Introduction

An earthquake with a moment magnitude (M) of 5.4 struck Pohang City in South Korea on November 15, 2017. Small to moderate earthquakes frequently occur in the coastal areas of South Korea. However, the Pohang earthquake is distinct from the other earthquakes in South Korea because it caused significant damage and thus was recorded as the second strongest earthquake (e.g., [17, 18, 20]). The focal depth of the Pohang earthquake was less than 4 km, which is considerably shallow, and it caused severe seismic loading on the ground. The Pohang earthquake induced sand boils near the epicenter. Because most liquefactions occurred in the rice paddies, there was no significant structural and geotechnical damage from liquefaction. However, note that liquefaction can occur in South Korea owing to small to moderate earthquakes.

Seed and Idriss [26] first proposed a simplified method to evaluate the triggering liquefaction at a certain depth with blow counts of the standard penetration test (SPT). Later, the liquefaction potential has been evaluated mainly using the blow counts of the SPT (e.g., [8, 12, 27, 29] and cone resistance of the cone penetration test (CPT) (e.g., [5, 21, 23, 25, 30]. The shear wave velocity (VS) measured from the downhole test, suspension PS logging test, and surface wave test have also been used in liquefaction assessment [2, 3, 16, 19].

Iwasaki et al. [14] suggested a liquefaction potential index (LPI) predicting the severity of liquefaction at a specific site. The LPI is calculated with factors of safety against liquefaction at various depths. It can be used as a preliminary guideline for evaluating soil liquefaction. When 0 < LPI < 5, the liquefaction potential is expected to low. However, when the LPI > 15, the liquefaction potential is considered to be high [13].

In this study, we calculated factors of safety against liquefaction (FSliq) following the guide from Andrus et al. [3]. We also calculate the LPI values as indices of liquefaction potentials at the five select sites near the epicenter of the Pohang earthquake. Liquefaction-induced sand boils were observed at the three sites and not at the other two sites. More details about the five sites will be discussed in the subsequent section.

Study area and sand boils

The epicenter of the Pohang earthquake was in the northern part of Pohang City, where most of the land is used for agricultural and residential fields. We define the study area covering the field test sites and the epicenter, as shown in Fig. 1. The geology of Pohang City is comprised of Quaternary, Cretaceous, and Tertiary systems. The soil deposits include sedimentary, colluvial, and fill soils underlain by soft rocks or weathered soil and rocks with low stiffness [18]. The study area is on the Quaternary Alluvium, including Heunghae formation, Idong Formation, and Duho Formation [10].

Fig. 1
figure 1

Map of study area in Pohang City, where the locations of field tests and the epicenter of Pohang earthquake are shown

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After the Pohang earthquake, Gihm et al. [11] observed that 601 sand boils occurred near Pohang City, of which approximately 96% occurred in a 5 km radius of the epicenter. Gihm et al. [11] reported that the extruded sand boils consisted of 10% clay and silt, 30% sand with gravel, and 60% sand. Photographs of the observed sand boils are shown in Fig. 2.

Fig. 2
figure 2

Photos of sand boils that occurred in rice paddies near the epicenter during the Pohang earthquake

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The information of the five sites are shown in Table 1. Site 1–3 are located at the rice fields in the northern part of Pohang city. Especially, Site 2 and 3 are very close to the epicenter of the Pohang earthquake. Site 4–5 are located close to the coast in the southern part of the city. We considered that Site 2–4 are liquefied sites based on observations of sand boils, and Site 1 and 5 are non-liquefied sites without sand boil observations.

Table 1 Epicentral distances, VS30, and estimated amax values for the five sites (see Fig. 1 for location)
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Shear wave velocity measurements

We obtained five VS profiles measured by suspension PS logging test from the National Disaster Management Research Institute [24]. In this study, the three VS profiles were measured by downhole tests. Andrus et al. [3] summarized the primary features of suspension PS logging and the downhole test for liquefaction evaluation. Both tests require a borehole and are appropriate for detailed site-specific evaluation where thin soil layers exist.

Figure 3a presents the VS profiles obtained by the suspension PS logging test at Site 1 (liquefied). The VS gradually increases with depth and is greater than 200 m/s at all depths. Figures 4a, 5 and 6a present the comparisons of VS profiles measured by the suspension PS logging (V SS ) and downhole (V DS ) tests at Sites 2–4 (all liquefied sites), respectively. In Fig. 4a, the V SS and V DS profiles are in sufficient agreement throughout all depths. The V SS and V DS are approximately 200 m/s up to a depth of 14 m; the velocities increase as the depth increases. Figure 5a presents the liquefied site where V SS and V DS are similar at depths of 4–11 m and are lower than 200 m/s. Exceeding a depth of 4 m, V SS is approximately 204 m/s, which is slightly higher than V DS (181 m/s). As shown in Fig. 6a, V SS and V DS are lower than 250 m/s throughout all depths, and V SS is slightly greater than V DS , up to a depth of 14 m. Figure 7a presents the V SS Site 5 (non-liquefied), which is lower than 200 m/s at all depths.

Fig. 3
figure 3

Profiles of a raw VS measured from the downhole test; b corrected VS by an overburden stress (VS1); c cyclic stress ratio and cyclic resistance ratio (CSR and CRR, respectively); and d factor of safety against liquefaction (FSliq) at Site 1, where sand boils were not observed (non-liquefied site). The LPI is shown at the top right of (d). The sand with clay at a depth of 6 m has a fines content of 16.2%

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Fig. 4
figure 4

Profiles of a raw VS measured from the downhole test and suspension PS logging (V SS and V DS , respectively); b VS1; c cyclic stress ratio and cyclic resistance ratio by the downhole test (CSRD and CRRD, respectively); d cyclic stress ratio and cyclic resistance ratio by suspension PS logging (CSRS and CRRS, respectively); and e FSliq by downhole test and suspension PS logging (FSD and FSS, respectively) at Site 2, where sand boils were observed (liquefied site). The LPI is shown at the top right of (e). The sand at a depth of 9 m has a fines content of 13.4%

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Fig. 5
figure 5

Profiles of a V SS and V DS ; b VS1; c CSRD and CRRD; d CSRS and CRRS; and e FSD and FSS at Site 3, where sand boils were observed (liquefied site). The LPI is shown at the top right of (e). The silty sand at a depth of 3 m has a fines content of 12.8%

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Fig. 6
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Profiles of a V SS and V DS ; b VS1; c CSRD and CRRD; d CSRS and CRRS; and e FSD and FSS at Site 4, where sand boils were observed (liquefied). The LPI is shown in at the top right of (e). The silty clay at a depth of 16 m has a fines content of 26.9%

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Fig. 7
figure 7

Profiles of a raw VS measured by the downhole test; b VS1; c CSR and CRR; and d FSliq at Site 5, where sand boils were not observed (non-liquefied site). The LPI is shown at the top right of (d). The clayey sand with gravel at a depth of 12 m has a fines content of 26.4%

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Liquefaction potential index

We calculated the cyclic stress ratio (CSR) with the simplified procedure proposed by Seed and Idriss [26]. The detailed guide from Andrus et al. [3] was adopted to assess the cyclic resistance ratio (CRR) based on the VS profiles from the field tests.

Cyclic stress ratio

Seed and Idriss [26] defined CSR as the seismic loading on the soil as follows:

$$ {\text{CSR}} = 0.65 \cdot \frac{{{\text{a}}_{\hbox{max} } }}{\text{g}} \cdot \frac{{\sigma_{\text{v}} }}{{\sigma_{\text{v}}^{'} }} \cdot {\text{r}}_{\text{d}} $$
(1)

where amax is the peak horizontal ground acceleration on the surface, g is the gravitational acceleration, \( \sigma_{v} \) is the total overburden stress in the vertical direction, \( \sigma_{v}^{'} \) is the effective overburden stress in the vertical direction, and rd is the stress reduction factor.

To estimate the amax for the five sites, we used the four Next Generation Attenuation relationships for Western United State (NGA-West2) ground motion prediction equations (GMPEs) (i.e., [1, 4, 7, 9]) with equal weights. This is because recorded ground motions were absent in the study area. Parameters such as M, epicenter distance, and time-averaged VS are required for the 30 m soil deposits (VS30) to estimate amax. Suspension PS logging and downhole tests were both considered individually to evaluate the VS30. The parameters and estimated amax for the five sites are presented in Table 1. The NGA-West2 GMPEs use the closest distance to the rupture plane (Rrup) and Boore-Joyner distance (Rjb). However, the rupture plane of the Pohang earthquake is not well defined yet, and is known to be shallow and small. Therefore, we used the epicentral distance for the NGA-West2 GMPEs. The calculated amax values were validated by Kim et al. [20] who compared the peak ground accelerations estimated by the select GMPEs with those from the recordings at the four nearest stations.

Site-specific soil conditions, such as soil type, ground water table (from the boring log at each site), and soil density (from the density logging test by NDMI [24], were considered in the calculation of \( \sigma_{v} \) and \( \sigma_{v}^{'} \). Figure 3c presents the calculated CSR profile at Site 1 (non-liquefied). The site is located 5 km away from the epicenter, and amax is 0.25 g, resulting in CSRs less than 0.3 throughout all depths. Figure 4c and d present the CSRs for the downhole and suspension logging tests (CSRD and CSRS, respectively) at Site 2 (liquefied). No difference is observed in CSRD and CSRS because both amax values are identical. The CSR increases to approximately 0.5 up to a depth of 9 m, below which the CSR decreases with depth due to rd. The CSRD and CSRS for Site 3 (liquefied), as shown in Fig. 5c, d, respectively, are similar to each other and increase up to approximately 0.6. Figure 6c and d present the CSRD and CSRS profiles for Site 4 (liquefied), and Fig. 7c presents the CSRD profile at Site 5 (non-liquefied).

Cyclic resistance ratio

VS is used to indicate the soil rigidity against liquefaction. Similar to other common penetration tests, the evaluation of liquefaction potential based on VS also requires the correction to a reference stress of 100 kPa (VS1) [3]. In addition, VS1 should be limited to the maximum upper value (\( {\text{V}}_{\text{S1}}^{ *} \)) as that of liquefaction evaluation based on the SPT test [3]. In this study, the depths at which VS1 is greater than \( {\text{V}}_{\text{S1}}^{ *} \) were considered non-liquefiable and excluded in the LPI calculation. An example of the VS1 calculation is shown in Fig. 3b through Fig. 7b.

Andrus and Stokoe II [2] suggested the CRR as follows:

$$ {\text{CRR }} = {\text{ MSF }} \cdot \left\{ {0.022\left( {\frac{{{\text{K}}_{{{\text{a}}1}} {{\text{V}}}_{{{\text{S}}1}} }}{{100}}} \right)^{2} + 2.8\left( {\frac{1}{{{\text{V}}_{{{\text{S}}1}}^{*} - ({{\text{K}}}_{{{\text{a}}1}} {{\text{V}}}_{{{\text{S}}1}} )}} - \frac{1}{{{\text{V}}_{{{\text{S}}1}}^{*} }}} \right){{\text{K}}}_{\text{a}}2 } \right\} $$
(2)

where MSF is the magnitude scaling factor to consider the effect of M [29]. Further, Ka1 and Ka2 are the age correction factors for uncemented Holocene soils to older soils [2]. In this study, Ka1 and Ka2 are regarded as unity because the sediments in Pohang are Quaternary unconsolidated soils.

Example calculations of CRRs are presented in Fig. 3 through Fig. 7. Note that CRRs increase considerably as the VS1 values approach \( V_{S1}^{ *} \) values in Eq. (2). Therefore, minor variations in VS1 can consequently cause significantly distinct CRRs, as shown in Fig. 4c, d.

Liquefaction potential index

The factor of safety against liquefaction (FSliq) is defined as the ratio of CRR to CSR. When CRR is greater than CSR, the liquefaction potential is considered to be low, and vice versa. FSliq varies with depth. Iwasaki et al. [14] proposed a liquefaction potential index that represents the susceptibility of ground to liquefaction at a site as follows:

$$ {\text{LPI = }}\mathop \int \limits_{ 0}^{{ 2 0 {\text{m}}}} {\text{F}}\left( {\text{z}} \right){\text{w}}\left( {\text{z}} \right){\text{dz}} $$
(3)

where z is the depth, w is the weighting function, which equals 10–0.5 z if z is less than 20 m. F is a function of FSliq at a given depth (i.e., F = 1 − FSliq if FSliq is less than 1; otherwise it is zero).

Figure 3d presents the calculated FSliq at Site 1. The FSliq value is greater than 1.0 at depths of 5–6 m. Below 6 m, VS1 is greater than the liming value; thus, the soil layers are not liquefiable. As a result, the LPI was calculated to be zero, which is consistent with the field observation: no sand boil was observed. Figure 4e presents FSliq at Site 2. The slight variation in VS resulted in a FSliq difference (i.e., FSD vs. FSS) of approximately 1.0 at depths of 6–9 m. The V SS1 varies from 185 to 194 m/s at these depths while V DS1 varies from 202 to 203 m/s. The difference in VS1 resulted in the difference in CRR. Although the V DS1 values are analogous to V SS1 , they are very close to the \( {\text{V}}_{\text{S1}}^{ *} \), causing greater values of CRRD than CRRS. Below a depth of 10 m, FSliq is lower than 1.0 for both downhole and suspension PS logging tests. The LPID was calculated to be 7.6, and the LPIS was 13.9. Numerous studies have reported that sand boils could occur when an LPI is greater than 5 [15, 22, 28]. Therefore, it can be concluded that both LPIs are in sufficient agreement with the sand boil observations at this site.

Figure 5e presents the FSliq at Site 3 (liquefied). The FSD and FSS are significantly similar throughout all depths, and the LPID and LPIS were calculated to be 9.8 and 11.2, respectively. It is known that clays are not susceptible to liquefaction. However, recently, lean clays are considered to be moderately susceptible to liquefaction (e.g., [6]). Without knowing exact composition of the clay layer at this site, we included the clay layer in the LPI calculation. When this clay layer was excluded, the LPIs for both downhole and suspension logging tests are zeros, which is not consistent with the sand boil observation. A further in-depth study is required for susceptibility of the clay layer at this site.

Figure 6e presents FSliq at Site 4 (liquefied), and the LPID and LPIS were calculated to be 2.9 and 1.5, respectively. It is worth noting that slight differences in measured VS from different methods can result in considerable differences in FSliq as shown in Fig. 6a, d. The V SS1 values at depths of 1–4 m and 7–13 m were greater than \( {\text{V}}_{\text{S1}}^{ *} \) and were excluded in calculation. At depths of 5–6 m, the differences between V DS1 and V SS1 are approximately 35.8–38 m/s, which resulted in the differences between FSD and FSS of approximately 3.9–11.4. Figure 7e presents that FSliq at Site 5 (non-liquefied) is near 1.0 at depths greater than 11 m. The LPI was calculated to be 0.3 for this site. The calculated LPIs at all sites are summarized in Table 1. The LPIs at the liquefied sites are higher than 1.0, and those at the non-liquefied sites are lower than 1.0.

Conclusions

This study presents the evaluation of liquefaction potentials based on the VS profiles measured by both downhole and suspension PS logging tests at five selected sites. The VS profiles from both tests were generally in good agreement. However, there are some cases with slight differences, resulting in varying CRR. In particular, when the values of VS1 approached that of \( V_{S1}^{ *} \), the CRR calculation became highly sensitive. Owing to the lack of ground motion records within the study area, we estimated the CSR by using the NGA-West2 GMPEs.

The LPIs from the suspension PS logging test were calculated to be approximately 1.5–13. 9 for the three liquefaction sites, and those from the downhole tests were approximately 2.9–9.8. The LPIs were calculated to be 0 and 0.3 at the two non-liquefied sites. Therefore, both downhole and suspension PS logging tests can be used to evaluate liquefaction potentials.