Introduction

During site selection and planning stages for the settlement areas and engineering structures, evaluation of the liquefaction potential of a liquefaction-prone area is one of the important tasks in geotechnical earthquake engineering. A number of studies on liquefaction and liquefaction-induced ground failures have been performed by many researchers after the devastating earthquakes of Alaska and Niigata, which occurred in 1964, where slope, bridge and foundation failures were observed as a result of soil liquefaction. Liquefaction and associated ground failures were widely observed during the devastating earthquakes in Turkey (1998 Adana-Ceyhan, 1999 Kocaeli and Duzce earthquakes) and Taiwan (1999 Chi-Chi earthquake).

The factor of safety against liquefaction (FL) of a saturated soil is expressed as the ratio of the cyclic resistance ratio (CRR) to the cyclic stress ratio (CSR). In-situ tests such as standard penetration test (SPT), conic penetration test (CPT), Becker penetration test (BPT) and shear wave velocity (Vs) are used as empirical tools to evaluate CRR of a soil layer which may liquefy during an earthquake (Youd et al. 2001). The conditions FL>1 and FL<1 indicate that the soils are classified as non-liquefiable and liquefiable, respectively, while the FL=1.0 represents limiting equilibrium. However, these boundaries are theoretical values for all limit equilibrium approaches used in classical analyses techniques such as slope stability. In other words, a layer may liquefy during an earthquake, although its FL>1.0.

Historical evaluations of the SPT-based method proposed by Seed and Idriss (1971) are briefly discussed here. The method is widely used in most countries including Turkey. This method, which is also known as “The Seed simplified procedure,” considers SPT-N values of the soil layer. The simplified procedure has been modified by researchers over the years depending on the number of cases used (Seed 1983; Seed et al. 1985; Seed and DeAlba 1986; Seed and Handler 1990). Youd et al. (2001) reported some recommendations and provided a consensus among the geotechnical community on the SPT, CPT, Vs and BPT-based methods after the workshops that convened in 1996 and 1998.

Although FL of a soil layer can be calculated by means of numerous methods mentioned above, it is not a sufficient tool for estimating liquefaction severity. Furthermore, FL is not a practical parameter to prepare liquefaction severity maps for liquefaction-prone areas. FL can be used to predict that a layer can either liquefy, or not liquefy but not degrees of severity. To overcome some limitations of FL, liquefaction potential index (LI) and its severity categories were proposed by Iwasaki et al. (1982). These researchers suggested that damage to engineering structures tends to be severe if the liquefiable layer is thick, shallow and FL calculated for the liquefiable layer is far less than 1.0. The original form of the LI is expressed by the following equations.

$$L_I = \int\limits_{0}^{20} {F(z)W(z)dz} $$
(1)
$$F(z) = 1 - F_{\rm L} \quad {\text{for}}\,F_{\rm L} < 1.0$$
(2a)
$$F(z) = 0\quad {\text{for}}\,F_{\rm L} \geq 1.0$$
(2b)
$$W(z) = 10 - 0.5z \quad {\text{for}}\,z < 20{\text{m}}$$
(2c)
$$W(z) = 0\quad {\text{for}}\,z > 20{\text{m}}$$
(2d)

Where z is the depth of the mid point of the soil layer in meters. The liquefaction severity categories proposed by Iwasaki (1982) consist of four classes called “very low,” “low,” “high” and “very high” depending on the value of the LI (Table 1). The areas showing different degree of susceptibility classes and non-susceptible areas may be classified on susceptibility maps such as landslide-prone. However, non-susceptible areas could not be distinguished based on the categories proposed by Iwasaki et al. (1982). Furthermore, although “high” and “low” liquefaction potential categories are defined, the category “moderate” is lacking in the categories listed in Table 1. The limitations of the LI and severity categories (Table 1) were discussed in detail by Sonmez (2003). To overcome these limitations, Sonmez (2003) modified F(z) term appearing the equation of LI by considering the threshold value of 1.2 between the non-liquefiable and marginally liquefied categories as follow:

$$F(z) = 0\quad {\text{for}}\,F_{\rm L} \geq 1.2$$
(3a)
$$F(z) = 2\times 10^6 e^{- 18.427F_{\rm L}} \hbox{for} 1.2>F_{\rm L}>0.95$$
(3b)
$$F(z) = 1 - F_{\rm L} \quad {\text{for}}\,F_{\rm L} < 0.95$$
(3c)
Table 1 Liquefaction potential categories based on LI (Iwasaki et al. 1982)
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Sonmez (2003) introduced two new categories into the classification proposed by Iwasaki et al. (1982) as “non-liquefiable” and “moderate” (Table 2). The boundary values of LI for the categories of “high” and “very high” by Iwasaki et al. (1982) were preserved by Sonmez (2003). When FL>1.2 throughout the soil column from surface to a depth of 20 m, LI of the soil column becomes zero and the column is classified as “non-liquefiable” by Sonmez (2003). However, Sonmez (2003) pointed out that the threshold value of FL between non-liquefiable and marginally liquefied conditions (FL=1.2) is open to discussion, and the threshold value for the non-liquefiable category suggested in his study can be changed depending on the data in future studies. Seed and Idriss (1982) mentioned that the values of FL against liquefaction ranging between 1.25 and 1.5 are acceptable. Yuan et al. (2003) stress that the deterministic methods evaluated are not the best judgement of whether liquefaction occurred in a post-earthquake investigation due to an unknown degree of conservatism that was generally used.

Table 2 Liquefaction potential classification proposed by Sonmez (2003)
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Chen and Juang (2000) and Juang et al. (2003) performed studies on the probabilities of soil liquefaction depending on the value of FL. Juang et al. (2003) proposed the following equation for estimating the probability of liquefaction. This equation ranges from zero to one as a function of FL.

$$P_{\rm L} = \frac{1}{{1 + \left({{\raise0.7ex\hbox{${F_L}$} \!\mathord{\left/{\vphantom {{F_{\rm L}} {0.96}}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{0.96}}} \right)^{4.5}}}$$
(4)

The likelihood of liquefaction of a soil layer can be defined based on the classification (Table 3) proposed by Chen and Juang (2000). Lee et al. (2003) evaluated liquefaction potential of the Yuanlin area where extensive soil liquefaction occurred during the 1999 Chi-Chi earthquake. These researchers considered the probability function (Eq. 4) suggested by Juang et al. (2003). They replaced the F(z) term of the LI index proposed by Iwasaki et al. (1982) with PL (Eq. 5) and also re-named LI as liquefaction risk index (IR).

$$I_R = \int\limits_0^{20} {P_L (z)W(z)dz}$$
(5)
Table 3 The classification of the probability of liquefaction proposed by Chen and Juang (2000)
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Lee et al. (2003) calibrated the boundary values of IR considering three categories using the liquefaction map of Yuanlin area prepared by a field observer after the Chi-Chi earthquake. While IR less than 20 and greater than 30 were classified as “low” and very high,” respectively, values of IR between 20 and 30 was classified as “high” based on the categories proposed by Lee et al. (2003). Similar limitations associated with categories proposed by Iwasaki et al. (1982) are also valid for the categories recently calibrated by Lee et al. (2003). Non-liquefiable areas could not be distinguished due to the limited number of categories proposed by Lee et al. (2003). The category of “moderate” also lacks similarity with Iwasaki’s categories. Moreover, the values of FL are equal to 1.306 and 1.159 for the boundary values of IR when FL is assumed as constant throughout soil column 20 m in thickness. The probabilities of liquefaction for the values of FL are equal to 1.306 and 1.159 fall into the class of “unlikely” in the classification given in Table 3. Therefore, the modifications on the categories proposed by Lee et al. (2003) are needed. By considering the reasons discussed here, a modified liquefaction severity classification based on Eq. 5 proposed by Chen and Juang (2000) for the probability of liquefaction is suggested. In addition, its performance is tested using the liquefaction map and borehole data of Yuanlin sites. Finally, the liquefaction potential map of a liquefaction-prone area at Marmara region of Turkey is prepared based on a possible earthquake scenario and the proposed index.

Liquefaction severity index and its classification

A natural hazard means the probability of occurrence within a specified period of time and within a given area of a potentially damaging phenomenon. Risk means the degree of loss to a given element or set of elements at risk resulting from the occurrence of a natural phenomenon of given magnitude (Varnes 1984). The term susceptibility applies in a general sense to division of the land surface into areas and the ranking of the areas according to the considered natural phenomenon such as landslide, liquefaction etc. The liquefaction indices proposed by Iwasaki et al. (1982), Sonmez (2003) and Lee et al. (2003) would only be used for the preparation of liquefaction susceptibility maps. Therefore, in this study, the term “liquefaction severity index (LS)” is preferred instead of “liquefaction risk index LR” proposed by Lee et al. (2003). The factor of safety is only one of the parameters, which plays an important role on the severity of the liquefaction as stated by Iwasaki et al. (1982). The relations between FL and the impact factors denoted by F(z) and PL(z) are shown in Fig. 1. As discussed previously, theoretically a soil layer with FL>1.0 can be treated as non-liquefiable, although it may liquefy during an earthquake. However, the probability of the liquefaction decreases while FL increases. Therefore, the use of probability-based impact factor for the FL is more realistic than the linear type relation given in Fig. 1. In this study, Eq. 5 proposed by Lee et al. (2003) was used, and only the term of “LS” is used instead of “IR.”

Fig. 1
figure 1

The relation between FL and the impact factors denoted by F(z) and PL(z)

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For construction of the liquefaction severity classification, the following steps given below are followed:

Step 1: “W(z)=10-0.5z” is put into the Eq. 5 and it was re-written.

$$L_S = \int\limits_0^{20} {P_{\rm L} (z)(10 - 0.5z)dz} $$
(6a)

Step 2: FL value appearing in PL(z) equation is assumed as a constant from the ground surface to a depth of 20 m, and Eq. 6a was solved.

$$L_S = P_L (z)\left. {\left({10z - \frac{{z^2}}{4}} \right)} \right|_0^{20} $$
(6b)
$$L_S = 100P_L (z)$$
(6c)

Step 3: Boundary values of LS are derived from Eq. 6c for each PL value given in Table 3, and tabulated in Table 4 with liquefaction susceptibility descriptions.

Table 4 Liquefaction severity classification suggested in this study
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As it can be seen from Fig. 2, the thickness of the liquefiable layer from the ground surface for PL and LS are equal to 1 (100% probability level) and 15 (upper boundary of the class “very low”), respectively, is about 1.57 m. In other words, the severity of a liquefiable layer with FL=0 and a thickness of 1.57 m can be evaluated as “very low” category based on the liquefaction severity classification proposed in this study. Similarly, to evaluate a soil layer as a “very high” class in terms of liquefaction susceptibility, thickness of layer (with PL=1 or FL=0) should be more than 12.2 m. This theoretical evaluation of Fig. 2 suggests that the severity classification terms based on LS can be considered as acceptable for susceptibility evaluations.

Fig. 2
figure 2

The relation between LS and thickness of liqufiable layer from the gound surface

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As discussed by Sonmez (2003), the threshold value of the FL to decide the soil liquefaction is still open to discussion. Although a soil layer with FL>1.2 is accepted as non-liquefiable by Sonmez (2003), FL for the upper boundary of “almost certain that it will not liquefy” class (FL=1.411) seems to be much more meaningful for this decision. The PL(z) term of LS is assumed as equal to zero for the layer with FL>1.411. FL cannot be determined if the corrected SPT-N value (N1(60)cs) is greater than 30 in the SPT-based method described in Youd et al. (2001). Besides, Youd et al. (2001) pointed out that the estimated CRR for the soil layer containing more than 35% fines content may be conservative. Therefore, the researchers recommend that the corrections based on fines content should be used with engineering judgment and caution. In some cases, soil layer with FL<1.0 can be evaluated as non-liquefiable based on some criteria such as proposed by Finn et al. (1994), and Andrews and Martin (2000), which consider Clay Content and Liquid Limit. Therefore, if the soil layer is evaluated as non-liquefiable based on the properties of fines, the PL(z) term is assumed as equal to zero to distinguish non-liquefiable area (Table 4).

The equations to be used for the determination of LS are given below.

$$L_S = \int\limits_0^{20} {P_{\rm L} (z)W(z)dz} $$
(6a)
$$P_{\rm L} (z) = \frac{1}{{1 + \left({{\raise0.7ex\hbox{${F_{\rm L}}$} \!\mathord{\left/{\vphantom {{F_L} {0.96}}}\right.\kern-\nulldelimiterspace}\!\lower0.7ex\hbox{${0.96}$}}} \right)^{4.5}}}\hbox{ for} F_{\rm L}\leq1.411$$
(6b)
$$\begin{array}{*{20}l}P_{\text{L}} \left( {\text{z}} \right) = 0 & {\text{for}} F_{\rm L} > 1.411 \\ & \hbox{ or } \\ & \hbox{The soil layer with} F_{\rm L} \leq 1.411 \hbox{ can be }\\ & \hbox{ considered as non-liquefiable layer considering Clay Content }\\ & \hbox{ and Liquid Limit.} \\ \end{array} $$
(bc)

Where, the term of W(z) is as same as those in Eq. 2c and Eq. 2d.

Verification of the suggested LS by a case from the Chi-Chi earthquake

The town of Yuanlin (population ~116,000 and area ~46 km2) located approximately 15 km from the Chelungpu fault rupture, was subjected to severe liquefaction (Chu et al. 2004). The widespread liquefaction phenomenon was observed during the Chi-Chi earthquake which occurred on 21 September 1999 in the early morning in Taiwan (Yuan et al. 2003). More than 2,400 people lost their lives and 11,000 people were injured by heavy damage (Lee et al. 2003). The moment magnitude (Mw) of the Chi-Chi earthquake was 7.6, and the maximum horizontal acceleration was measured as 0.19 g in N–S direction at a ground motion station (TCU 110) located at the town of Yuanlin (Yuan et al. 2003). The liquefaction is one of the main reasons for heavy damage observed on the building, bridges and life-lines in the town of Yuanlin. The distribution of the observed liquefactions and major faults are illustrated in Fig. 3. The main geological units of Yuanlin area are composed of a thick alluvial deposit. Depth to bedrock increases from east to west, reaching a depth of more than 200 m (Fig. 4; Yuan et al. 2003). While the western part of the Yuanlin area is composed of thick alluvial deposits which were subjected to widespread liquefaction, the eastern part of the Yuanlin area is composed of geological unit which is not susceptible to liquefaction.

Fig. 3
figure 3

Distribution of liqufaction sites after the 1999 Chi-Chi earthquake (http://www.ces.clemson.edu/chichi)

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Fig. 4
figure 4

The simplified geological map of Yuanlin area (Lee et al. 2003)

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The geotechnical data of Yuanlin area was obtained from extensive field and geotechnical borehole studies performed by Moh and Associates (Yuan et al. 2003; MAA 2000). These investigations included some in-situ tests such as SPTs, CPTs, seismic cross-hole tests and surface-wave tests (Yuan et al. 2003). Geotechnical data used in this study were downloaded from the website of http://www.ces.clemson.edu/chichi. The factor of safety necessary for determination of LS is calculated using the SPT-based method; therefore, 42 geotechnical borehole logs including SPT-N values and geotechnical laboratory test results, such as clay content, liquid limit, etc. were selected from the geotechnical data. Geotechnical data between 0 m and 20 m for the boreholes labeled as YL-BH-16 and YL-BH-22 could not continuously be obtained. Besides, depth of the groundwater table in borehole YL-BH-48 is measured 7.3 m and considered as a questionable depth based on the GWT level of the other boreholes. Therefore, 39 of 42 geotechnical borehole data from the Yuanlin area are considered valid and used for the verification of LS and associated classification proposed in this study. To calculate FL for each soil layer throughout the boreholes, liquefaction analyses are performed considering the conventional procedure originally developed by Seed and Idriss (1971) and recently modified by Youd et al. (2001). The overburden correction factor (CN) proposed by Liao and Whitman (1986) is preferred to normalize the SPT-N values. The estimated CRR for the soil layers with fines content more than 35% may be conservative if the procedure suggested by Youd et al. (2001) to obtain an equivalent (N1)60 for clean sand ((N1)60cs) is used. To overcome this limitation, the criterion given in Table 5, which was suggested by Andrews and Martin (2000), is employed for the soil layers with fines content more than 35%. The soil layers with liquid limits and clay contents greater than 32% and 10%, respectively, are evaluated as non-liquefiable even if FL<1.4.

Table 5 Liquefaction susceptibility of silty and clayey sands (after Andrews and Martin 2000)
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The LS and severity classes for all boreholes are given in Table 6. The liquefaction susceptibility map of Yuanlin is constructed by using triangulation with linear interpolation technique considering the calculated LS values and the coordinates of boreholes (Fig. 5). The areas where liquefaction was observed generally fall into the moderate and high-severity classes. Although the north of the investigated area has moderate severity class, liquefaction was not observed on the ground surface. However, liquefaction severity indices of the north of the investigated area vary between lower and mid-ranges of the moderate potential class. Besides, the traces of the liquefaction in the north of the investigated area might not be reached to the surface due to the cap soil. The liquefaction severity map of the Yuanlin area is prepared in this study based on geotechnical data obtained from boreholes drilled after Chi-Chi earth. Therefore, the soil properties may be changed due to the shaking of the earthquake. A more representative susceptibility map could be prepared if boreholes had been drilled before the earthquake. However, LS values calculated from the boreholes drilled on various sites where the effects of the liquefaction were widely observed on the ground surface are generally greater than those drilled on the other sites (Fig. 6). Consequently, this comparison indicates that the performance of the LS and associated classification proposed in this study seems to be valid.

Table 6 The LS values with severity classes estimated for all boreholes drilled in the town of Yuanlin
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Fig. 5
figure 5

Liquefaction severity map of Yunalin based on LS

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Fig. 6
figure 6

The LS values of the liquefied and non-liquefiable boreholes

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Application of the proposed LS to a site in Turkey

Liquefaction and liquefaction-induced failures occured widely during the past devastating Turkish earthquakes such as 1992 Erzincan Earthquake, 1998 Adana-Ceyhan Earthquake and 1998 Kocaeli and Duzce Earthquakes. The most severe structural damage and loss of life were observed during the 1999 Kocaeli Earthquake, which occurred in the Marmara Region. The town of Inegol is located in the Marmara region, a seismically active region due to the presence of active fault segments of the North Anatolian Fault Zone (NAFZ). The NAFZ which is a right-lateral strike slip fault splits into two branches between Goynuk and Akyazi settlements (Fig. 7). Inegol is located at the south of the southern branch of the NAFZ, which passes through Geyve, Iznik and Gemlik (Fig. 7). The liquefaction phenomenon was not observed during the 1999 Kocaeli Earthquake, which occurred on the northern branch of NAFZ in Marmara Region, because the Inegol Basin is about 100 km far from the epicenter of this earthquake with Mw of 7.4.

Fig. 7
figure 7

Seismotectonic map of Marmara Region (modified from Saroglu et al. 1992)

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A geological map of the Inegol Basin was prepared by by MTA (General Directory of Mineral Research and Exploration). The Inegol Basin is composed of Pre-Neogene-aged basement rocks, Neogene-aged units and Queternary alluvial deposits (Fig. 8). The presence of a shallow groundwater table and loose granular alluvial deposits increase the susceptibility of liquefaction potential of the soils below Inegol Basin. A total of 20 geotechnical boreholes performed by Tutuz et al. (2000) were evaluated for the construction of a liquefaction susceptibility map for Inegol. The disturbed SPT samples obtained at intervals of 1.5 m through the boreholes were used to determine grain-size distribution and Atterberg limits of the soils (Tutuz et al. 2000). Three faults close to the Inegol Basin were considered to describe the design moment magnitude and maximum horizontal acceleration for the proposed scenario earthquake considered in preparation of the liquefaction susceptibility map of the Inegol Basin. The first fault is the southern branch of the NAFZ (Geyve-Iznik-Gemlik segment), the second and third ones are the Yenisehir fault and Eskisehir-Inonu fault zone, respectively (Fig. 7). Although the moment magnitude of the scenario earthquake can be estimated by using the length of the fault in empirical equations proposed by Wells and Coppersmith (1994), the relationship between magnitude and surface rupture length based on the Turkish earthquake data proposed by Aydan (1997) is preferred to obtain more representative assessment for scenario earthquakes which may occur in the Marmara region. The surface rupture lengths are assumed to be equal to the length of the fault segment. The estimated surface magnitudes (MS) of earthquake scenarios are obtained using their lengths given in Fig. 9. MS are converted to moment magnitudes (MW) using the empirical equation (Eq. 7) suggested by Ulusay et al. (2004) based on the Turkish earthquake data. The maximum horizontal ground acceleration, which may occur as a result of a scenario earthquake at the Inegol Basin, is estimated from attenuation relationship (Eq. 8) proposed by Ulusay et al. (2004).

$$M_{\rm W} = 0.6798M_{\rm S} + 2.0402$$
(7)
$$a_{\max} = 2.18\exp [0.0218(33.3M_{\rm W} - R_{\rm e} + 7.8427S_{\rm A} + 18.9282S_{\rm B})]$$
(8)

where, amax is the peak ground acceleration, SA and SB are site condition constants (SA=0 and SB=0 for rock sites, SA=1 and SB=0 for soil sites, SA=0 and SB=1 for soft soil sites) and Re is the distance to epicenter. The length of three faults, the closest distances to the Inegol Basin, moment magnitudes and maximum horizontal accelerations of the scenario earthquakes are given in Table 7. The most severe damage may occur if the scenario earthquake occurs on the southern branch of the NAFZ (Geyve-Iznik-Gemlik segment) on which the highest maximum horizontal ground acceleration value was obtained among the earthquake scenarios considered in this study. Therefore, Mw and amax considered in the liquefaction analyses are assumed to be equal to 7.6 and 426 gal, respectively. The proposed liquefaction severity indices for all boreholes are calculated and given in Table 8. The liquefaction susceptibility map of Inegol Basin was constructed by using triangulation with linear interpolation technique considering LS values and coordinates of boreholes (Fig. 10). As can be seen from Fig. 10, a large horizon from NE to SW is represented by “moderate” to “low” liquefaction severity classes.

Table 7 Length of the faults, their distances to the Inegol Basin, moment magnitudes and maximum horizontal ground accelerations considered in scenario earthquakes
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Table 8 Liquefaction severity index values with severity class estimated for all boreholes drilled in the town of Inegol considering the earthquake scenario with Mw=7.6 and amax=426 gal.
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Fig. 8
figure 8

The simplified geological map of the Inegol Basin.

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Fig. 9
figure 9

The relationship between surface magnitude (MS) and surface rupture length proposed by Aydan (1997)

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Fig. 10
figure 10

Liquefaction severity map of the town of Inegol based on LS

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Results and conclusions

The following results and conclusions can be drawn from the present study:

  1. a.

    Although susceptibility maps are of great importance for planners, decision makers and/or engineers, the existing indices for the assessment of liquefaction susceptibility purposes have some limitations. To overcome these limitations, the LS and its classification are introduced in this study.

  2. b.

    To verify the performance of the LS, the town of Yuanlin (Taiwan) area where widespread liquefaction phenomenon was observed during the Chi-Chi earthquake which occurred in September 21, 1999 in Taiwan is used. The results revealed that the LS values of boreholes drilled on the locations where liquefaction was observed on the ground surface are greater than those drilled on locations where liquefaction was not observed on the ground surface. The soil base may have been changed due to the shaking of the Chi-Chi earthquake. A more representative susceptibility map might be obtained if geotechnical data had been obtained from boreholes drilled before the earthquake. However, the result of the verification obtained from Yuanlin revealed that the performance of the LS and its classification is good.

  3. c.

    As an application case, the town of Inegol (Bursa, Marmara region of Turkey) is considered. Inegol is located at the south of the southern branch of NAFZ. In addition, the presence of a shallow groundwater table and loose granular alluvial deposits increase the susceptibility of liquefaction potential of the soils below Inegol Basin. According to the liquefaction susceptibility map of Inegol town, a large horizon from NE to SW has moderate to low liquefaction severity classes.

  4. d.

    The authors believe that the performance of the LS and its classification introduced in this study should be controlled and refined by further utilization in selected liquefaction-prone areas.