2000) suggest the values of \(V_{{s_{\hbox{max} } }}\) = 215 m/s, a = 0.022 and b = 2.8 in Eq. 23. Uyanık (2002, 2006) suggests these values as 0.025, 4 and 250 m/s, respectively. Furthermore, Uyanık and Taktak (2009) defined \(V_{{s_{\hbox{max} } }}\) values ranging from 220 to 250 m/s which are related to the fine content of soil.

MSF is a correction coefficient calculated according to earthquake magnitude. The equation developed by Youd et al. (1997) is expressed by the following formula:

$${\text{MSF}} = \,\left( {\frac{{M_{w} }}{7.5}} \right)^{n} \,\,\,\,\,\,\,\,\,\,\,\,\,(n = \, - 2.56\,\,\,\,M_{\text{w}} \,{ > }7.5\,\,\,\,\,{\text{and}}\,\,\,n = \, - 3.3\,\,\,\,M_{\text{w}} \le \,7.5\,\,\,),$$
(25)

where n is exponential constant. Andrus and Stokoe (1997, 2000) propose the following values for the exponential constant (n) obtained depending on the magnitude of the earthquake.

Shear stress ratio (SSR) is the other term required to calculate the factor of safety in terms of liquefaction potential as a function of V s. CSR and SSR are physically in similar meaning. Nevertheless, the SSR relies on the V s of the soil deposit and the acceleration as well as the period of the earthquake. The CSR term (in Eq. 11), suggested by Seed and Idriss (1971), is modified as follows using V s by Uyanık (2002, 2006) and Uyanik et al. (2013a).

$${\text{SSR}} = \,\,\left( {\frac{{a_{\hbox{max} } }}{g}} \right)\left( {\frac{{\sigma_{{V_{\text{s}} }} }}{{\sigma_{{V_{\text{s}} }}^{\imath } }}} \right)r_{\text{d}}$$
(26)
$$\begin{aligned} \sigma _{{V_{{\text{s}}} }} & = 0.25T\left( {\sum\limits_{{i = 1}}^{n} {\gamma _{i} } V_{{{\text{s}}_{i} }} } \right) \\ \sigma _{{V_{{\text{s}}} }}^{l} & = \sigma _{{V_{{\text{s}}} }} - u = 0.25T\left( {\sum\limits_{{i = 1}}^{n} {\gamma _{i} } V_{{{\text{s}}_{i} }} - V_{{{\text{s}}_{n} }} \left( {\gamma _{{{\text{sa}}}} - \gamma _{{\text{d}}} } \right)} \right) \\ r_{{\text{d}}} & = 1 - 0.00765z\quad z \le 9.15\;{\text{m}} \\ r_{{_{{\text{d}}} }} & = 1.174 - 0.0267z\quad 9.15 < z \le 23\;{\text{m}} \\ r_{{_{{\text{d}}} }} & = 0.744 - 0.008z\quad 23 < z \le 30\;{\text{m,}} \\ \end{aligned}$$
(27)

where \(\sigma_{{V_{\text{s}} }}^{'}\) is the effective vertical stress (kN/m2); \(\sigma_{{V_{\text{s}} }}\) is the dynamic vertical stress at the investigated depth defined by V s and earthquake wave period (kN/m2); a max is the peak ground acceleration (g), g is the acceleration of gravity, T is the dominant period of the earthquake (s); γi is the unit weight of soil layers (kN/m3); γsa saturated unit weight of soil (kN/m3); γd unit weight of unsaturated soil (kN/m3); \(V_{{{\text{s}}_{i} }}\) is the V s velocities of soil unit (m/s); n is the number of layers; z is the depth of layer considered in liquefaction analyses (m) (Uyanık 2002; Uyanık and Taktak 2009; Uyanik et al. 2013a); r d is a stress reduction coefficient dependent to depth (Robertson and Wride, 1997; Liao and Whitman, 1986).

To obtain the SSR values from V s, the V s values measured in the field should be corrected by a reference overburden stress using the correction factor (Andrus and Stokoe 1997, 2000; Uyanık 2006; Uyanik et al. 2013a).

$$V_{{{\text{s}}_{\text{c}} }} = \,V_{\text{s}} \left( {\frac{{P_{\text{a}} }}{{\sigma `_{vo} }}} \right)^{0.25} ,$$
(28)

where \(\sigma_{{V_{\text{o}} }}^{'}\) is the effective vertical stress in kPa; \(V_{{{\text{s}}_{\text{s}} }}\) is the corrected V s (m/s) and P a is the reference stress which is accepted to be 100 kPa. The SSR is calculated using the earthquake period and V s values as well as the earthquake acceleration. The SSR value reveals more accurate results when these parameters are used. In this study, the relationships developed by Uyanik et al. (2013a) are used for the calculation of SSR and SRR values.

Results of the liquefaction analyses

Using the SPT, V s, soil type, groundwater level and earthquake scenarios, the units in the first 20 m in the study area were evaluated in terms of liquefaction potential. As can be seen from the liquefaction potential maps prepared according to the LPI and LSI methods (Fig. 6a–f), the liquefaction potential is determined to be high to very high in all three earthquake scenarios in the coastal sections of the Lake Van as well as the Zilan Creek in the western part of Erciş and Irşat Creek. However, LPI and LSI values are determined to be low in the western and northern parts of the study area.

Fig. 6
figure 6

Liquefaction potential maps of Erciş and its surrounding according to LPI (a–c) and LSI (d–f) methods

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\(V_{{{\text{s}}_{30} }}\) value for a depth of 30 m was calculated using seismic methods in the study area, as well (Eq. 28). The \(V_{{{\text{s}}_{30} }}\) velocities in the study area are generally between 200 and 250 m/s in recent alluvial deposits; however, they vary between 250 and 300 m/s in old lacustrine sediments (Fig. 7).

Fig. 7
figure 7

\(V_{{{\text{s}}_{30} }}\) map of the study area

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$$V_{{{\text{s}}_{30} }} = \,\frac{30}{{\sum\nolimits_{i = 1}^{n} {\frac{{h_{i} }}{{V_{{{\text{s}}_{i} }} }}} }}.$$
(29)

where h i is the thickness (m) and \(V_{{{\text{s}}_{i} }}\) is the V s of the ith layer.

V s-based threshold acceleration criteria and safety factor were also used to signify the liquefaction potential of the research area (Fig. 8a–f). Similar to the results of LPI and LSI, it was determined that the liquefaction potential is medium to high nearby the Lake Van and in the western region.

Fig. 8
figure 8

V s-based threshold acceleration criteria (a–c) and safety factor (d–f) liquefaction potential maps of Erciş and its surrounding

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Discussion and results

According to four different methodologies (SPT-based LPI and LSI, V s-based threshold acceleration and safety factor) and three different earthquake scenarios, the liquefaction potential was evaluated for the Erciş district, which suffered the most damage in 2011 Van earthquake. After all these evaluations, it was determined in all four methods that the liquefaction potential of the study area near the coastal parts of the Lake Van and the western part of the study area is higher than the other regions. This indicates that the soil tightness and groundwater level control the liquefaction potential. When three different earthquake scenarios are examined, a high liquefaction potential in Erciş settlement area is determined if Erciş–Kocapınar fault creates an earthquake, which is the closest fault to the study area and there is high-moderate liquefaction potential in the scenarios considering the Çaldıran and Van faults. When all results obtained from those analyses are considered, it is concluded that the LPI and LSI values calculated according to the borehole data and the safety factor liquefaction analyses calculated on the basis of V s are more compatible than the threshold acceleration criteria. In addition, it was determined that the location of lateral spreading and sand boils observed in the field after the 23rd October 2011 Van earthquake overlap with the scenario boundaries in this study. Since seismic work can be performed quickly and easily in all types of soil conditions, the use of V s-based safety factor liquefaction analyses, which reveals consistent results with the SPT-based analyses, is also recommended for the liquefaction assessments.

When liquefaction potential is evaluated according to the methods used in this study, it can be derived that liquefaction type surface deformations may occur after a possible large earthquake in the vicinity of Erciş, especially near the Lake Van from Erciş–Patnos road and in areas close to the rivers. For this reason, considering that the present research is a comprehensive study of the region, liquefaction potential should be evaluated in detail during geotechnical studies carried out for new constructions and soil improvement studies should be executed in areas where liquefaction potential exists.

The raw SPT-N blow counts beneath the groundwater level vary between 4 and 32 when the borehole data and the results of SPT-based liquefaction analyses are considered. Furthermore, it is also concluded that the shallow soils having low shear wave velocity values reveal high liquefaction potential which are compatible with the SPT data. Thus, the use of V s-based liquefaction analysis in collaboration with the SPT results is quite advantageous to determine the liquefaction potential of a specific site. On the other hand, the SPT data may be misleading where gravelly layers exist within a liquefiable soil whilst the collection of V s data is rapid and practical.