Introduction

Slope instability is responsible for damage to public and private property every year. Slope failures can be manifested as landslides or by slower processes such as soil creep. Buildings and infrastructure located on or in the path of a landslide can be seriously damaged or destroyed. Slope instability is a complex phenomenon that can occur at many scales and for many reasons. Slope stability analyses and stabilization require an understanding and evaluation of the processes that govern the behavior of slopes. Examples of triggering mechanisms or agitation factors of slopes include earthquakes, water, slope angle, and slope strength characteristics.

The essential geological, hydrological and seismological properties of a slope must be understood as well as the methods for obtaining the necessary input data for reliable slope stability analyses. Scientists and engineers utilize many tools to investigate all aspects of slope instability. Key factors in slope stability investigation include determining the boundaries of the slope instability, establishing a history of previous slope movement, assessing landslide cause, modeling landslide initiation and the travel paths taken by moving landslide debris, assessing the damage to affected buildings and structures, and preparing recommendations for stabilizing slopes.

Primarily, slope failure is related to the following:

  • soil properties or soil type of slope,

  • geometry of slope,

  • weight,

  • water content (one of the most aggressive factors),

  • shear strength reduction in the slope,

    * tension cracks,

    * vibrations and earthquakes.

Estimation of earthquake risk in city planning is one of the most important tasks in avoiding natural disasters. Seismic risk evaluation includes the vulnerability of the value at risk and the hazard. Slope instability generated by seismic events was investigated in the present study. Several studies on seismic slope stability analysis have been reported (Matasovic 1991; Bourdeau et al. 2004; Cherubini et al. 2004).

The main goal of the research carried out in Gurpinar (Istanbul) as a case study was to evaluate current techniques of static and seismic slope analysis and mitigation of earthquake-induced landslides produced by seismically induced ground deformations.

Earthquakes and slope failures

Earthquakes and related slope failures in Japan were investigated by Tamura (1978); in Fig. 1, Df is the distance from a fault to the outer boundary of the zone where many slope failures have occurred; df is the distance from a fault to the outer boundary of the zone where few slope failures have occurred; Dp is the distance from an earthquake epicenter to the outer boundary of the zone where many slope failures have occurred; and dp is the distance from an earthquake epicenter to the outer boundary of the zone where few slope failures have occurred.

Fig. 1
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Relationship between magnitude and distance to slope failure in Japan (Tamura 1978; ISSMFE 1993)

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In the Manual for Zonation on Seismic Geotechnical Hazards (prepared by the Technical Committee for Earthquake Geotechnical Engineering, TC4, of the International Society for Soil Mechanics and Geotechnical Engineering), the magnitude–distance criteria and historic information are summarized in Figs. 2 and 3.

Fig. 2
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Comparison of relationships between magnitude and maximum distance from a fault or an epicenter (ISSMFE 1993)

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Fig. 3
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Comparison of relationships between magnitude and distance from a fault or an epicenter causing different percentage of slope failures (ISSMFE 1993)

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The curves shown in Fig. 4, giving maximum epicentral distance for slope failure as a function of magnitude, are recommended by ISSMFE (1993) for use in microzoning.

Fig. 4
figure 4

General relationships between magnitude and the epicentral distance of slope failures (ISSMFE 1993)

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Slope stability evaluation methods

Slope stability evaluation methods may be categorized as static and seismic methods.

Slices method (static load state) for effective soil pressure

The factor of safety (FS) for slope stability with undrained shear strength parameters ϕ′, c′ are given by:

$$ {\text{FS}} = {\frac{{\Upsigma {{c^{\prime}b_{\text{i}} } \mathord{\left/ {\vphantom {{c^{\prime}b_{\text{i}} } {\cos \alpha_{\text{i}} + \tan \phi^{\prime}\Upsigma W_{\text{i}} \cos \alpha_{\text{i}} - {{ub_{\text{i}} } \mathord{\left/ {\vphantom {{ub_{\text{i}} } {\cos \alpha_{\text{i}} }}} \right. \kern-\nulldelimiterspace} {\cos \alpha_{\text{i}} }}}}} \right. \kern-\nulldelimiterspace} {\cos \alpha_{\text{i}} + \tan \phi^{\prime}\Upsigma W_{\text{i}} \cos \alpha_{\text{i}} - {{ub_{\text{i}} } \mathord{\left/ {\vphantom {{ub_{\text{i}} } {\cos \alpha_{\text{i}} }}} \right. \kern-\nulldelimiterspace} {\cos \alpha_{\text{i}} }}}}}}{{\Upsigma W_{\text{i}} \sin \alpha_{\text{i}} }}}, $$
(1)

where u is pore water pressure (\( u = h_{w} \gamma_{w} \)), and other parameters are given in Fig. 5.

Fig. 5
figure 5

Slope parameters for undrained shear strength parameters ϕ′, c′

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Slices method (seismic load state) for effective soil pressure

Parameters used in seismic slope stability analysis are shown in Fig. 6. Forces acting on the failure surface are:

Fig. 6
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Parameters for seismic slope stability [redrawn from Das (1993)]

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  1. (a)

    weight of wedge, W

  2. (b)

    inertia force on the wedge, k h W, where k h is the average coefficient of horizontal acceleration, and

  3. (c)

    resisting force per unit area s, the shear strength of soil acting along failure surface ABC.

The FS with respect to strength is given by:

FS = resisting moment about O/overturning moment about O

$$ {\text{FS}} = s\left( {\text{ABC}} \right){R \mathord{\left/ {\vphantom {R {WL_{ 1} }}} \right. \kern-\nulldelimiterspace} {WL_{ 1} }} + k_{\text{h}} WL_{ 2} , $$
(2)

In the analysis of slope stability, it is assumed that the soil is homogeneous. However, in a given slope, layered soil can be encountered. This method is shown in Fig. 7.

Fig. 7
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Parameters for seismic slope stability analysis [redrawn from Das (1993)]

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The FS for this slope is given by (Das 1993):

$$ {\text{FS}} = {\frac{{\sum\nolimits_{1}^{\text{n}} {P_{\text{n}} \left( {cB_{\text{n}} \sec \alpha_{\text{n}} + W_{\text{n}} \cos \alpha_{\text{n}} \tan \phi } \right)} }}{{\sum\nolimits_{1}^{\text{n}} {P_{\text{n}} \left( {W_{\text{n}} \sin \alpha_{\text{n}} + k_{\text{h}} W_{\text{n}} \left[ {{{L_{\text{n}} } \mathord{\left/ {\vphantom {{L_{\text{n}} } R}} \right. \kern-\nulldelimiterspace} R}} \right]} \right)} }}} , $$
(3)

where α n may be either positive or negative.

Analysis for study area

Study area: general geology and landslide features

The study area is shown in Fig. 8a. The general geology comprises the Trace Formation, Gurpinar Formation, Kirklareli Formation, Sazlidere Formation, Bakirköy Formation, and Çukurçeşme Formation (Alparslan et al. 2006). The Gurpinar Formation is Miocene and upper Oligocene in age, and includes sandstone, limestone and claystone units, and several soil components, mainly clays. Landslides in this area are mainly observed in the fissured and over-consolidated plastic clays in Gurpinar Formation and are the rotational and retrogressive types (Dalgic 2005). The landslide morphology in many cases is not observable; due to construction work, the landslide morphology has been destroyed by landfill and excavations (Dalgic 2005; Dalgiç et al. 2009).

Fig. 8
figure 8figure 8figure 8figure 8

a Location of study area. b Recorded data for the site. The active and passive source surface-wave records were taken in the field for both active and passive sources over 1–2 s. For the passive source, 6–7 records over about 35 s were taken. The data is obtained by overlaying these records. These figures are obtained from passive seismic sources. Is it not possible to represent both active and passive source data from the same area since the active source represents the shallow parts of the study area? c Formation of the dispersion curve (site 36). Phase velocities and frequencies are determined from time-spatial surface-wave data using 2-D Fourier analysis. d Phase velocity–frequency curve for slope. e S-velocity versus depth of slope section. f (i) Borehole log in project area, 0–20 m. f (ii) Borehole log in project area, 21–40 m. f (iii) Borehole log in project area, 41–50 m

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Geophysical and geotechnical studies

In the early 1980s spectral analysis of surface waves (SASW), a method of generating near-surface shear wave profiles, was carried out (Nazarian and Stokoe 1984). SASW uses the spectral analysis of ground roll generated by an impulsive source and recorded by a pair of receivers. This method has been widely and effectively used in many geotechnical engineering projects (Stokoe et al. 1994). The necessity of recording repeated shots into multiple field deployments at a given site increases the time and labor requirements over a multichannel procedure. Multichannel analysis of surface waves (MASW) tries to overcome the few weaknesses of the SASW method (Park et al. 1999) and can deal with surface waves in the lower frequency range (e.g., 1–30 Hz) suitable for shallow-depth investigation work (e.g., a few meters to a few tens of meters) (Park et al. 2007).

Shear wave velocities and profiles were obtained by MASW, giving the phase velocity-dispersion curve and shear wave velocity profile for the upper 50 m of soil. An example of the application for the slope site is shown in Fig. 8b, which shows the records that were dependent on field conditions for different geophone intervals.

Linear arrays were applied in our study area. Processing the field data is carried out to obtain the phase velocities for different frequencies using Pickwin software. Finally the dispersion curve is obtained (Fig. 8c). SeisImager software combines Pickwin and Plotrefa software modules; SeisImager/SW-1D consists of the Pickwin and WaveEq modules; and SeisImager/SW-2D consists of the Pickwin, WaveEq, and GeoPlot modules. Surface Wave Analysis Wizard is not a separate module but automatically calls on specific subroutines from Pickwin, WaveEq, and GeoPlot to explain the analysis process. Passive (microtremor) and active source surface-wave data analyses:

  • calculate phase velocity and automatically plot the dispersion curve,

  • perform inversion to iteratively find the 1-D S-wave velocity (V s) curve and 2-D V s cross-section,

  • allow active and passive source dispersion curves to be combined for a high-resolution result over all depths sampled,

  • allow flexible geometry options to suit a wide range of site configurations and conditions,

  • are based on robust methods: tau-p frequency domain, CMP cross-correlation for active source MASW; spatial autocorrelation (SPAC) for passive source microtremor array measurements (MAM),

  • and include QC editing of velocity functions and velocity modeling.

During the field studies, seismic refraction data were also collected. The initial model obtained from this data was used in the initial model. By using both forward and inverse solutions algorithms, S-wave velocities are calculated and drawn depending on distance (Figs. 8d, e).

In this study, a Geometrics Smart Seis SE seismic instrument, geophone, and other seismic tools are used. Records were controlled in the field and, after making the necessary adjustments to obtain refraction data, soil structure were modeled by using Seis Imager 1D Pickwin/Surface Wave Analysis software.

In the study area, boreholes were logged to 50 m depth at nine locations; a typical drilling log is shown in Fig. 8f.

Seismic hazard analysis of study area

Seismic hazard analysis refers to the probability of occurrence per unit time of certain levels of ground motion caused by earthquakes (Erdik et al. 1999; Erdik and Durukal 2004). This analysis is often summarized by a seismic hazard graph of the annual probability of exceedance versus ground motion amplitude. Both deterministic and probabilistic seismic hazard analyses were used to evaluate the seismic hazard in the region. The potential earthquake source was taken to be the North Anatolian Fault in the Marmara Sea.

Deterministic seismic hazard analysis

Required input for deterministic hazard analysis is a designation of active faults or earthquake sources in the region. For the Marmara region (Fig. 9a, b), magnitudes were estimated for three models (A, B, and C) for seismic hazard analysis (JICA-IBB Report 2002):

Fig. 9
figure 9

a Proposed models A, B, C for seismic hazard analysis in the Marmara region. A approximately 119 km rupture length; B approximately 108 km rupture length; C approximately 174 km rupture length. b Seismogenetic fault for the study area

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  • Model A: approximately 119 km rupture length;

  • Model B: approximately 108 km rupture length; and

  • Model C: approximately 174 km rupture length (Tables 1, 2).

    Table 1 Equations for rupture length and magnitude estimations
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    Table 2 Rupture length and magnitude estimations. Model A: approximately 120 km rupture length; Model B: approximately 108 km rupture length; Model C: approximately 174 km rupture length
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Probabilistic seismic hazard analysis of region

Table 3 refers to earthquakes within about 100 km radius of the study area. Gutenberg-Richter recurrence relationships were determined from:

$$ \log N = 3.0 - 0.71M. $$
(4)
Table 3 Number of earthquakes within about 100 km radius of the study area, calculated from Eq. (3)
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The earthquake occurrence probabilities in Table 4 are obtained from:

$$ R_{\text{m}} = 1 - e^{ - N\left( M \right) D} , $$
(5)

where R m is risk value (%); D is duration; N(M) refers to the value of M used in Eq. (4).

Table 4 Probabilities of earthquake occurrence for region
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The attenuation relationship was defined by two attenuation models: from a set of attenuation relationships, the design acceleration value for the city was calculated to be 0.41 g [Joyner and Boore (1981) model] and 0.4 g [Campbell (1997) model] with a 50-year exceedance probability of 20%. Finally, the hazard curve for the region was estimated (Fig. 10). Estimated acceleration values for magnitude 7.5 earthquakes are given in Table 5.

Fig. 10
figure 10

Hazard curve for the region (Joyner and Boore (1981) attenuation model)

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Table 5 Estimated acceleration values for 7.5 magnitude, 15 km epicentral distance (∆, km) and 15 km focal depth (H, km)
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The design acceleration coefficient, k h was determined from:

$$ k_{\text{h}} = 0.3\left( {I + 1} \right)A_{0} $$
(5)

and/or

$$ k_{\text{h}} = 0.2\left( {I + 1} \right)A_{0} , $$
(6)

where I is the structure importance factor (1 ≤ I ≤ 1.5), A 0 is the estimated earthquake acceleration (0.43 g). In this study, k h coefficient was selected as 0.20 g.

The relationship between earthquake and slope failure is shown in Figs. 1, 2 and 3. For an epicentral distance of 15 km from the main fault in the study area, a minimum of magnitude 6.0 may trigger slope failure in the study area. For this reason, a detailed seismic slope stability analysis was carried out in the study area.

Detailed slope stability analysis for static and seismic conditions

In the study area, in situ SPT tests were carried out and laboratory samples were obtained from six boreholes (maximum depth 50.0 m) to determine soil classification and strength characteristics. Geophysical studies (seismic refraction and MASW) were also carried out for estimation of the structure and strength characteristics of the slope to 50.0 m depth. All field and laboratory data were used to predict the mechanical and structural (geometrical) behavior of the slope. Three soil slope models were considered.

The geometrical features and failure surface of the first, second, and third models are shown in Figs. 11a, b, and c. Analysis results are given in Tables 6, 7, 8, 9.

Fig. 11
figure 11

a First model b second model c third model

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Table 6 Safety factor for static and dynamic conditions with geometrical and mechanical parameters for first slope model (R = 73.70 m)
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Table 7 Safety factor for static and dynamic conditions with geometrical and mechanical parameters for second slope model (R = 169.40 m)
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Table 8 Safety factor for static and dynamic conditions with geometrical and mechanical parameters for third slope model (R = 151.98 m), assuming clay soil
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Table 9 Safety factor for static and dynamic conditions with geometrical and mechanical parameters for third slope model (R = 151.98 m), assuming sandy soil
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Results and discussion

Matasovic (1991) has pointed out that the seismic stability of natural slopes is a subject about which much uncertainty still exists. The main problems associated with predicting slope behavior during and after earthquake motion are connected with the shear strength parameters of the material and the estimation of adequate seismic loading. In addition, both local topography and the presence of surface layers are likely to have caused the observed amplification effects that are thought to have contributed to the triggering of some of the hundreds of landslides related to this seismic event (Bourdeau et al. 2004).

The stability of a slope during or after a seismic event was studied using the pseudostatic approach which estimates the stability of a slope under dynamic loading, incorporating the dynamic safety factor. Cherubini et al. (2004) have suggested that this approach is not able to account for either the seismic displacements of the slope or the influence of the duration and the time variation of the seismic shock acceleration over the slope displacements. In the first phase of the present study, seismic hazard analysis of the study region was carried out by deterministic and probabilistic means to determine the level of ground motion that triggers slope failure. Relationships between the magnitude of an earthquake causing slope failures and their distance from a fault or an epicenter were also examined in the study area context. The main seismogenetic source of the region is the North Anatolian Fault Zone in the Marmara Sea.

Both static and seismic slope stability analyses were carried out and the safety factor of the slope was determined. While no stability problem was found for the static case, unsafe seismic safety factors of 0.8 and 0.9 were obtained. Slope improvement is proposed for the study area.