1.Introduction

Landslides constitute a common type of secondary geological disaster that occurs during an earthquake and results in widespread damage and large economic losses(Kou et al.,2018;Han et al.,2018).It is estimated that around 20%of recorded landslides have been triggered by earthquakes(Wen et al.,2004).For example,the 1994 Northridge earthquake,which registered a magnitude of 6.7 on the Richter scale,triggered more than 11000 landslides over an area of approximately 10000 km2.Some of these landslides damaged and destroyed homes and other structures,blocked roads,disrupted pipelines,and caused other serious damage(Parise and Jibson,2000).On May 12,2008,a magnitude-8.0 earthquake struck Wenchuan County in Sichuan Province,China.Due to the notably high magnitude and long duration of vibration of the earthquake and the complicated geoenvironment of the disaster area,the Wenchuan earthquake caused a significant number of landslides.Dozens of landslides with volumes greater than 107 m3 occurred(Huang,2009).According to damage statistics(Huang and Li,2009),landslides and other geohazards,including the Wangjiayan landslide,accounted for one third of all deaths caused by the earthquake.Consequently,assessment of the seismic stability of slopes has attracted considerable attention in geotechnical Engineering and earthquake engineering.

海岸电台是我国提供水上安全通信服务的岸基载体。它是国际海事组织（IMO）注册公布并指定的船舶遇险与安全通信的国际值班台和海上安全信息的国际播发台。全国共设有18座海岸电台，其中南海海域设有汕头、广州、湛江、北海、海口、八所和三亚共7座海岸电台，由南海航海保障中心下属的汕头、广州、湛江、南宁和海口通信中心负责管理。

The state-of-the-art seismic stability analysis method for slopes is time-domain analysis,which provides a powerful tool for seismic design of a geotechnical structure.However,this technique requires reliable constitutive models and appropriate dynamic boundary conditions,which are not usually available in practice(Kontoe et al.,2013).These difficulties limit the application of the dynamic approach.Consequently,such advanced techniques are justified only in major projects or for extremely large earthquakes,and the conventional pseudo-static method is still widely used in engineering design due to its simplicity(Baker et al.,2006;Loaiciga,2015;Loukidis et al.,2003;Shinoda,2015;Yang and Chi,2014;Zhao et al.,2016).

In the pseudo-static method,the seismic loading is modeled as a statically applied inertial force,the magnitude of which is a product of a seismic coefficient k and the weight of the potential sliding mass.Generally,the k values are much smaller than a mh/g,where a mh is the maximum horizontal acceleration expected at the site,and g is the acceleration of gravity.For comparison with the displacement analyses,Seed(1979)calibrated the pseudo-static method for seismic stability analysis of earth dams with soils that do not suffer significant strength loss during earthquakes.It was concluded that for earthquake magnitudes of 6.5 and 8.5,k=0.10 and k=0.15 are recommended,respectively,together with are quired factor of safety of1.15.The work of Seed(1979)is regarded as an important milestone because of its wide use and development.Similarly,Hynes-Griffin and Franklin(1984)recommended that the k value should be half of the peak bedrock acceleration and a design factor of safety of 1.0 should be required,though this method is not recommended for areas that are subject to large earthquakes or that have embankments with liquefiable soil.Bray et al.(1998)also developed a pseudo-static method for analyzing the stability of solid-waste land fills.The procedure calls for a k value that is 0.75 times the maximum bedrock acceleration.By reviewing recommendations of different codes,Baker et al.(2006)found that,although the pseudo-static method is recommended for conventional projects by most design guidelines and codes(e.g.,Eurocode 8(ECS,2004),SP117(CGS,2008),GB 50330-2013,and IITK-GSDMA(2005)),the magnitudes of the recommended k values and the corresponding stability safety criteria are different.The Technical Code for Building Slope Engineering(GB 50330-2013)of China and the Guidelines for Evaluating and Mitigating Seismic Hazards in California(SP117)are the most representative design codes.Therefore,a comparative study on the pseudo-static methods based on GB 50330-2013 and SP117 was performed.This paper first summarizes the pseudo-static slope stability analysis method based on the two design codes and subsequently examines the factors influencing the seismic coefficient k.Two example analyses were comparatively performed to verify the reliability and rationality of the pseudo-static method.

2.Comparison of GB 50330-2013 and SP117

2.1.Introduction of GB 50330-2013

where σx=are the static and dynamic horizontal stresses of the element,respectively;andare the static and dynamic vertical stresses of the element,respectively;and andare the static and dynamic shear stresses of the element,respectively.The seismic stability of the slopes in the time history analysis is evaluated using the minimum mean factor of safetyproposed by Liu et al.(2003)as follows:

where G is the gravity of the slip mass or element;and k h is the horizontal seismic coefficient,which is determined by the basic earthquake intensity and maximum horizontal acceleration(a mh)expected at the site,as shown in Table 1.

Generally,the seismic coefficient k h can be calculated as follows:

where f eq is the seismic equivalence reduction factor used to narrow the difference between the calculation results and the actual seismic behavior of slopes during earthquakes.According to Table 1 and Eq.(2),the f eq values are equal to 0.25 for any maximum horizontal acceleration.In other words,the pseudo-static method recommended by GB 50330-2013 specifies a single value for f eq.

According to GB 50330-2013,the stability of slopes can be divided into four types of status:unstable,stable-,stable,and stable+according to the factor of safety,as shown in Table 2.

For permanent slope engineering under earthquake conditions,F st values for different safety levels of slope engineering are shown in Table 3.

The safety level of slope engineering can be determined by the severity of the slope failure,slope types,and slope height H.For soil slopes,the safety level can be determined as shown in Table 4.

2.2.Introduction of SP117

If the sites are located in the Seismic Hazard Zone maps published by the California Division of Mines and Geology on the Newmark displacement analysis in SP117.Bray and Rathje(1998)found that the Newmark displacement(u)is a function of k y,k max,and D5-95,and presented a relationship to predict the median value of the slope displacement.The yield seismic coefficient k y is the ratio of the seismic acceleration a y,yielding a factor of safety equal to unity,to the acceleration of gravity g;k max is the ratio of maximum horizontal equivalent acceleration(a mhe)over the duration of earthquake shaking to the acceleration of gravity g;and D5-95 is the significant duration of shaking measured as the time between 5%and 95%of the normalized Arias intensity.The median values of D5-95 （（D5-95）med）on rock can be estimated as follows(Abrahamson and Silva,1996):

(CDMG),the pseudo-static method is recommended by SP117(Blake et al.,2002)for screen analysis.The purpose of the screen analysis is to filter out sites that have no potential or low potential for landslide development.If F s＞1,the screen analysis will satisfy the requirement for the stability of seismic slopes.If F s≤1,a quantitative evaluation such as the Newmark displacement analysis(Newmark,1965)will be performed to assess the seismically induced landslide hazards.

A de-stabilizing horizontal seismic coefficient is utilized with a conventional LEM.The seismic coefficient represents the fraction of the weight of the sliding mass that is applied as an equivalent horizontal force acting through the centroid of the sliding mass.The seismic coefficient to be used in the analyses is as follows:

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where a mhr is the maximum horizontal acceleration at the site for a soft rock site condition.Unlike GB 50330-2013,the f eq values specified by the SP117 guidelines are not constant,but a function of magnitude and site-source distance(Stewart et al.,2003).This approach has a rational basis.In addition to the slope height,slope angle,and unit weight and shear strength of the geomaterial,the main factors influencing seismic slope stability are a mhr,magnitude,and site-source distance.It is easy to understand that earthquakes with greater a mhr and magnitude tend to result in poorer slope performance than earthquakes with smaller a mhr and magnitude.The reasons for this outcome are that greater a mhr means stronger shaking,and earthquakes with greater magnitude have longer durations of shaking.

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Depending on the magnitude and distance,the f eq values are identified using a model for seismic slope displacements based where M denotes magnitude,and r denotes site-source distance.

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甘肃省河西内陆河流域总面积27万km2，包括石羊河、黑河、疏勒河（含苏干湖区的哈勒腾河等）等3个水系。年径流量在1亿m3以上独立出山的河流有15条，其中石羊河水系6条；黑河水系6条；疏勒河水系3条。水资源总量61.3亿m3，人均水资源量1 250 m3，耕地亩均水资源量570 m3，分别为全国平均水平的54%和38%，属资源性缺水地区。

Bray and Rathje(1998)presented a relationship to predict the median value of slope displacement,which is described as follows:

The seismic equivalence reduction factor f eq can be related to magnitude,distance,and a mh based on the following assumptions and observation:

(1)f eq is related to k y/k max.The rationale for this relationship is described in detail by Stewart et al.(2003).

For further comparison of the pseudo-static methods in SP117 and GB 50330-2013,the seismic stability of two homogeneous soil slopes was evaluated using the time-history analysis method and the Newmark displacement analysis method.

(3)k max is related to the product of a mhr/g and F nr,where F nr is the factor that accounts for the nonlinear response of the materials above the slide plane and can be approximated as follows:

for 0.1＜a mhr/g＜0.8(Bray et al.,1998).

Thus,f eq can be obtained as follows:

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2.3.Comparison of GB 50330-2013 and SP117

Both SP117 and GB 50330-2013 recommend the use of the pseudo-static method for seismic stability analysis of slopes.As mentioned previously,the pseudo-static method is used for a screen analysis in SP117.If the site fails the screen,a Newmark analysis will be performed(Blake et al.,2002).According to GB 50330-2013,the pseudo-static method is recommended to divide the seismic slopes into four types of stability status:unstable,stable-,stable,and stable+.However,the largest difference between SP117 and GB 50330-2013 in terms of their utilization of the pseudo-static method is the calculation procedure for the horizontal seismic coefficient k h.The factors of k h considered in SP117 and GB 50330-2013 are shown in Table 5.

According to GB 50330-2013,k h is determined based on the basic earthquake intensity and a mh.The problems posed by basic earthquake intensity are significant to seismic structure design because of its subjectivity.Moreover,the f eq values are equal to 0.25 for any a mh values and are independent of magnitude or distance.The duration of strong shaking has a significant influence on the seismic stability of slopes,but it is not considered in the calculation of f eq in GB 50330-2013.

where F s0 denotes the factor of safety in the static status,and F smin denotes the minimum factor of safety in the seismic time history.

3.Examples

3.1.Example 1

A seismic stability problem of a simple homogeneous soil slope with a slope inclination angle of α =36.87° and a height of H=15 m was investigated,as shown in Fig.1.The soil unit weight γ was 20 kN/m3,the cohesive strength c was 35 kPa,and the internal Friction φ was 15°.The seismic equivalence reduction factors and factors of safety for different ranges of a mhr,M,r,and u were calculated using the Morgenstern-Price method(Morgenstern and Price,1965)with the pseudo-static method recommended by GB 50330-2013 and SP117.The results are shown in Figs.2 and 3.

The following conclusions can be drawn from Figs.2 and 3:

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(2)When the threshold displacement is equal to 5 cm,the averages of f eq from SP117 are 0.479,0.591,and 0.712 for M=6.0,7.0,and 8.0,respectively.When the threshold displacement is 15 cm,the averages of f eq from SP117 are 0.316,0.428,and 0.549 for M=6.0,7.0,and 8.0,respectively,because with the increase of the threshold displacement,the slope performance inevitably worsens,and the f eq values decrease.Thus,the factors of safety obtained by SP117 increase with the threshold displacement,as shown in Fig.3.Because the f eq values are independent of the threshold displacement in GB 50330-2013,the factors of safety are invariable with the threshold displacement.

(1)The values of f eq specified by GB 50330-2013 are equal to 0.25 and are much smaller than those of SP117 except for M=6.0,r=10 km,a mhr=0.1g,and u=15 cm.The seismic inertial forces applied on the sliding mass calculated by GB 50330-2013 are much smaller than the inertial forces calculated by SP117 for most cases.Thus,under the same conditions,the factors of safety of the seismic slopes evaluated by GB 50330-2013 are greater than those evaluated by SP117,as shown in Fig.3.It is also shown that with increasing a mhr,the difference in the factors of safety obtained by two design codes also increases.

(4)With the increase in the distance r,the f eq values increase,and the factors of safety obtained by SP117 decrease.However,with increasing magnitude,the influence of distance on f eq and the factors of safety both decrease.This result is also due to the effect of the duration on the seismic stability of slopes.

(3)The results also show that for a given a mhr,the f eq values obtained by SP117 increase with the magnitude,and the factors of safety decrease,i.e.,it is thought that the duration of the earthquake is one of the most important factors.

(5)With the increase of a mhr,the f eq values from SP117 first increase and subsequently decrease,and the factors of safety decrease throughout.

(6)The slip surfaces predicted by SP117 and GB 50330-2013 are nearly the same.The slip surfaces for M=7.0,r=20 km,a mhr=0.2g,and u=5 cm are shown in Fig.4.

3.2.Example 2

(2)Two values of the threshold Newmark displacement are used in SP117:5 cm and 15 cm.It should be noted that the Newmark displacements provide only an index of slope performance.The 5-cm threshold value distinguishes conditions in which very little displacement is likely from conditions in which moderate or higher displacements are likely.The 15-cm threshold value distinguishes conditions in which small to moderate displacement are likely from conditions in which large displacements are likely(Stewart et al.,2003).The use of these two threshold displacements is intended to enable engineers and regulatory agencies to exercise judgment over the level of performance that they wish to enforce.

The dynamic response of a slope subjected to a given time history of an earthquake is governed by the following equation:

where M,C,and K denote the mass,damping,and stiffness matrices,respectively;¨u,˙u,and u denote the vectors of slope acceleration,velocity,and displacement,respectively;and¨ug denotes the vector of earthquake acceleration.Rayleigh damping was used in the analysis,i.e.,damping in the form of C= ηM+ ξK,where η = λω,ξ= λ/ω,λ denotes the damping ratio,and ω denotes the natural angular frequency.Eq.(8)can be solved using the Wilson-θ method.

According to the static and dynamic stresses obtained by the FEM,the factor of safety of the seismic time-history stability analysis can be calculated as follows:

where ci and φi are the cohesive strength and internal friction angle at element i from undrained triaxial shear tests,respectively;li is the length of slip surface at element i;and σn i and τi are the normal and shear stresses on the slip surface at element i,respectively:

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GB 50330-2013 recommends seismic stability analysis for permanent slopes in earthquake zones where the basic intensity is 7 or greater.If no important buildings are present in the sliding areas,a pseudo-static method combined with the limit equilibrium method(LEM)or finite element method(FEM)can be used to assess the seismic slope stability.The horizontal seismic loads Q e acting on each slip mass or element can be calculated as follows:

对特质焦虑和手机成瘾进行积差相关分析，所得结果见表1。特质焦虑与手机成瘾呈中度正相关；特质焦虑与戒断性、突显性分别均呈中度正相关，与持续性、技术性、冲突性分别均呈低度正相关；正性情绪与手机成瘾、持续性、技术性均无相关关系，与冲突性和突显性分别呈低度正相关，与戒断性呈中度正相关；负性情绪与持续性、技术性、冲突性分别呈低度正相关，与手机成瘾、突显性、戒断性分别呈中度正相关。

Numerous factors,including magnitude,distance,and threshold displacement,are considered in the determination of k h in SP117(Blake et al.,2002).In addition to the duration of the earthquake,f eq is also related to the slope threshold displacement because f eq is introduced to narrow the difference between the calculation results and actual seismic performance,and the slope displacement is an effective calibration for measuring the actual seismic behavior.Consequently,in the pseudo-static method,it is necessary to consider the different levels of slope performance as indexed by displacement.

基于中介效应模型，如果自变量X不仅直接对因变量Y产生影响，而且还通过中介变量M间接对Y产生影响，那么M就是X对Y影响的作用渠道。金融发展(FD)是本文的中介变量M。回归模型(1)已经考察了金融开放对经济增长的总影响，为了验证金融开放是金融发展对经济增长的间接影响渠道，提出回归模型(3)

The Newmark displacement analysis(Newmark,1965)is also applied to assessment of the seismic stability of slopes.Based on the LEM,the concept of yield acceleration is used in Newmark displacement analysis.The permanent displacement of the slopes can be determined by two integrations of the average acceleration,which exceeds the yield acceleration.

The seismic stability of two simple homogeneous soil slopes(shown in Fig.1)was evaluated using the Morgenstern-Price method(Morgenstern and Price,1965)with the pseudostatic method(recommended by GB 50330-2013 and SP117),the time-history analysis method,and the Newmark analysis method.The slope information and soil shear strength parameters are shown in Table 6.The threshold displacement of the slopes was assumed to be 5 cm.

For the time-history analysis and Newmark analysis,eight sets of observed earthquake waves(PEER,2010)were input at the bottom of the slopes(as shown in Table 7 and Fig.5).

产业创新速度对创新效益的作用机制如图1所示，包括微观叠加机制和宏观作用机制。所谓微观叠加机制，起源于产品创新速度，即若干企业的若干产品创新速度的提升，带来整个产业创新效益的提升;所谓宏观作用机制，主要指产业整体的环境要素对企业创新速度的影响机制与方式。

If the minimum mean factor of safety ＜1 and the Newmark displacement u is larger than the threshold displacement(5 cm for this example),the slope is identified as unstable.Otherwise,the slope is identified as stable.According to the magnitude and distance of the input earthquake waves,the f eq values of the pseudo-static method can be calculated,and the factor of safety can be determined.The slope status can also be divided into stable(F s＞1)and unstable(F s＜1)categories using the pseudo-static method recommended by SP117 and GB 50330-2013.

Compared with the time-history analysis,the results of the pseudo-static method recommended by SP117 or GB 50330-2013 can be deemed coincident,conservative,or risky.If the slope status evaluated by the pseudo-static method is the same as that by the time-history analysis,the results of the pseudostatic method can be regarded as coincident.If the slope is unstable as evaluated by the pseudo-static method,while the slope is stable according to the time-history analysis,the results of the pseudo-static method are said to be conservative.Otherwise,the results are determined to be risky.The results are shown in Tables 8 and 9.

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The results indicate that the types of slope stability status evaluated by SP117 are in agreement with those of the seismic time-history stability analysis and Newmark displacement analysis.Note that although the seismic factor of safetyof Slope A is 0.958 when the 2000 Tottori earthquake wave is input,the Newmark displacement is only 2 cm.Hence,the stability status is identified as stable by the time-history analysis.However,the pseudo-static factor of safety evaluated by SP117 is 0.933 under the same conditions,and thus the stability status is considered to be unstable.Although the types of stability status evaluated by the seismic time-history analysis and SP117 are different,the results from SP117 can be regarded as conservative.Similarly,when the 2000 Tottori and 2014 Jinggu earthquake waves are input to Slope B,the results from SP117 are regarded as conservative as well.Consequently,the factors of safety determined by SP117 can be used in practice to supply a safe design.

For slopes A and B,the factors of safety calculated by GB 50330-2013 are greater than 1.0 under all seismic conditions,and even the Newmark displacement far exceeds the threshold value.As a result,the types of stability status evaluated by GB 50330-2013 are not in agreement with those of seismic time history stability analysis and Newmark displacement analysis.The factors of safety calculated by GB 50330-2013 are risky for seismic slope design.

4.Conclusions

(1)Both SP117 and GB 50330-2013 recommend the use of the pseudo-static method for the seismic stability analysis of slopes.Seismic slopes can be divided into four different types of stability status according to the factors of safety from GB 50330-2013,but the pseudo-static method is used for screen analysis in SP117.

(2)According to GB 50330-2013,the f eq values are equal to 0.25 for any a mh and are independent of magnitude or distance,which lacks a rational basis.The f eq values specified by SP117 are dependent on magnitude and distance.Additionally,the slope threshold displacement is considered.

(3)The pseudo-static method recommended by SP117 and GB 50330-2013 was applied to the seismic stability problem of a single homogeneous soil slope.The results show that the f eq values obtained from GB 50330-2013 are much smaller than those from SP117 for most cases.Consequently,the factors of safety determined by GB 50330-2013 are much greater than those of SP117.With the increase of a mhr,the difference in the factors of safety obtained by two codes increases.The results also indicate that the magnitude,distance,and threshold displacement have a certain influence on the f eq and factors of safety obtained by SP117.

(4)Comparison of the time-history stability analysis,the Newmark displacement analysis,and the pseudo-static method recommended by the two codes indicates that the types of slope stability status evaluated by SP117 are in good agreement with the seismic time-history stability analysis and Newmark displacement analysis.The factors of safety determined by SP117 can be used in practice to supply a safe design.

(5)The types of stability status evaluated by GB 50330-2013 are not in agreement with seismic time-history stability analysis and Newmark displacement analysis.The factors of safety determined by GB 50330-2013 are risky for seismic slope design.

(6)For future revision of GB 50330-2013,it is advised that the f eq values and safety standard should be properly improved based on further composite analysis of the seismic behavior and stability of slopes under earthquake conditions.For larger values of a mh,assessment of seismic slope stability should be combined with time-history stability analysis and quantitative evaluation analysis,such as the Newmark displacement method.

References

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Baker,R.,Shukha,R.,Operstein,V.,Frydman,S.,2006.Stability charts for pseudo-static slope stability analysis.Soil Dynam.Earthq.Eng.26(9),813-823.https://doi.org/10.1016/j.soildyn.2006.01.023.

Blake,T.F.,Hollingsworth,R.A.,Stewart,J.P.,2002.Recommended Procedures for Implementation of DMG Special Publication 117 Guidelines for Analyzing and Mitigating Landslide Hazards in California.Southern California Earthquake Center,Los Angeles.

Bray,J.D.,Rathje,E.M.,1998.Earthquake-induced displacements of solid waste land fills.J.Geotech.Geoenviron.Eng.124(3),242-253.https://doi.org/10.1061/(ASCE)1090-0241(1998)124:3(242).

Bray,J.D.,Rathje,E.M.,Augello,A.J.,Merry,S.M.,1998.Simplified seismic design procedure for geosynthetic-lined,solid-waste land fills.Geosynth.Int.5(1-2),203-235.https://doi.org/10.1680/gein.5.0119.

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