On seismic landslide hazard assessment

Transcription

1 Yang, J. (27). Géotecnique 57, No. 8, doi: 1.168/geot TECHNICAL NOTE On seismic landslide azard assessment J. YANG* KEYWORDS: eartquakes; landslides; slopes INTRODUCTION Seismic landslides are one of te most deastating effects of eartquakes, as eidenced by many istorical records (Keefer, 1984; Turner & Scuster, 1996). To date, arious models ae been deeloped for spatially distributed landslide azard assessment, and almost all of tem are based on infinite slope idealisation combined wit te Newmark sliding-block and pseudo-static analysis (e.g. Jibson et al., 1998; Miles & Keefer, 21). Altoug no slope perfectly satisfies te assumptions of te infinite slope model, many, if not most, natural landslides are predominantly translational, wit relatiely low tickness-to-lengt ratios. Te infinite slope idealisation terefore proides a useful approximation tat can elp to identify te landslide azard at te reconnaissance leel. In Newmark sliding-block teory, a potential landslide is modelled as a rigid friction-block resting on an inclined plane (Newmark, 1965). Te seismic inertial force on te sliding mass is regarded as pseudo-static, and is usually represented using a orizontal seismic coefficient tat is expressed as a percentage of te graity. Te Newmark analysis calculates te cumulatie permanent displacement of te friction-block as it is subjected to te acceleration time-istory of a gien eartquake, by double-integrating tose parts of te acceleration time-istory tat exceed te so-called yield acceleration. Te seismic landslide azard is often assessed using te calculated Newmark displacement. As an example, Table 1 gies te categories of landslide azard tat are proposed by te US Geological Surey using te normalised Newmark displacement for infinite slope models (Miles & Keefer, 21). Tere are six leels of relatie azard, ranging from Low, wit a normalised displacement of between and.2, to Very Hig, wit a normalised displacement of Note tat te Newmark displacement ere sould be considered as a relatie index of slope performance rater tan a real deformation. Te existing models ae tended to focus on te orizontal seismic force and disregard te ertical acceleration, altoug a real eartquake will subject te sliding mass to bot. Tis common practice is due partly to te consideration tat most eartquakes produce a peak ertical acceleration tat is small compared wit te peak orizontal acceleration, and te effect of ertical acceleration is negligible (Day, 22). A limited number of studies ae discussed tis effect on eart structures and appeared to offer different opinions. Te elegant pseudo-static analysis of Sarma (1975) for stability of eart dams indicates tat te Manuscript receied 6 Marc 26; reised manuscript accepted 13 June 27. Discussion on tis paper closes on 1 April 28, for furter details see p. ii. * Department of Ciil Engineering, Te Uniersity of Hong Kong. Table 1. Categories of relatie azard for landslides (after Miles & Keefer, 21) Leel of azard Normalised Newmark displacement Low (L).. 2 Moderately low (ML) Moderate (M) Moderately ig (MH).1.2 Hig.2.5 Very ig.5 1. Normalised by te alue of 1 cm. effect is minor, wereas te analysis of Ling & Lescinsky (1998) for dry, reinforced soil structures as suggested tat te effect is significant. In dealing wit tis issue, some obserations from recent eartquakes are wort noting. First, significantly large ertical accelerations ae repeatedly been recorded in te near field of moderate and large eartquakes, wic sows tat te rule-of-tumb ratio, 1/2 or 2/3, between peak ertical and orizontal ground acceleration may not be a good descriptor (NCEER, 1997). For example, te peak ertical acceleration at te surface of a reclaimed site during te 1995 Kobe eartquake was found to be twice as ig as te peak orizontal acceleration (Yang & Sato, 2). Second, te ground motion amplification, particularly in te ertical direction, can be significantly affected by groundwater conditions (Yang & Sato, 21; Yang et al., 22). Tese obserations imply tat arious possible combinations of te groundwater and ground motion conditions may need to be examined to identify a particularly seere state of azard for eart structures. In iew of te aboe obserations, tis study aims to explore te possible effect of ertical acceleration wit regard to landslide azard assessment, by taking account of a wide range of magnitudes of te ertical and orizontal accelerations and a arying water table. Effort is made to sow ow significant te effect could be on te factor of safety, yield acceleration and, particularly, permanent displacement tat is directly associated wit azard estimation. INFINITE SLOPE ANALYSIS Te simplified infinite slope model is sown in Fig. 1. Tis is a two-dimensional model describing a slope wit a potential sliding plane tat is taken parallel to te surface of te slope at a dept z, wit te water table being at z w ¼ mz. Clearly, for dry slopes m ¼, and for saturated slopes m ¼ 1. Factor of safety Consider a ertical slice of a unit widt tat as a weigt W and is subjected to bot ertical and orizontal ground accelerations (Fig. 1). Te pseudo-static seismic forces act- 77

2 78 YANG z w β Unit widt ing on te slice are represented by F ¼ k W and F ¼ k W, were k and k are known as te orizontal and ertical seismic coefficients respectiely. In tis paper, negatie k corresponds to te upward inertial force. Te factor of safety of te infinite slope, FS, is determined as te ratio between te aailable sear strengt and te sear stress deeloped on te failure plane, from c9 þ ðó uþtan ö9 FS ¼ ½ð1 þ k Þsin â þ k cos ⚪z cos â F Fig. 1. Infinite slope model were c9 is te effectie coesion, ö9 is te effectie friction angle, ª is te unit weigt of te soil, ó is te total normal stress on te failure plane, and u is te pore water pressure. Equation (1) can be furter written as c9 þ ½ð1 þ k Þcos â k sin ⚪ ð1 þ k Þª FS ¼ w m cos âgz cos â tan ö9 ½ð1 þ k Þsin â þ k cos ⚪z cos â F W u were ª w is te unit weigt of water. Because of te difficulty and uncertainty inoled in determining te eartquake-induced excess pore water pressure, tis effect is not included in te analysis, in order to retain te simplicity of te pseudo-static metod. Te aboe general expression can be readily simplified for seeral special cases tat ae been discussed in te literature: Special case 1: Dry and static conditions, tat is, k ¼ k ¼, m ¼ FS ¼ c9 þ ªz cos2 â tan ö9 (3) ªz sin â cos â Special case 2: Saturated and static conditions, tat is, k ¼ k ¼, m ¼ 1 FS ¼ c9 þ ð ª ª wþz cos 2 â tan ö9 (4) ªz sin â cos â were ª sould be taken as te saturated unit weigt of te soil. (c) Special case 3: Dry slopes subjected to orizontal acceleration only, tat is, k ¼, k 6¼, m ¼ FS ¼ c9 þ ð cos â k sin âþªz cos â tan ö9 (5) ðsin â þ k cos âþªz cos â (d) Special case 4: Saturated slopes subjected to orizontal acceleration only, i.e. k ¼, k 6¼, m ¼ 1 FS ¼ c9 þ cos â k ð sin âþª ª w cos â z cos â tan ö9 ðsin â þ k cos âþªz cos â (6) c, φ z Hypotetical sliding plane (1) (2) Reduction of factor of safety due to ertical motion To quantify te effect of ertical ground acceleration, it is useful to introduce a reduction factor for te factor of safety, defined as te ratio between te factor of safety under combined ertical and orizontal accelerations, (FS) þ, and te factor of safety under orizontal acceleration only, (FS). In so doing, equation (2) is first rewritten in te form ðfsþ þ ¼ a 1 k þ a 2 k þ a 3 (7) a 4 k þ a 5 k þ a 6 were a 1 ¼ 𪠪 w mþz cos 2 â tan ö9 a 2 ¼ ªzsin â cos â tan ö9 a 3 ¼ c9 þ ðª mª w Þz cos 2 â tan ö9 a 4 ¼ ªz sin â cos â a 5 ¼ ªz cos 2 â a 6 ¼ ªz sin â cos â From equation (7) te factor of safety for te slope subjected only to orizontal acceleration can be readily gien as ðfsþ ¼ a 2 k þ a 3 (8) a 5 k þ a 6 Te reduction factor can ten be establised as r F ¼ ðfsþ þ ½ð ¼ a 1 p þ a 2 Þk þ a 3 Šða 5 k þ a 6 Þ (9) ðfsþ ½ða 4 p þ a 5 Þk þ a 6 Šða 2 k þ a 3 Þ were p ¼ k /k. Yield acceleration Te yield acceleration is conentionally determined to be te orizontal acceleration tat results in a pseudo-static factor of safety equal to 1.. From equation (7) te coefficient of yield acceleration, k y, can be gien as k y ¼ a 1 a 4 a 5 a 2 k þ a 3 a 6 a 5 a 2 (1) It is eident from equation (1) tat te coefficient of yield acceleration witout taking account of te effect of ertical acceleration as te form k9 y ¼ a 3 a 6 (11) a 5 a 2 Furtermore, a reduction factor for te yield acceleration r y can be introduced to quantify te effect of ertical acceleration suc tat r y ¼ k y ¼ 1 (12) k9 y 1 p were ¼ (a 1 a 4 )=(a 5 a 2 ). Clearly, ¼ tan(ö9 â) wen m ¼. Permanent displacement A Newmark analysis calculates te cumulatie displacement of te friction-block as it is subjected to te acceleration time-istory of a gien eartquake. Because of its simplicity, te metod is widely used in seismic design of eart structures. A conentional Newmark analysis inoles determination of te yield acceleration, selection of an appropriate eartquake record, and double integration of te

3 parts in te acceleration time-istory tat exceed te yield acceleration. To facilitate applications of tis metod, seeral simplified models ae been deeloped for estimating te Newmark displacements of slopes (e.g. Ambraseys & Menu, 1988; Jibson et al., 1998). Tese models are usually establised based on regression analyses for a large number of selected eartquake records. For te first instance, te model of Ambraseys & Menu (1988) is used ere to sow ow te permanent displacement is influenced by ertical acceleration. In tis model, te permanent displacement d (in cm) is expressed as a function of te ratio a y /a max, were a y is te yield acceleration and a max is te peak orizontal acceleration. " log d ¼ :9 þ log 1 a 2 : 53 # 1 : 9 y ay (13) a max a max Gien a peak orizontal acceleration and te determined yield acceleration, equation (13) allows prediction of te permanent displacement. As already indicated by equation (12), inclusion of ertical acceleration may affect te yield acceleration and, subsequently, te permanent displacement. Assuming tat d and d9 are te displacements calculated using a y and a9 y respectiely, were a y is te yield acceleration tat includes te effect of ertical acceleration and a9 y is te yield acceleration excluding tis effect, an amplification factor A d is introduced ere to quantify te effect for te permanent displacement. " A d ¼ d # 2 : 53 d9 ¼ r 1: 9 1 r y a9 y =a max y (14) 1 a9 y =a max were r y is te reduction factor for te yield acceleration, defined in equation (12). NUMERICAL RESULTS AND DISCUSSION Te expressions establised in te preceding section enable one to quantify te effect of ertical acceleration in a conenient way. Using equation (2), Fig. 2 sows te factor ON SEISMIC LANDSLIDE HAZARD ASSESSMENT 79 of safety for a slope of inclination angle 158 under different alues of seismic coefficient. Te slope is assumed to be in eiter a saturated or a dry state, wit c9 ¼ and ö9 ¼ 358. For a saturated slope te unit weigt is taken as 2 kn/m 3, and for a dry slope it is assumed to be 17 kn/m 3. Te dept of sliding plane is assumed to be a representatie alue, 3 m (Keefer, 1984). Compared wit te case were te effect of ertical acceleration is neglected, one may note tat inclusion of positie k causes an increase in te factor of safety, wereas negatie k reduces te factor of safety. Tis suggests tat te upward inertial force gies a critical case. Terefore te following discussion will concentrate on te case of negatie k. It is also noted tat te effect of ertical acceleration is negligible wen k <. 2, but tends to become significant wen k >. 4. Te reduction of te factor of safety can be better quantified using r F, as sown in Fig. 3. Comparison of te two plots in Fig. 3 suggests tat te degree of reduction is more significant for saturated tan for dry slopes. For a saturated slope at k ¼.4 and k ¼ (.5)k, te factor of safety is about 84% of tat determined by ignoring te effect of ertical acceleration. At te same k but wit k ¼ ( 1. )k, te factor of safety is reduced by about 35%. Note tat it is not uncommon to record a peak ertical acceleration tat is as great as te peak orizontal acceleration, as eidenced by recent ground motion data. Figure 3 implies tat te effect of ertical acceleration is related to groundwater conditions. To proide a better ealuation of tis effect, te reduction of te factor of safety is calculated as a function of te groundwater table (Fig. 4). It can be seen tat, under oterwise identical conditions, te factor of safety is reduced more for a iger groundwater table. Under te same groundwater conditions, te factor of safety decreases wit increasing alues of k and decreasing alues of p (i.e. k /k ). Figure 5 sows te ariation of yield acceleration wit te strengt parameters and inclination angle for saturated slopes wit te ertical motion effect excluded. It is clear tat te yield acceleration increases wit increasing sear strengt, and decreases wit increasing inclination angle. Depending c c 1 2 k 1 k 1 2 Factor of safety against sliding 8 4 k 5 k k 5 k k Factor of safety against sliding 8 4 k 1 k k 5 k k 5 k k k 1 k k 1 k k k Fig. 2. Factor of safety of a saturated slope under arious combinations of k and k : dry conditions; saturated conditions

4 71 YANG k / k 2 8 k / k k / k 5 k / k k / k 5 k / k c c k k Fig. 3. Reduction factor for factor of safety under arious combinations of k and k: dry conditions; saturated conditions 1 1 k / k 2 k / k 5 9 k / k k / k 1 c 8 7 k / k 5 k / k 1 Dry Saturated m m Fig. 4. Reduction factor for factor of safety as a function of water table: k. 2; k. 4 on te groundwater conditions and te alue of p, te yield acceleration can be largely reduced by ertical acceleration, as sown in Fig. 6. Moreoer, te reduction of yield acceleration appears to be more significant for gentle slopes, and slopes wit a ig friction angle. Of particular interest is te influence of ertical acceleration on slope displacement. Using equation (14), Fig. 7 sows te displacement amplification tat is induced by te inclusion of ertical acceleration. At low alues of te ratio a9 y =a max,say.2, te amplification factor is between 1 and 2 for bot saturated and dry slopes, were te lower bound is for p ¼.5 and te upper bound is for p ¼ 1.5. At iger alues of a9 y =a max, say. 8, te amplification factor aries from 5 to as muc as 2 for dry slopes and from 2 to 6 for

5 4 ON SEISMIC LANDSLIDE HAZARD ASSESSMENT β 15 Coefficient of yield acceleration, k y 3 2 c 1 kpa c 5 c Coefficient of yield acceleration, k y 3 2 c 1 kpa c c φ : degrees β: degrees Fig. 5. Yield accelerations for saturated slopes, neglecting ertical motion effects 1 1 β 15 φ 25 Reduction factor for yield acceleration, r y Dry Saturated β 15 β 1 β 1 Reduction factor for yield acceleration, r y Dry Saturated φ 25 β p ( k / k ) p ( k / k ) Fig. 6. Reduction factor for yield acceleration saturated slopes. It is to be noted tat te large amplification of displacements is in a relatie sense, being associated wit small displacements. In order to identify te effect of ertical motion better, Table 2 gies comparisons of te Newmark displacements in tree cases k /k ¼,. 5 and 1. for saturated slopes subjected to two scenario peak orizontal accelerations:.3g and.6g. A range of friction angles and sloping angles are taken into account. Following te US Geological Surey classification system, te relatie azard for eac case is also determined and included in te table. Te comparisons suggest tat te inclusion of ertical acceleration may cause a cange in te Newmark displacement and, consequently, a redefinition of te azard leel in some cases.

6 712 YANG 1 1 β 1 β 1 k / k 1 5 Amplification factor for displacement, A d 1 k / k 1 Amplification factor for displacement, A d 1 k / k 1 5 k / k 1 k / k 5 k / k a y / a max a y / amax Fig. 7. Amplification factor for permanent displacement: dry conditions; saturated conditions Table 2. Newmark displacements predicted for arious conditions ö9: degrees a max ¼.3g a max ¼.6g â ¼ 18 â ¼ 158 â ¼ 18 â ¼ 158 D :cm D 1 :cm D 2 :cm D :cm D 1 :cm D 2 :cm D :cm D 1 :cm D 2 :cm D :cm D 1 :cm D 2 :cm (M) (ML) (L) (M) 3. (ML). 83 (L) (MH) (ML) (L) (.VH) (.VH) (.VH) (MH) (MH) (MH) (MH) (ML) (M) (M) (M) (MH) (M) (MH) (.VH) (.VH) (.VH) Notes: â ¼ inclined angle of slope; ö9 ¼ friction angle of soil; c9 ¼ ; m ¼ 1 (saturated conditions); ª ¼ 2 kn/m 3. D ¼ displacement predicted by neglecting effect of ertical ground motion (k /k ¼.). D 1 ¼ displacement predicted by taking account of effect of ertical ground motion (k /k ¼.5). D 2 ¼ displacement predicted by taking account of effect of ertical ground motion (k /k ¼ 1.). Letter in parenteses indicate relatie azard leel. CLOSING REMARKS Tis study seeks to explore te possible effect of ertical ground motion, wic as long been ignored in te practice of seismic landslide azard analysis. For te infinite slope model, matematical expressions ae been establised tat allow a quick quantification of te effect on te factor of safety, yield acceleration and permanent displacement. Te effect is sown to be related to seeral factors, including te sear strengt of te soil (bot c9 and ö9), te groundwater condition, te slope angle, and te magnitudes of te ertical and orizontal accelerations. Te study indicates tat, under some combinations of tese factors (e.g. large alues of k and small alues of p), simply disregarding te effect would not be appropriate. Using te US Geological Surey classification system, two sets of analyses ae been conducted, wic sow tat te inclusion of ertical acceleration may bring about a redefinition of te azard leel in some cases. Finally, it is to be noted tat current practice is based mainly on te pseudo-static approac and Newmark slidingblock teory. Altoug tis proides a simple way of screening for arious stability problems, it does not adequately account for some situations in real eartquakes, suc as time-arying amplitudes and frequencies of ertical and orizontal ground accelerations, split in time of te peak alues for ertical and orizontal ground accelerations, and deformations associated wit significant build-up of excess pore pressures. Wen tere is a need to go beyond pseudostatic analysis, compreensie procedures suc as effectie-

7 stress-based, non-linear finite element analyses in te time domain can proide a useful way of gaining insigt into te performance of slopes and oter eart structures. ACKNOWLEDGEMENTS Tis work was supported by te Researc Grants Council of Hong Kong under Grant No. HKU 7127/4E. Tis support is gratefully acknowledged. NOTATION a max peak orizontal acceleration a y, a9 y yield accelerations including and excluding effect of ertical motion respectiely A d amplification factor for Newmark displacement c9 coesion of soil d, d9 Newmark displacements calculated using a y and a9 y respectiely k, k seismic orizontal and ertical coefficients respectiely k y, k9 y coefficients of yield acceleration including and excluding effect of ertical motion respectiely m parameter caracterising groundwater tables p ratio between seismic ertical and orizontal coefficients (k /k ) r F, r y reduction factors for factor of safety and yield acceleration respectiely â inclination angle of slope ª, ª w unit weigt of soil and unit weigt of water respectiely ö9 effectie friction angle of soil REFERENCES Ambraseys, N. N. & Menu, J. M. (1988). Eartquake-induced ground displacements. Eartquake Engng Struct. Dynam. 16, No. 7, ON SEISMIC LANDSLIDE HAZARD ASSESSMENT 713 Day, R. W. (22). Geotecnical eartquake engineering andbook. New York: McGraw-Hill. Jibson, R. W., Harp, E. L. & Micael, J. A. (1998). A metod for producing digital probabilistic seismic landslide azard maps: an example from te Los Angeles, California area, Open-File Report California: US Geological Surey. Keefer, D. K. (1984). Landslides caused by eartquakes. Geol. Soc. Am. Bull. 95, Ling, H. I. & Lescinsky, D. (1998). Effects of ertical acceleration on seismic design of geosyntetic-reinforced soil structures. Géotecnique 48, No. 3, Miles, S. B. & Keefer, D. K. (21). Seismic landslide azard for te cities of Oakland and Piedmont, California, US Geological Surey Miscellaneous Field Studies Map MF California: US Geological Surey. NCEER (1997). Proceedings of te FHWA/NCEER Worksop on National Representation of Seismic Ground Motion for New and Existing Higway Facilities, Tec. Report NCEER Buffalo, NY: National Center for Eartquake Engineering Researc. Newmark, N. M. (1965). Effects of eartquakes on dams and embankments. Géotecnique 15, No. 2, Sarma, S. K. (1975). Seismic stability of eart dams and embankments. Géotecnique 25, No. 4, Turner, A. K. & Scuster, R. L. (1996). Landslides: inestigation and mitigation, Transportation Researc Board Special Report 247. Wasington, DC: National Academy Press. Yang, J. & Sato, T. (2). Interpretation of seismic ertical amplification obsered at an array site. Bull. Seismol. Soc. Am. 9, No. 2, Yang, J. & Sato, T. (21). Analytical study of saturation effects on seismic ertical amplification of a soil layer. Géotecnique 51, No. 2, Yang, J., Sato, T., Saidis, S. & Li, X. S. (22). Horizontal and ertical components of ground motions at liquefiable sites. Soil Dynam. Eartquake Engng 22, No. 3,