Landslides (2017) 14:249–268DOI 10.1007/s10346-016-0684-8Received: 30 July 2015Accepted: 1 February 2016Published online: 30 March 2016© Springer-Verlag Berlin Heidelberg 2016

C. Massey I F. Della Pasqua I C. Holden I A. Kaiser I L. Richards I J. Wartman I M. J. McSaveney IG. Archibald I M. Yetton I L. Janku

Rock slope response to strong earthquake shaking

Abstract The 2010–2011 Canterbury earthquakes triggered manymass movements in the Port Hills including rockfalls, debrisavalanches, slides and slumps, and associated cliff-top cracking.The most abundant mass movements with the highest risk topeople and buildings were rockfalls and debris avalanches sourcedfrom up to 100m high cliffs inclined at angles >65°. Cliffs lowerthan 10m in height generally remained stable during the strongshaking, with only isolated release of a few individual boulders. Weused site-specific data to investigate the factors that controlled theresponse of the cliffs to the main earthquakes of the Canterburysequence, adopting two-dimensional finite element seismic siteresponse and stability modeling that was calibrated using the fieldobservations and measurements. Observations from the assessedcliffs in response to the earthquakes show the taller cliffs experi-enced larger amounts of permanent cliff-top displacement andproduced larger volumes of debris than the smaller cliffs. Resultsindicated a mean KMAX amplification ratio for all sites under studyof 1.6 (range of 1.1–3.8). Field data and numerical modeling results,however, show that amplification of shaking does not necessarilyincrease linearly with increasing cliff height. Instead, ourresults show that accelerations are amplified mainly due tothe impedance contrasts between the geological materials,corresponding to where strong differences in rock mass shearwave velocity exist. The resulting acceleration contrasts androck mass strength control cliff stability. However, the amountof permanent slope displacement and volume of debris leav-ing the cliffs varied between the sites, due to site-specificgeometry and rock mass strength.

Keywords Canterbury earthquakes . Co-seismic landslides . PortHills . Rock slope response . Slope stability . Site effects

IntroductionThe 2010–2011 Canterbury earthquakes, New Zealand, triggeredmany mass movements in the Port Hills of Christchurch includingrockfalls, debris avalanches and slides and associated cliff-topcracking, and soil slumps (Fig. 1). About 100 homes were damagedby rockfalls and debris avalanches, leading to the temporary evac-uation of many hundreds of residents. The 2010–2011 Canterburyearthquakes commenced on 4 September 2010 (New Zealand timeUTC + 12 hours) with the MW 7.1 Darfield earthquake, situated40 km west of the Port Hills (Fig. 1, inset). The damage and lossinflicted by the Darfield earthquake was eclipsed by the MW 6.2Christchurch earthquake of 22 February 2011, which occurreddirectly under the Port Hills (Fig. 1). Widespread mass movementswere triggered in the Port Hills including—using the scheme ofKeefer (1984)—disrupted rockfalls, debris avalanches and associ-ated cliff-top cracking, and coherent soil slumps and slides (e.g.,Dellow et al. 2011). Of the mass movements triggered in the PortHills by the Canterbury earthquake sequence, rockfalls and debrisavalanches were the most abundant type and caused the highestrisk to people and buildings (Massey et al. 2014a). Rockfalls, debris

avalanches and cliff-top cracking were also triggered by after-shocks on 16 April, 13 June, and 23 December 2011 (Massey et al.2014a).

This paper presents the results of our investigations into theresponse of several largely bedrock cliffs in the suburban areas ofthe Port Hills to the main 2010–2011 Canterbury earthquakes. Thecliffs investigated are as follows: (1) Quarry Road, (2) Redcliffs, (3)Cliff Street, and (4) Richmond Hill.

Seismic response of rock slopesPrevious research has shown that the dynamic response of a slopeduring an earthquake comprises a complex interaction betweenseismic waves and the hill slope (e.g., Sepulveda et al. 2005). Theresponse of a slope to an earthquake is thought to be controlled bythe following: (1) the nature of the earthquake source; (2) wavepropagation path effects; and (3) local site conditions and theireffects on amplifying or de-amplifying shaking (Kramer 1996;Sepulveda et al. 2005 Kaiser et al. 2013). Path effects are taken intoaccount in our modeling with application of the same regionalattenuation functions for each event and site. In this study, wefocus on the way ground amplification varies with differentsources and site conditions. This is because the sites are very closeto each other and to the earthquake sources, meaning that that theearthquake source to rock-slope site path lengths are short(Table 1), and therefore, a strong variability in path effect isunlikely.

Research has shown that firstly, amplified ground motions inslopes can result from near-surface impedance contrasts associat-ed with material velocity contrasts caused by (i) local surficialdeposits (fill, colluvium, alluvium, etc.) overlying rock (e.g.,Bourdeau and Havenith 2008; Del Gaudio and Wasowski 2011);(ii) weathered materials overlying less weathered materials; (iii)highly fractured zones within more intact materials and discretelarge-scale fracture zones (e.g., Moore et al. 2011; Gischig et al.2015). Secondly, focusing of seismic waves by surfacemorphology—mainly slope inclination, height and shape, e.g.,convex, concave, or planar—may result in topographic amplifica-tion (e.g., Geli et al. 1988; Benites and Haines 1994; Meunier et al.2008; Hough et al. 2010), at larger “ridge-scales” and at smaller“site-scales” (Kaiser et al. 2014). For slopes, the characteristic siteperiod can be influenced by both local slope materials and theircontrasts, together with topography, and provides an indication ofthe frequency at which the most significant amplification can beexpected (Kramer, 1996). Earthquake ground motions of similaramplitude, duration, and location are thought to affect the slope indifferent ways depending on the frequency content of the earth-quake, which is strongly influenced by earthquake magnitude andsource-to-site distance. Therefore, the effects of amplification andresultant permanent slope displacement are likely to be largerwhen excited by earthquakes with predominant frequencies simi-lar to the fundamental frequency of the slope. A laboratory study

Landslides 14 & (2017) 249

Original Paper

(Wartman et al. 2003) concluded that the accuracy of permanentcoseismic displacement estimates (i.e., permanent slope displace-ments adopting sliding block procedures) is a function of the“tuning ratio,” defined as the ratio of predominant frequency ofthe earthquake motion to the fundamental frequency of the slidingmass. Previous studies have inferred that all these phenomena causelocalized amplification effects in hillside areas, which can have sub-stantial control on the patterns and concentration of building andground damage, including landslides (e.g., Harp and Jibson 2002;Sepulveda et al. 2005; Buech et al. 2010; Parker 2013).

For coseismic landslide studies, the response of a slope to anearthquake is typically assessed using metrics that describe boththe (1) amplification effects and (2) amounts of permanent dis-placement. Amplification effects are usually described as a ratiobetween the measured/modeled peak ground acceleration (PGA),peak ground velocity (PGV), Arias intensity or spectral accelera-tion, in the free field, compared to those measured or modeled at(i) the slope crest, (ii) various locations in the slope, and (iii) alongthe slide surface of an assumed sliding mass (e.g., Makdisi andSeed 1978; Ashford and Sitar 2002; Bray and Travasarou 2007;Athanasopoulos-Zekkos and Seed 2013). Estimates of the amountof permanent slope displacement can be made using multipletechniques (a good summary is provided by Jibson (2011))ranging from Newmark (1965) rigid block to decoupled and

fully coupled procedures incorporating seismic site-responseassessments (e.g., Bray and Travasarou 2007; Strenk andWartman 2011; Rizzitano et al. 2014; Gischig et al. 2015) in bothtwo and three dimensions.

Several studies have investigated the relative contributions thatthe earthquake source, path and local site effects (e.g., topography,material contrasts, and geological structure) have on the amplifi-cation of shaking and amount of permanent slope displacement(e.g., Jibson, 2011; Del Gaudio and Wasowski 2011; Strenk andWartman 2011; Moore et al. 2011). There is, however, no consensusbetween the authors on what factors are more important, probablybecause different factors will be important in different situations,and much of the focus of these studies is on the relativeimportance of topographic versus material factors. Rizzitanoet al. (2014) and Gischig et al. (2015) used numerical modeling tosystematically assess the relative contributions to slope amplifica-tion and stability from the earthquake characteristics (intensity,frequency content, and duration of shaking) and from local siteeffects. Ashford and Sitar (2002) attempted to decoupletopographic and material effects on amplification; however, theresults from Rizzitano et al. (2014) show that a complex interactionexists between topographic and material effects on theamplification of ground motion and that the two site effectscannot be evaluated independently or easily decoupled. Gischig

5 kmNorth

Central

Christchurch

Main Port Hills area affectedby landslides triggeredby the 22 Feb earthquake

Main Port Hills areaaffected by landslidestriggered by the13 Jun earthquake

Richmond Hill

Lyttleton

Redcliffs

LPCC

PARS

LPCC

HVSC

GODS

CRLZ

CMHS

D15C

D14C

D13C

Earthquakes (Dates NZST)

Mw 7.1 04/09/2010

Mw 6.2 22/02/2011

Mw 5.3 16/04/2011

Mw 6.0 13/06/2011

Mw 5.8 23/12/2011

Mw 5.9 23/12/2011012

km

Mw 7.1 04/09/2010

PortHills

170°E

40°S

45°S

No LiDARcoverage

Rockfall runout areas

Rockfall source areas

Debris avalanchesDebris slides and slumps

Main cliff sites

GeoNet seismic stations (Holden et al., 2014)

Cliff Street

Quarry Road

40 km west

Fig. 1 Map showing the location of the landslides generated by the main 2010/2011 Canterbury earthquakes, together with the four cliff sites considered in this paper

Original Paper

Landslides 14 & (2017)250

et al. (2015) found that the strongest spectral amplifications wererelated to material (velocity) contrasts and the presence of com-pliant large-scale discontinuities within the mass forming thehillside, but that for homogenous slopes that do not deforminternally, slope height, and topography have little net effect onamplification and slope displacement. Gischig et al. (2015) alsoreport that internal fracturing of the displacing mass during anearthquake—in this case with reference to large deep-seatedlandslides—can lead to an underestimate of the amount of esti-mated permanent slope displacement if simplified Newmark-typemethods are used, as such methods do not take internal deforma-tion of the displacing mass into account. Although the resultsreported by, for example, Rizzitano et al. (2014) and Gischig et al.(2015) provide insight into the causes and relationships betweenslope amplification and coseismic displacements, they are, how-ever, based on numerical simulations adopting simplified slopegeometries and materials, rather than on case studies or invento-ries of actual slope behavior during earthquakes. The observationsand measurements made of rock slope performance during the2010–2011 Canterbury earthquakes provide a unique set of casestudies (i.e., multiple earthquakes of varying magnitudes, dis-tances, and azimuths), to further explore the behavior of rockslopes in response to strong ground shaking, during an earthquakesequence.

Geology and failure modes of the cliffs in the study areasThe Port Hills are the northern sector of the eroded extinctLyttelton basalt volcano (centered on 43.603° S, 172.719° E) whichcomprises five overlapping volcanic cones (Hampton 2010). Therocks forming the 400–500 m high ridge, slopes, and sea cliffs ofthe Port Hills belong to the Lyttelton Volcanic Group rocks of lateTertiary (Miocene) age and are about 10–12 million years old(Forsyth et al., 2008). These volcanic rocks comprise layers ofhard, jointed, basalt, and trachy-basalt lava flows cut by numer-ous dykes, and interbedded with breccia (scoria), agglomerate(coarse angular gravel), epiclastic beds (tuff or tuffaceoussandstone, intercalated with or grading into fine to coarsepebbly lapilli tuffs and gravelly sandstone and conglomerate),and ancient (Miocene) buried soils. Older volcanic depositsare cut by infrequent dykes. All of the volcanic rocks aremantled by much younger (upper Quaternary age) wind-blown deposits of fine sandy silt (loess) and colluviallyreworked loess mixed with boulders. The mantling depositsare generally about 1 m thick and locally exceed 5 m thick(Bell and Trangmar 1987). The slightly to highly weatheredlava flows and scoria are cliff-forming and are closely andirregularly jointed (mainly cooling joints), forming steepblocky rock masses. The lava flows and scoria were the mainsources of the debris avalanches triggered by the Canterburyearthquakes.

The slopes in the Port Hills are typically long, narrow (at theirbase) ridges, which represent the nature of the lava flow sequencesthat formed them. These ridges tend to end abruptly at the coast,to form steep cliffs, many of which have now been abandoned bythe sea. These cliffs are steep (65°–90° to locally overhanging) andhigh (10–100 m) and were susceptible to rockfalls and debrisavalanches such as those that occurred at Redcliffs and RichmondHill (Fig. 2). Smaller cliffs, less than 10 m in height but still steep(inclined >65°) also occur in the Port Hills, such as those at QuarryTa

ble1Propertiesforthe

mainsoilandrock

massesformingthecliffs

adoptedforthe

numericalseism

icsiteresponse

andstabilityassessments

Lithologicalunit

Laboratorytesting

ofintactsamples

Measuredinsitu

shear-w

ave

velocity(m/s)

Shear

modulus

(GS)(MPa)

Geologicalstrength

index(mean

values

inbrackets)

Soil/rock

massproperties

Unitweight

(kN/m3 )

Poisson’sratio

Cohesionc

(kPa)

Friction

ϕ(°)

Tensile

strength

(MPa)

Rock

mass

modulus

(EM)

(MPa)

Loess

170.3–0.4

130–600

30–610

N/A

5-35

25–35

0.01–0.05

N/A

Colluviu

m17

0.3

200–400

70–270

N/A

0-10

28–30

0N/A

Fill

170.3

200–400

70–270

N/A

0-10

25–30

0N/A

BasaltLava

27–28

0.2

400–950

450–2500

35–80(50)

670–3100

68–69

10–15

3300–13,000

Basaltbreccia

18–19

0.1–0.3

300–800

160–1700

40–80(70)

40–270

21–49

0.2–0.5

130–880

Trachy

basaltLava

260.2

2300

14,000–26,000

35–80(50)

1000–2000

53–61

10–11

3100–6700

Trachy

basaltbreccia

200.3

600

730–4600

40–80(70)

140–280

30–41

0.1–0.3

600–3100

Strengthparameterswerederived

fromlaboratorytestingandfieldmapping.Rockmassstrengthswerederived

usingthegeologicalstrengthindex.Theparameterswerecalibratedusingnumericalbackanalysisofstability,asdescribed

byMasseyetal.2014b,c,d,e

Landslides 14 & (2017) 251

Road and Cliff Street. Many of these cliffs also failed during theearthquakes, but the amounts of cliff-top cracking and the vol-umes of debris falling from them were considerably smaller thanthose measured at the larger cliffs. Nevertheless, the performanceof these smaller cliffs makes a useful comparison with the perfor-mance of the large ones.

Engineering geology of the cliffsEngineering geological models for the study site cliffs were devel-oped from the following data sources: (1) surveying and interpre-tation of aerial photographs; (2) field mapping of cliff geology,morphology, and cracks; (3) drilling and trenching; (4) downholegeophysical surveys; and (5) geotechnical laboratory testing. Ex-ample cross sections are presented in Fig. 4, and the detailedresults from the field investigations are contained in Masseyet al. (2014b, 2014c, 2014d, 2014e). Images of the cliffs can currentlybe viewed on GigaPan® (http://gigapan.com/profi les/GarthArchibald). Surveying of the slopes was carried out usingrepeat airborne Light Detecting and Ranging (LiDAR) and terres-trial laser scan (TLS) surveys using a RIEGL LMS-Z420i laserscanner, to establish cliff geometry and morphology. The cliff-face geology was mapped in the field using orthorectified imagesoverlain on shade models derived from TLS surveys. The maingeological units were identified along with the main cracks(discontinuities) apparent on the cliff faces. Given the danger ofaccessing cliff faces during an active earthquake sequence, discon-tinuity data were also derived from terrestrial photogrammetryand laser scan surveys using semiautomated software (Brideauet al., 2012). Geomorphological mapping of the morphology,materials, and their genesis was also carried out for the wider

area around the sites (Townsend and Rosser 2012; Massey et al.2014b, 2014c, 2014d, 2014e). Trial pits to depths of up to 4 mwere excavated in soils on the tops of some of the cliffs in orderto explore the depth of cracking in the loess and to determinewhether cracks extended into the underlying rock. Both rotary-cored triple tube and cone penetrometer holes were drilled atmost of the cliff sites. Logging of the cores was carried out asper New Zealand Geotechnical Society guidelines (2005). Incli-nometers and piezometers were installed in selected drillholes,and shear-wave velocity surveys were carried out in mostdrillholes.

Geotechnical strength parameters were assigned to the mate-rials forming the cliffs based on the results of in-house labora-tory tests and other published testing results (Carey et al. 2014;Mukhtar 2014). The uniaxial compressive strengths of the lavasare generally over 100 MPa and the breccias below 10 MPa.Summaries of the results are included in Table 1. In order toderive rock-mass strength parameters that take into account thenature of the discontinuities, the Geological Strength Index(GSI) (Hoek 1999) was used to reduce the strengths derivedfrom the laboratory tests of intact samples using the RocscienceRocData software. The GSI values adopted for the main rockunits range from 35 to 80 (mean of about 50) for the lavas and40 to 80 (mean of about 70) for the breccias. The structure ofthe trachy-basalt and basalt lavas is typically blocky to veryblocky, and in some locations blocky disturbed, from earth-quake damage. The surface conditions of the discontinuitiesare typically fair to good and in some places very good. Thestructure of the trachy-basalt and basalt breccias is different tothe lavas and is typically intact or massive ranging to blocky,with surfaces that are mainly good to fair but can be poor

BA

DC

Fig. 2 Aerial views of the main study sites. a The northern end of the Redcliffs site, taken shortly after the 22 February 2011 earthquakes. b The same site taken after the13 June 2011 earthquakes. c The southern end of the Redcliffs site taken after the 22 February 2011 earthquakes, where two people lost their lives. d The Richmond Hillsite, taken after the 22 February 2011 earthquake. Photographs taken by G.T. Hancox

Original Paper

Landslides 14 & (2017)252

in parts, where clays have been noted along the surfaces. Giventhe volcanic emplacement mechanisms of these materials, thelateral and vertical persistence of the different rock unitsforming the cliffs are highly anisotropic, therefore making therock mass structure highly anisotropic.

Cliff failure mechanismsThe geotechnical properties of the volcanic breccia and lava, whichform the majority of the cliffs, are quite different and they per-formed differently during the earthquakes (Fig. 3). The basalt lavaflow sequences are dominated by cooling joints (spacing 1–3 mand persistence from 1 m to the unit thickness—typically 5 m) thatare highly variable both vertically and laterally. Given the highintact strength of the lava and high shear-wave velocities,earthquake-induced permanent slope displacements were ac-commodated via the dilation and movement along existingdiscontinuities. Failure modes comprised mainly toppling andwedge failures of individual or multiple discontinuity-boundlava columns, forming rockfalls and debris avalanches, but inrare cases, blocks rotated without leaving the source. Someexamples of the cliff failure mechanisms are shown in Fig. 3.

The basalt and trachy-basalt breccias tend to be massive, withfew discontinuities apparent before the earthquakes, and thesematerials form most of the exposed cliff faces in this study. As aresult of earthquake-induced deformation and cracking, the brec-cias in these cliffs now contain many new discontinuities, whichtend to be open and dilated with variable persistence from a fewmetres to the unit thickness (the defect length can be greater than30 m where multiple discontinuities link) and roughness rangingfrom slickensided planar to undulating rough (NZGS, 2005). Themajority of the larger volume failures occurred in these materialsand most occurred as a result of fracturing through the intactbreccia—around and through clasts—forming persistent defects.Failure modes ranged from (i) slumping—where the displacedmass is relatively intact and the debris did not leave the cliff—to (ii) cliff-top recession and debris avalanches—where thedisplacing mass nearest the cliff face breaks free and falls fromthe face (Hungr et al. 2013). In many of the larger cliffs, the cliff-topdeformation patterns and displacement vectors, measured acrosscracks and from instruments, support relatively deep-seated fail-ure mechanisms, where displacement of the mass is likely to haveoccurred along multiple discontinuities—both preexisting andthose formed by earthquake-induced displacement—at depthwithin the cliff. At the cliff crests, the crack frequency, persistence,and the displacement magnitudes across them tend to increasetoward the cliff face, especially the vertical components. In somelocations, the cliff face had fallen away, indicating displacementsgreater than those measured. One of the authors was standing onthe edge of a large coastal rock cliff during the 13 June 2011earthquake. The eyewitness account suggests that failure of thecliff started at the outside edge, where displacement was morevertical, and retrogressed into the slope away from the cliff edgewhere displacement became more horizontal.

In the larger debris avalanches, failure of the basalt and trachy-basalt lava appears to have occurred due to failure of the under-lying breccias during the strong earthquake shaking. Failures inthe rock mass forming the cliffs were also noted to have occurredalong discrete preexisting and sometimes clay-infilled discontinu-ities (e.g., Cliff Street, Massey et al. 2014b, 2014c, 2014d, 2014e) andalong material boundaries, e.g., through volcanic colluvium over-lying rockhead, or through weaker epiclastic layers separating thelava-flow sequences (e.g., Quarry Road, Massey et al. 2014d). AtRichmond Hill, slickensides (in clay) were found on multiplediscontinuities within blocks of breccia that fell from the cliffs.These are not thought to be related to the original emplacementof the breccia, but rather to later gravitational displacementafter considerable in situ weathering. In many of the cliffs, theobserved failures comprised combinations of all of the differentfailure modes discussed. The life-safety risks resulting from thecollapse of these cliffs and the runout of the debris onto thetalus and flat land at their toe are the subject of several reports(for example, Massey et al. 2012, 2014b, 2014c, 2014d, 2014e).Due to the highly variable geology and the location spacing andpersistence of the discontinuities, it was difficult to apply tradi-tional kinematic rock slope mapping and stability techniques toassess rock slope stability. Such approaches were complicatedfurther as discontinuity patterns changed in response to themain earthquakes. In many of the cliffs, new discontinuitieswere formed and preexisting ones were revealed as debris fellaway from the cliffs.

BA

C

Fig. 3 Cliff failure mechanisms at the Richmond Hill site. a Toppling and wedgefailures near the cliff crest. b Example of incipient toppling failure, note the dilatedrock mass forming the cliff. c Toppling failure in the upper trachy-basalt lava, witha large crack extending from its base into the underlying trachy-basalt lava breccia.Photographs taken by C. Massey

Landslides 14 & (2017) 253

Methods

Earthquake-induced permanent cliff displacementsPermanent displacements of the cliff tops in response to the mainearthquakes were inferred from multiple data sources, including(1) field measurement of crack apertures—relative displacementsacross cracks in both the horizontal and vertical directions; (2)surveying of cadastral survey marks before and after the earth-quakes; and (3) continuous GPS monitoring at locations at the clifftop, carried out by GeoNet. Details of the methods used at eachsite are described in Massey et al. 2014b, 2014c, 2014d, 2014e. Theestimated displacements are listed in Tables 2 and 3. These wereused in the study to calibrate the numerical models, to ensure thatthe adopted material parameters, synthetic earthquake accelera-tions and calculated stresses were capable of explaining the re-corded permanent displacements.

Ground-motion modelingThere were no seismological instruments at these particular cliff sitesfor the main earthquakes (listed in Tables 2 and 3), and it is notappropriate to use the data from those instruments that wereinstalled elsewhere in the Port Hills. This is because records fromthose instruments are influenced by (i) the variable distances be-tween the instrument site and the earthquake source and (ii) stronglocal site effects (including nonlinear behavior) caused by localtopography and geology at the location of the instrument, that maybias ground motion estimates at the study sites (e.g., Kaiser et al.2013; Van Houtte et al. 2012). We calculated synthetic broadbandfree-field rock outcrop synthetic seismograms for the largest MW

5.9+ aftershocks of the 2010–2011 Canterbury earthquake sequence atthe sites of interest. We also calculated synthetic seismograms at thesites of interest for theMW 5.3 aftershock on the 16 April 2011, as thisearthquake epicenter was close to the sites of interest and triggeredlocal rockfalls. The procedure is detailed in Holden et al. (2014).These synthetic seismograms are used as input motions for the site-specific modeling. We employed a stochastic approach to computethe seismograms (Motazedian and Atkinson 2005) that is not onlycontrolled by detailed kinematic source models but also by regionalparameters derived using spectral inversion of the extensive Canter-bury strongmotion dataset (Oth and Kaiser, 2014; Kaiser et al., 2013).These parameters include (1) a regional frequency-dependent atten-uation relationship; (2) site-specific horizontal and verticalfrequency-dependent amplification functions; and (3) stress dropestimates for each source. Note, that the path is included in themodeling as realistically as possible using a regional frequency-dependent relationship specifically determined for this area (Othand Kaiser 2014; Kaiser et al., 2013).

The synthetic seismograms are expected to provide a goodrepresentation of the expected motions over the frequency rangeof 0.1 to 10 Hz. We tested the method by comparing and obtaininggood agreement between recorded seismograms and syntheticseismograms computed at strong motion sites within 20 km ofthe earthquake sources. Results show that using appropriatesource stress-drop values and site-specific amplification functionshelps greatly to reproduce key engineering parameters such aspeak ground acceleration (PGA), peak ground velocity (PGV),Arias intensity, and acceleration response spectra (Holden et al.2014). The technique is particularly efficient for “moderate inten-sity shaking” events such as the localMw 5.3, 16 April event and the

distantMw 5.9, 23 December event. For larger events such as the 22February and the 13 June events, key parameters were also wellreproduced for sites exhibiting approximately linear response be-havior. These results (in Holden et al. 2014), give us confidencethat the input motions calculated for each location of interestassuming rock site conditions, i.e., negligible frequency-dependent amplification or a “flat” response, are a good represen-tation of the free-field accelerations at the site.

Seismic site response and stability modelingFor the four selected sites (Richmond Hill, Redcliffs, Cliff Street, andQuarry Road), the magnitude of earthquake-induced permanentdisplacements was numerically assessed for selected cross sections(Fig. 4) adopting the decoupled method of Makdisi and Seed (1978).This decoupled seismic slope deformation method is a modifiedversion of the classic Newmark (1965) sliding block method thataccounts for the dynamic response of the sliding mass. The“decoupled” assessment is conducted in two steps: (1) a dynamicresponse assessment and (2) a displacement assessment using theNewmark (1965) “rigid-block” double-integration procedure.

The dynamic site-response assessment was carried out usingthe two-dimensional Quake/W FEM software using verticallypropagating shear waves. In general, the slopes in the Port Hillstend to be long, narrow (at their base) ridges, which represent thenature of the lava flow sequences that formed them and are,therefore, well approximated by two-dimensional models (e.g.,Massey et al. 2014b, 2014c, 2014d, 2014e). Synthetic earthquaketime acceleration histories—using vertical and horizontal compo-nents at 0.02 s sampling intervals—representing the main earth-quakes on 22 February, 16 April, 13 June, and the 23 December (theMW 5.9 only) 2011 (Tables 2 and 3) were used as inputs. For themodel mesh setup, the lateral boundaries were moved away fromthe region of interest (WM, Fig. 4e) to ensure that reflected wavesdid not adversely affect the model results. The model height (Z)was varied for each site to ensure that the results were not ad-versely affected by wave reflection and amplification/deamplification caused by the model height below the slope toe.This was done, for each earthquake modeled, by checking that themodeled peak acceleration in the free field at the cliff toe wassimilar to the peak of the free-field synthetic input motion (AFF).Mesh elements were varied from 1 to 2 m (height and width) in thearea of interest and up to 5 m (height and width) away from thearea of interest. This was done to avoid the numerical procedureproviding artificial filtering of the high-frequency componentfrom the input motions (e.g., Rizzitano et al. 2014). For the staticand dynamic assessment, no vertical or horizontal motions rela-tive to the input motions were allowed at the mesh nodes formingthe bottom of each model. To prevent model-edge effects fromaffecting the results, the mesh nodes forming the lateral bound-aries were allowed to move only in the vertical direction for thestatic assessments, and only in the horizontal direction for thedynamic assessments. We used the equivalent linear soil behaviormodel, assuming drained conditions (i.e., no groundwater), alongwith the ranges of geotechnical material parameters shown inTable 1 and detailed in Massey et al. 2014b, 2014c, 2014d, 2014e.Strain-dependent shear-modulus reduction and damping-ratiofunctions for the rock materials were based on data from Schnabelet al. (1972) and Choi (2008). For the simulations, the slope surfaceat the time of a given earthquake was used, which was derived

Original Paper

Landslides 14 & (2017)254

Table2Summaryoffieldmeasurementsandtheresults

fromtwo-dimensionalseism

icsiteresponse

andstabilitysim

ulations

inresponsetothefourmainsynthetic

earthquakes.The

results

fromthesensitivityassessmentfor

RichmondHillarealso

included-Earthquakeinputsandmodelset-up

Site

Earthquake

Topographic

modele

Measured

displacementat

cliffcrest(m)

Input:Synthetic

ground

motioncharacteristics

Modeldimensions

Date

Mag

(MW)

Distance,

source

tosite(km)

Year

From

(m)

To (m)

Dominant

frequencya

(Hz)

Horiz.

A FF(g)

Vert.

A FF(g)

Z/H 1

WM

(m)

Fundam

entalsite

FrequencyF Slopeb

(Hz)

RichmondHill

3/09/2010

7.1

48.0

2003

0

22/02/2011

6.2

5.9

2003

00.2

3.6

0.7

0.4

1.1–1.4

610

2.4

H=56

m16/04/2011

5.3

2.1

2011a

02.8

0.0

0.0

610

Slopeθ=72°

13/06/2011

6.0

1.6

2011a

0.2

0.6

3.3

0.5

0.3

610

23/12/2011

5.9

6.0

2011c

00.1

2.4

0.2

0.1

610

RichmondHillsensitivity

0

Horizontalonly

22/02/2011

2003

00.2

3.6

0.7

0.4

1.1–1.4

610

Horizontalonly

13/06/2011

2011a

0.2

0.6

3.3

0.5

0.3

610

Horizontal&

verticalinphase

22/02/2011

2003

00.2

3.6

0.7

0.4

610

Horizontal&

verticalinphase

13/06/2011

2011a

0.2

0.6

3.3

0.5

0.3

610

Horizontal&

verticalHom

ogenousc

22/02/2011

2011a

00.2

3.6

0.7

0.4

610

Redcliffs

3/09/2010

7.1

46.0

2003

0

22/02/2011

6.2

4.0

2003

0.3

1.3

8.9

0.9

0.7

1.1–1.4

660

1.5

H=52

m16/04/2011

5.3

3.1

2011a

02.0

0.0

0.0

660

Slopeθ=72

13/06/2011

6.0

0.8

2011a

0.2

0.6

7.5

0.4

0.3

660

23/12/2011

5.9

5.4

2011c

00.0

7.4

0.2

0.1

660

QuarryRoad

3/09/2010

7.1

44.5

2003

0

22/02/2011

6.2

3.0

2003

0.1

0.9

7.3

1.0

0.7

1.1–1.2

275

4.2

H=15

m16/04/2011

5.3

4.1

2011a

01.1

0.0

0.0

275

Slopeθ=65

13/06/2011

6.0

2.3

2011a

00.1

2.0

0.4

0.2

275

23/12/2011

5.9

6.0

2011c

00.0

2.7

0.2

0.1

275

Cliff

Street

3/09/2010

7.1

47.5

2003

0

22/02/2011

6.2

5.5

2003

0.1

0.1

6.2

0.6

0.7

1.2–1.4

445

8.3

H=16

m16/04/2011

5.3

2.6

2011a

05.5

0.0

0.0

445

Slopeθ=55

13/06/2011

6.0

0.8

2011a

00.1

4.0

0.3

0.4

445

23/12/2011

5.9

5.3

2011c

00.0

1.9

0.2

0.1

445

aBasedon

theFourieramplitude

spectra

oftheinputm

otionforthe

0to

25Hz

frequency

range

bDerived

fromspectralaccelerationoftheresponse

ofthecliffto

thesim

ulated

earthquakes,fromlocations

withintheassumed

displacingmass

cValues

aretakenfromthetwo-dimensionalm

odelingresults,usingthedatafromthe50

credibleslide

surfaceswith

thelowestyieldaccelerations

(KY)

dAssumes

theentireslope

isformed

oftrachy-basaltlava

e2011arefersto

theMarch

2011

LIDARsurvey

and2011crefersto

theJuly2011

LIDARsurvey

Landslides 14 & (2017) 255

Table3Summaryoffieldmeasurementsandtheresults

fromtwo-dimensionalseism

icsiteresponseandstabilitysim

ulations

inresponsetothefourmainsynthetic

earthquakes.The

results

fromthesensitivityassessmentfor

RichmondHillarealso

included-M

odelresults

Modelledseism

icresponse

Modelledpermanentd

isplacementa

Horiz.

A MAX

(g)

Vert. A M

AX(g)

K MAXa (g)

K MAX variation

(gats1)

Max (m

)Min (m

)Avg. (m

)Uncertainty

(mats1)

K Y(g)

K Yvariation

(gats1)

L-M

axlength

offailuremass

(m)

RichmondHill

Nomodelling

1.1

1.1

1.2

0.15

0.2

0.0

0.1

0.03

0.3

0.02

40-45

H=56

m0.2

0.1

0.1

0.01

0.0

0.0

0.0

0.00

0.2

0.01

40–45

Slopeθ=72°

1.1

0.9

0.9

0.08

0.4

0.1

0.2

0.06

0.3

0.02

40–45

0.6

0.6

0.5

0.07

0.0

0.0

0.0

0.00

0.3

0.01

40–45

RichmondHillsensitivity

Horizontalonly

1.4

0.6

1.0

0.17

0.1

0.0

0.1

0.03

0.3

0.03

40–45

Horizontalonly

1.3

0.4

0.6

0.09

0.3

0.0

0.1

0.07

0.3

0.02

40–45

Horizontal&

verticalinphase

1.5

1.1

1.3

0.17

0.2

0.1

0.1

0.05

0.3

0.03

40–45

Horizontal&

verticalinphase

1.4

1.0

0.7

0.13

0.4

0.0

0.2

0.10

0.3

0.02

40–45

Horizontal&

vertical

Homogenousb

2.3

1.4

2.3

0.28

0.4

0.2

0.3

0.08

0.3

0.02

40–45

CliffStreet

Nomodelling

2.3

2.0

1.8

0.30

1.7

0.2

0.8

0.39

0.3

0.06

25–35

H=52

m0.2

0.1

0.2

0.05

0.0

0.0

0.0

0.00

0.2

0.05

25–35

Slopeθ=72

0.9

1.1

0.8

0.24

0.7

0.0

0.1

0.18

0.3

0.08

25–35

0.5

0.6

0.6

0.10

0.1

0.0

0.0

0.04

0.3

0.04

25–35

QuarryRoad

Nomodelling

2.1

1.6

2.1

0.12

0.5

0.2

0.3

0.05

0.4

0.01

20–25

H=15

m0.1

0.1

0.05

0.01

0.0

0.0

0.0

0.00

0.2

0.00

20–25

Slopeθ=65

0.9

0.6

0.5

0.01

0.0

0.0

0.0

0.00

0.4

0.01

20–25

0.6

0.3

0.3

0.01

0.0

0.0

0.0

0.00

0.4

0.01

20–25

CliffStreet

Nomodelling

1.1

0.9

0.6

0.02

0.1

0.0

0.0

0.01

0.2

0.01

16–26

H=16

m0.1

0.0

0.04

0.05

0.0

0.0

0.0

0.00

0.2

0.01

16–26

Slopeθ=55

0.4

0.6

0.4

0.02

0.0

0.0

0.0

0.00

0.2

0.01

16–26

0.5

0.2

0.3

0.02

0.0

0.0

0.0

0.00

0.2

0.01

16–26

aValues

aretakenfromthetwo-dimensionalm

odellingresults,usingthedatafromthe50

credibleslide

surfaceswith

thelowestyieldaccelerations

(KY)

bAssumes

theentireslope

isformed

oftrachy-basaltlava

Original Paper

Landslides 14 & (2017)256

from the relevant airborne LiDAR survey data. We used the Slope/W software (Slope/W 2012) to model the magnitude of any per-manent slope displacements caused by the simulated earthquakes.

The average acceleration time history, averaged along the baseof the slide surface of a potential sliding mass, is calculated tocapture the cumulative effect of the nonuniform acceleration

profile (horizontal and vertical) acting on the slide mass. Theaverage acceleration time history is then double integrated, usingthe classic Newmark (1965) rigid sliding-block method, to estimatethe permanent displacement along the given slide surface. Themethod is simplified compared to fully coupled methods (e.g.,Bray and Travasarou 2007; Jibson 2011; Arnold et al. 2015), but it

BA

C D

E

0 2000

HRockslopeheight

Slope toe

Talus

Rock slope(cliff)

Edge of cliff(crest)

Zone of cliff top crackingand displacementlimit of main

cliff-top cracks

Cracks

Slopeinclination

(angle)

W

Wm

Z

Base of model

L

AMAX

KMAX

Height ofmodel

AFF

H1Slopeheight

Potential length of displaced mass

Potential slide surface

0

10

20

30

40

100 110 120 130 140 150 160 170

0

10

20

30

40

0 10 20 30 40 50 60 70

160 180 200 220 240 260 280

Distance (m)

RICHMOND HILL

Distance (m))

m(

no

it

av

el

E

0

10

20

30

40

50

60

70

80

20 40 60 80 100 120 140

REDCLIFFS

Distance (m)

)m

(n

oi

ta

ve

lE

CLIFF STREET

Loess and colluvium

Basaltlava breccia

Epiclastic

Basalt lava

Basaltlava breccia

2011c (June 2011)2011a (March 2011)

2003

Pre-2003debris

Trachy basalt lava

Trachy-basaltlava breccia

Mixedbasalt/breccia

Epiclastic

Loess, colluvium and fill

2011c (June 2011)2011a (March 2011)

2003

Tuff and epiclastics

Loess

Basalt lava

Basalt lava

LoessFill

)m

(n

oi

ta

vel

E

0

10

20

30

40

50

60

70

80

Distance (m)

)m

(n

oi

ta

ve

lE

QUARRY ROAD

Pre-2003debris

Zone of cliff top crackingand displacement

Zone of cliff top crackingand displacement

Zone of cliff top crackingand displacement Zone of cliff top cracking

and displacement

Colluvium

Weak layer identifiedin drillhole

Basalt lava breccia

Basalt lava breccia

Colluvium

Daylighting planardiscontinuity withclay infill

BH-RHR01

-100

0 2000

BH-MB02

-10

-10 -10

BH-QR04

4000

Area ofcliff-facecracking

Area ofcliff-facecracking

Area ofcliff-facecracking

Area ofcliff-facecracking

Deformation(bulging)at cliff toe

m/s

m/s

m/s

Fig. 4 Example cross sections used in the two-dimensional seismic site response and stability assessments. a Richmond Hill. b Redcliffs, c Cliff Street. d Quarry Road. eSchematic section showing the notations used in this paper. The vertical red bars are the down-hole shear-wave velocity survey results plotted against depth, units arem/s

Landslides 14 & (2017) 257

is still useful to assess the relative magnitude of permanent slopedisplacement, especially when calibrated using field data. Thefailure mechanism assessed was failure of the slope through therock mass, mainly basalt breccia adopting both semicircular andplanar slide surfaces.

Tuning ratios—defined as the fundamental frequency of thesliding mass/the predominant frequency of the earthquakemotion—were also used to investigate the role of earthquakefrequency on cliff amplification. The fundamental frequency ofeach simulated cliff—at model locations within the inferreddisplacing mass—was estimated from site to reference spectralratios, using the four main earthquakes. These were calculated asthe ratio between the Fourier amplitude spectra—from the two-dimensional site-response simulations—and the input (reference)spectra—calculated from the synthetic earthquakes. The spectrawere smoothed using a Konno and Ohmachi (1998) windowingfunction for the frequency range 0–25 Hz and using the 0.5–20 Hzrange for the analysis.

Seismic arraysWe installed small-scale temporary seismometer arrays behind thecliff edges at the Redcliffs site, and a semipermanent seismometernear the cliff crest of the Richmond Hill Road site. Data from theseinstruments were analyzed to characterize the seismic site responseand assess the extent to which amplification influenced groundmotions. The purpose of these arrays was to quantify site amplifica-tion and ground-motion polarization using horizontal-to-vertical(H/V) and site-to-reference spectral ratio methods applied to after-shocks of the Canterbury earthquake sequence to determine theeffects of topographic and stratigraphic influences on ground-motion amplification and provide field data to calibrate the models.Earthquakes included in the analysis ranged inmagnitude fromM1.5to M5.2; hence, results are based on weak-motion records. Kaiseret al. (2014) contains the methodology and results from this work,which comprised estimating (i) PGA amplification factors betweenarray stations and (ii) amplification in terms of frequency-dependentspectral ratios. The relevant results from Kaiser et al. (2014) areincluded here as they provide a useful comparison to the resultsderived from the numerical models.

Results

Seismic cliff response and stability

Topography, geology, and amplificationThe simulated maximum horizontal and vertical acceleration(AMAX) at the slope crest in response to the modeling of eachsynthetic earthquake time history has been plotted in Fig. 5a, bagainst the maximum rock-outcrop free-field acceleration (AFF) ofthe input motion. The slope crest was defined as the convex breakin slope between the lower steeper slope and the upper less steepslope (Fig. 6). Each point on the graph represents the meanresponse of multiple sampling points 5–10 m either side of thislocation, to a given earthquake input motion. AMAX showed anoverall increase with increasing input peak ground acceleration(AFF) and variable degrees of crest amplification with respect tothe input free-field motion, i.e., AMAX/AFF > 1.

The maximum crest amplification was calculated in terms ofthe AMAX/AFF ratio (Fig. 5c). The simulation results showed that

higher cliffs (Richmond Hill and Redcliffs) had larger amplifica-tion ratios (mainly in the vertical component) than those for thesmaller cliffs (Quarry Road and Cliff Street). The crest amplifica-tion at low AFF < 0.3 g was variable, ranging from 2.0 to 3.9(horizontal) with a mean of 3.1, and 1.5–5.7 (vertical) with a meanof 3.3. These results are slightly higher than the equivalent meanweak-motion PGA amplification ratios reported by Kaiser et al.(2014) of 2.5 for horizontal and 3.0 for vertical, based on recordsfrom the small-scale temporary arrays installed on the surface atRedcliffs. These ratios derived from the arrays, however, arethought to be lower than the modeled ratios because there wereno “true” free-field motions that could be used for comparison, asit was difficult to locate instruments in free-field positions. Athigher AFF >0.3 g, the variability of modeled crest amplificationAMAX/AFF tended to reduce, ranging from 1.3 to 2.6 (horizontal)with a mean of 2.0, and 1.3–3.0 (vertical) with a mean of 2.3.

The average acceleration versus time plot for a given number ofslide surfaces through each cliff was used to take the nonuniformaccelerations acting on a cliff into account in the assessments(Fig. 5d, e). Model amplification was measured in terms of KMAX/AFF (Fig. 5f) where KMAX represents the mean of the maximumacceleration value taken from the simulated average accelerationversus time plots (averaged over the given slide surface), for 50simulated and “credible” slide surfaces (per modeled section) withthe lowest yield accelerations (KY). KMAX differs fromAMAX, which isthe simulated maximum horizontal and vertical acceleration at apoint at the cliff crest, because the accelerations are averaged alongthe potential slide surface and thus better represent the nonuniformaccelerations acting on the slide mass. For the larger cliffs, theamplification ratios based on KMAX values were sometimesmarkedlyless than those based on AMAX values. For all cliffs (large and small)KMAX/AFF amplification ratios varied between the sites and betweenearthquakes, possibly reflecting the “averaging” effect, caused by thelength of the simulated slide surfaces in the larger cliffs being longerthan those in the smaller cliffs (the “L” dimension given in Tables 2and 3). The KMAX/AFF ratios are plotted individually for each cliff inFig. 7a. The mean KMAX/AFF at AFF <0.3 g (for AFF horizontal) for allsimulated cliffs was 2.1 (range of 1.1–3.8), and for AFF >0.3 g, themeanwas 1.6 (range of 1.1–2.1). For AFF vertical, the mean ratio was 3.3 atlow AFF <0.3 g, reducing to 2.2 at higher AFF >0.3 g (Fig. 7a). Thisvariability was caused by the strain-dependent damping and shear-modulus reduction functions used in the simulations, where AFF

>0.3 g leads to higher strains and increased damping and a reductionin the shear modulus, compared to strains at AFF <0.3 g.

Figure 6 shows that the distribution of the peak horizontalground accelerations calculated from the models of the Redcliffsand Richmond Hill sites are nonuniform, from the slope toe to thecliff crest. In general, the simulated maximum out-of-slope hori-zontal accelerations tended to increase with slope height. Theacceleration profiles, however, were not smooth, but insteadreflected variations in the geology caused by contrasting materialmodulus and damping characteristics. At Richmond Hill, thetrachy-basalt breccia is significantly weaker and has a much lowershear-wave velocity and shear modulus (Table 1) than the overly-ing mixed basalt lava and breccia, and the underlying trachy-basaltlava. These contrasts show in the simulated acceleration profile(Fig. 6). At Redcliffs, the maximum horizontal accelerations out ofthe slope also show the effect of the contrasting geology, but in thiscase, the upper basalt breccia/ignimbrite is slightly weaker and has

Original Paper

Landslides 14 & (2017)258

a lower shear-wave velocity and modulus than the lower basaltbreccia. At Redcliffs, the geological control on the simulated ac-celerations is not as pronounced as at Richmond Hill. This isbecause the impedance contrasts (where the impedance of thematerial is defined as the product of its density and velocity)between the geological materials (shown in Fig. 6a) at Redcliffsrange between 0.4 and 1.0 (where a ratio of 1 = no contrast), whileat Richmond Hill, the ratios range between 0.2 and 0.4 (shown inFig. 6b). These differences affect the stability of a cliff during anearthquake, not only because they influence the degree of ampli-fication but also because the velocity contrasts across boundarieslead to sharp gradients in the simulated stresses and strains.

Earthquake frequency and amplificationTo investigate the “tuning ratio” effect (Wartman et al. 2003) onamplification of shaking, the tuning ratio for each simulatedearthquake at each cliff was plotted against the corresponding

amplification ratio (KMAX/AFF(horizontal)) (Fig. 7b). Results showedthat there were significant variations in the amplification ratios atsimilar tuning ratios, especially for the larger cliffs (Richmond Hilland Redcliffs). These results suggested that for the cliff simulationspresented in this paper, the frequency content of theearthquake—and therefore the tuning ratio—is not a dominantfactor controlling the amplification ratio (KMAX/AFF), althoughonly a small sample of earthquake ground motions were used inthese simulations.

Results from the site and reference spectra (Figs. 8 and 9) andsite-to-reference spectral ratios (Fig. 10) show that generally forall cliffs, the fundamental site frequency—taken as that at thepeak of the geometric mean spectral ratio—varies only slightly inresponse to the simulated earthquakes, even though the domi-nant frequencies of the synthetic earthquakes vary (Tables 2 and3). The spectral ratios (SSR) and horizontal-to-vertical spectralratios (HVSR) from the site response modeling were compared

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0

Horiz

.AM

AX

(g)

Horiz. AFF (g)

A

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0

Vert

. AM

AX

(g)

Vert. AFF (g)

B

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0

K MA

X(g

)

Horiz. AFF (g)

D

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0 0.5 1.0 1.5 2.0

K MA

X(g

)

Vert. AFF (g)

E

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

MA

X/A

FF)

Horiz. AFF (g)

C

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2

MA

X/A

FF)

Horiz. AFF (g)

F

Richmond Hill

Legend

Redcliffs Quarry Road Cliff Street

Fig. 5 Results from the two-dimensional seismic site assessments from the calibrated slope models (Massey et al. 2014b, 2014c, 2014d, 2014e). a, b The peakacceleration of the response of the slope crest (AMAX) plotted against the peak horizontal and vertical accelerations of the synthetic free-field rock outcrop time accelerationhistories at each site (AFF). Each data point represents the mean response of four locations at the cliff crest, from points located either side of the crest. Error barsrepresent the variation between the maximum and minimum values measured at these locations. The modeled earthquakes are the 22 February, 16 April, 13 June, and 23December 2011. c The horizontal amplification ratio (AMAX/AFF) plotted against the horizontal AFF. d, e KMAX (defined as the mean of the maximum acceleration valuetaken from the simulated average acceleration versus time plots (averaged over the given slide surface), for 50 simulated and “credible” slide surfaces (per modeledsection) with the lowest yield accelerations), plotted against horizontal AFF. f The KMAX amplification ratio (KMAX/AFF) plotted against the horizontal AFF.

Landslides 14 & (2017) 259

to the observed HVSR measured at Richmond Hill and Redcliffs(Fig. 11). At Redcliffs, there was a good correlation betweenobserved HVSR and modeled amplification. Peak observedHVSR (at station R2 of Kaiser et al. 2014) exhibited similaramplitude and frequency (1.5 - 2 Hz) to that of the modelledHVSR and SSR (peak frequency 1 - 2 Hz). At Richmond Hill, thefundamental frequency was similar in observed and modeledratios (i.e. between 2-3 Hz), but at higher frequencies the overallcorrelation is not as good. These differences between the ob-served and modeled results could be related to a number ofthings, e.g., (i) simplifications in the model compared to reality,i.e., a more heterogeneous material or gradual velocity gradientscould produce broader, lower amplitude peaks; (ii) the observedrecords represent only weak-motion earthquakes associated withno measured permanent cliff displacements, compared to themodeled strong-motion earthquakes that led to measured per-manent cliff displacements; and (iii) e.g. differences in modelledvs. observed vertical motion which affect HVSR and SSR

differently. However, in general, the model results do show agood correlation with the observations.

Cliff stabilityStability was assessed in terms of the estimated permanent slopedisplacement at different ratios of KMAX/KY, in response to the fourmain earthquakes. ThemeanKYvalues for themodelled cross sectionsat all cliffs, based on the back analysis of measured displacements(Massey et al. 2014b, 2014c, 2014d, 2014e) of 50 simulated slide surfaceswith the lowest KY, ranged from about 0.2 to 0.4 g (a mean of 0.3 g)(Tables 2 and 3). However, the amount of permanent slope displace-ment and volume of debris leaving the cliffs varied greatly between thesites, as a function of site-specific geometry and rock mass strength.Permanent displacements and debris volumes were larger for thehigher slopes (Richmond Hill and Redcliffs) than those associatedwith the smaller slopes (Quarry Road and Cliff Street) for similarKMAX/KY ratios (Fig. 12), due to the largermass of the displacing cliffsat Richmond Hill and Redcliffs. The amounts of permanent

Distance (m)

80

70

60

50

40

30

Ele

vatio

n(m

ab

ove m

ean

sea level)

20

10

0

0 20 40 60 80 100 120 140 160 180-10

A

B

0.8

11

1.2

1.8

1.8

22.2

2.4

Loess

Upper basalt breccia

Basalt lava

Epiclastic

Lower basalt breccia

Talus

1.6

1.41.2

(ignimbrite)

Redcliffs

PGA Horizontal (g)

AMAXProfile 2

Profile 2

Modelled 50 slide surfaces withthe lowest yield accelerations

2003

2011a

2011c

Zone of crackingand displacement

Pre 22 February2011 cliff crest

Distance (m)

20 40 60 80 100 120 140 160 180 200 220 240 260 280

Ele

vatio

n(m

ab

ove m

ean

sea level)

-10

0

10

20

30

40

50

60

70

80

90

-10

0

10

20

30

40

50

60

70

0 0.5 1 1.5

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5 2.5

2

Redcliffs

2

Richmond Hill

2.5

22/02/2011

16/04/2011

13/06/2011

23/12/2011

22/02/2011

16/04/2011

13/06/2011

23/12/2011

0.8

0.8

0.8

1

1.2

1.2

1.41.6Loess

Mixed asalt lavaband breccia

Trachyte reccia-basalt b

Trachyte ava-basalt l

Profile 1 AMAX

Modelled 50 slide surfaces withthe lowest yield accelerations

Pre 22 February2011 cliff crest

Zone of crackingand displacement

Richmond Hill

PGA Horizontal (g)

Profile 1

Impedance ratio = 0.4

Impedance ratio = 0.2

Impedance ratio = 0.4

Impedance ratio = 1.0

Impedance ratio = 0.5

Fig. 6 Results from the seismic site-response assessment for cross sections at Richmond Hill and Redcliffs. The contours are simulated peak horizontal groundaccelerations (PGA) for the 22 February 2011 earthquake. The slope surfaces shown as 2003 and 2011a represent the position of the cliff-face before the 22 February 2011earthquakes (2003) and before 13 June 2011 earthquake (2011a) respectively. AMAX is the maximum acceleration measured at the given location at the cliff crest. Theprofiles (1 and 2) show the maximum horizontal acceleration out of the slope at a given height above the model base, taken from the model along the labeled profile

Original Paper

Landslides 14 & (2017)260

displacement generally increase as the KMAX/KY ratio increases.However, this was not true for Richmond Hill, where the calculatedvolumes lost and permanent displacements were greater for the 13June 2011 earthquake than those calculated for the 22 February 2011earthquake, even though the AFF values (horizontal and vertical) forthe 13 June earthquake were lower than those associated with 22February. This relationship was thought to be due to either or both of(i) the several large amplitude acceleration peaks associated with the13 June earthquake and (ii) preconditioning (weakening) of the rockmass in response to previous earthquakes.

Discussion

Cliff geology, geometry, and amplification of shakingField observations and modeling results showed that cliff perfor-mance in this study was mainly controlled by site-specific varia-tions in cliff topography and geology. The KMAX/AFF amplificationratio—where KMAX is the peak of the average acceleration versustime plot calculated for a given number of characteristic slidesurfaces—was found to be a useful indicator of permanent cliffdisplacement, as it took into account the nonuniform vertical and

0.0

1.0

2.0

3.0

4.0

0.0 0.5 1.0M

AX/A

FF)

FF) (g)

RichmondHill

0.0

1.0

2.0

3.0

4.0

0 1 2 3 4 5

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Fig. 7 a KMAX/AFF amplification ratio for each site plotted against horizontal AFF. b KMAX/AFF amplification ratio for each site plotted against the tuning ratio (dominant sitefrequency divided by the dominant earthquake frequency). Each data point represents the mean KMAX of the 50 slide surfaces (shown as gray symbols) with the lowestyield accelerations (KY), simulated at each site in response to the 22 February, 16 April, 13 June, and 23 December 2011, synthetic earthquakes, using the horizontal andvertical time-acceleration histories

Landslides 14 & (2017) 261

horizontal accelerations acting along a potential slide surface at agiven time step during an earthquake. These ratios were relativelysimilar—mean KMAX/AFF ratio of 1.6 at AFF >0.3 g—for all cliffs,small or large. This is thought to be due to KMAX being calculatedfrom an averaging of the non-uniform profile of accelerations (inthe model) acting along a potential slide surface at each giventime-step during an earthquake, with greater averaging with in-creasing length of slide surface (and therefore more “slices” in themodel to be averaged).

Sensitivity assessments were carried out for the Richmond Hillcliff, where cliff displacements during the earthquakes were well-constrained from cGPS and survey observations. Simulations wererun assuming (i) the horizontal component of the synthetic inputearthquakes only and (ii) when the horizontal and vertical synthetic

components of the input motions were in phase (defined as when thepeak horizontal acceleration occurs at the same time-step as the peakvertical acceleration). Results show that when only the horizontalcomponent of the simulated earthquakes were used as inputs; AMAX

horizontal values increased, AMAX vertical values decreased, andKMAX values did not vary significantly, in comparison with thesimulation results adopting horizontal and vertical out-of-phase(defined as when the peak horizontal acceleration does not occurat the same time-step as the peak vertical acceleration) input mo-tions. The results (Tables 2 and 3) showed that when in-phase verticaland horizontal motions were used as inputs, as expected, AMAX

vertical and horizontal, and KMAX values were all higher than thosesimulated using out-of-phase input motions. However, there waslittle difference in the simulated permanent displacements estimated

Cliffstreet - 22-Feb-11 Cliffstreet - 16-Apr-11 Cliffstreet - 13-Jun-11 Cliffstreet - 23-Dec-11

QuarryRd - 22-Feb-11 QuarryRd - 16-Apr-11 QuarryRd - 13-Jun-11 QuarryRd - 23-Dec-11

Redcliffs - 22-Feb-11 Redcliffs - 16-Apr-11 Redcliffs - 13-Jun-11 Redcliffs - 23-Dec-11

RichmondHill - 22-Feb-11 RichmondHill- 16-Apr-11 RichmondHill - 13-Jun-11 RichmondHill - 23-Dec-11

Fig. 8 Fourier amplitude spectra of the horizontal input and response for each modeled seismic response site. The spectra shown are for the 22 February, 16 April, 13June, and 23 December 2011 earthquakes. Input (blue lines) and simulated response (red lines). The input spectra are calculated from the horizontal time-accelerationhistory for a given synthetic earthquake at a given site used as the input for the modeling. The simulated spectra are calculated at each modeled site, from the horizontaltime-acceleration history for “history points” located inside the inferred displacing mass, and represent the response of this location to a given earthquake input. The datashown are for the 22 February, 16 April, 13 June, and 23 December 2011 earthquakes

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using in-phase or out-of-phase input motions. There was also littledifference in the simulated displacements when only the horizontalcomponents of the input motions were used; this could be due to anumber of things: (i) the horizontal component, used as the inputmotion, induces vertical accelerations in the model that are thenused in the stability assessment; (ii) the simulated displacementusing the decoupled method is not particularly sensitive to thevertical motions; and (iii) vertical motions tend to be less thanhorizontal motions. The modeled permanent displacements mayalso be different if the sensitivity assessment were to be carried outusing a fully coupled model.

Note that the procedure adopted for the simulations was two-dimensional and “decoupled” where the assumed sliding mass wastreated as being rigid. In reality, permanent displacementswould have occurred along cracks within the larger displacing

mass, indicating that the slide masses were not rigid. Howev-er, given that the permanent slope displacements caused bythe different earthquakes were all that could be measured atthe cliff sites, and the models were calibrated using thesedisplacements, they provide a reasonable proxy for slopedamage in terms of the magnitude of permanent slopedisplacement, even if they do not capture the actual internaldeformation of the sliding block. The Newmark (1965) methodalso assumes that the mass only accrues displacement duringthe earthquake at accelerations above the yield acceleration.No progressive failure mechanism that might occur post shak-ing, is considered.

The two-dimensional decoupled modeling highlights theimportance of site geology—mainly the impedance contrastsbetween the different geological materials—in energy

Cliffstreet - 22-Feb-11 Cliffstreet - 16-Apr-11 Cliffstreet - 13-Jun-11 Cliffstreet - 23-Dec-11

QuarryRd - 22-Feb-11 QuarryRd - 16-Apr-11 QuarryRd - 13-Jun-11 QuarryRd - 23-Dec-11

Redcliffs - 22-Feb-11 Redcliffs - 16-Apr-11 Redcliffs - 13-Jun-11 Redcliffs - 23-Dec-11

RichmondHill - 22-Feb-11 RichmondHill- 16-Apr-11 RichmondHill - 13-Jun-11 RichmondHill - 23-Dec-11

Fig. 9 Fourier amplitude spectra of the vertical input and response for each modeled seismic response site. The spectra shown are for the 22 February, 16 April, 13 June,and 23 December 2011 earthquakes. Input (blue lines) and simulated response (red lines) vertical, Fourier amplitude spectra for each site. The input spectra arecalculated from the horizontal time-acceleration history for a given synthetic earthquake at a given site used as the input for the modeling. The simulated spectra arecalculated at each modeled site, from the vertical time-acceleration history for “history points” located inside the inferred displacing mass, and represent the response ofthis location to a given earthquake input. The data shown are for the 22 February, 16 April, 13 June, and 23 December 2011 earthquakes

Landslides 14 & (2017) 263

2.4–2.5 4.8–5.2

2.52.41.51.4–1.6

8.77.65.35.4–1.48.2

9.7 12.811.712.2

2.4 5.3 8.6 9.0

Horizontal

Horizontal

Horizontal

lacitreVlatnoziroH

Vertical

Vertical

Vertical

teertSffilCteertSffilC

sffilcdeRsffilcdeR

lliHdnomhciRlliHdnomhciR

daoRyrrauQdaoRyrrauQ

Fig. 10 Spectral ratios calculated by dividing the smoothed simulated spectra by the smoothed input spectra, for both horizontal and vertical components of the input synthetic time-acceleration histories and those of the simulated response. The data shown are for the 22 February, 16 April, 13 June, and 23 December 2011 earthquakes. Peak ratios are labeled

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amplification within a slope. For example, the results fromRichmond Hill site (Fig. 6a) showed that it was the lowvelocity of the trachy-basalt breccia forming the mid portionof the slope that caused the steep gradients in the horizontalacceleration and dynamic strain profiles out of the cliff, and itwas this response coupled with the lower strength of thatmaterial that lead to the development of the observed perma-nent slope displacements and volumes of debris falling fromthe cliff. As with the findings reported by Rizzitano et al.(2014), the simulation results did not allow the relative con-tributions from topography and geological material contrastson slope amplification to be decoupled, as they were inher-ently “coupled.” This is because it was not possible to inves-tigate and characterize the materials at each of the seismicarray stations or at locations where ground investigation datawas not available, as such data was limited to boreholes andcliff-face mapping. It is therefore possible that localized dam-age to the rock masses forming the cliff crests and near to thesharp changes in topography is the primary cause of amplifi-cation, instead of the surface morphology alone.

Earthquake frequency and amplificationThe spectral ratio results from the Port Hills cliffs indicated thateach site had its own characteristic site period of vibration (fun-damental frequency), which reflected the site geology, materialcontrasts, and topography. However, the results from the two-dimensional seismic site response assessment showed that in

general, there was no discernible increase in the KMAX/AFF ampli-fication ratio at predominant earthquake frequencies similar to thefundamental frequencies of the cliffs. Hence, the site responseappears to be relatively consistently independent of earthquakesource frequency and magnitude. The observed and simulatedresults from the cliffs in the study were in response to near-field

Redcliffs Richmond Hill

Fig. 11 Horizontal-to-vertical spectral ratios (HVSR) and site-to-reference spectral ratios (SSR) for Redcliffs and Richmond Hill. Geometric mean of the spectral ratios (SSR)are calculated as the ratio between the Fourier amplitude spectra—from the two-dimensional site-response simulations—and the input (reference) spectra—calculatedfrom the four synthetic earthquakes. Geometric mean of the horizontal to vertical spectral ratios (HVSR) is calculated from (i) the two-dimensional site responsesimulations (labeled from the model) of the four synthetic earthquakes and (ii) aftershocks of the Canterbury earthquake sequence (labeled field observations) recorded bycliff-top seismometers at Redcliffs (station R2, Kaiser et al. 2014) and Richmond Hill

Richmond Hill

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Fig. 12 The modeled permanent slope displacements plotted against the ratio ofKMAX/KY, where each point represents the mean of the 50 slide surface with thelowest KY. All the plotted data are contained in Tables 2 and 3. Error barsrepresent one standard deviation

Landslides 14 & (2017) 265

(within 10 km) earthquakes of moderate magnitude (M5.3–6.2),which had relatively similar dominant frequencies (2–5 Hz), andtherefore did not allow the impact of the tuning ratio effect onamplification (e.g., Wartman et al. 2003) to be fully investigated.Most of the simulated permanent cliff displacements occurredduring one or two high-amplitude peaks in the time sequence ofaverage accelerations rather than through cumulative displace-ments during many lower amplitude peaks where the accelerationswere below the yield acceleration. Earthquakes of longer durationwith different frequency contents, possibly may affect these sites indifferent ways. However, the peak amplitudes in distant, but longerduration earthquakes are likely to be lower and may only triggerlesser amounts of permanent cliff displacement or none at all.

Results in Fig. 11 and those from Kaiser et al. (2014) show thatHVSR—calculated from data recorded from the temporary seis-mic stations installed at the cliff crests in the Port Hills—have astrong and consistent amplification at 1–2 Hz at all sites, which islikely to arise from the two-dimensional “ridge-scale” geometry ofthe sites. However, the higher frequency amplification (>2–5 Hz),is seen only in data from the seismic stations nearer the cliff edges,suggesting that this fundamental site frequency is due to a com-bination of local material contrasts (i.e., the ground nearer the cliffedges is more open and dilated), and the sharp breaks in slopeassociated with the cliff edges (Kaiser et al. 2014). It is thereforepossible that certain failure geometries, and failure modes, may bemore susceptible to earthquakes possessing frequency contentssimilar to the fundamental frequency of that failure mode. Toinvestigate this hypothesis, more complex, fully coupled modelingtechniques would be needed.

Cliff stability and preconditioningResults from the simplified numerical assessments presented in thispaper suggested that cliff response, in terms of permanent displace-ment, was a function of the peak earthquake amplitude (AFF) andamplification of the peak amplitude, caused mainly by local sitetopography, geological materials and their impedance con-trasts. Field observations indicated that temporal changes tothe rock mass in response to earthquake-induced permanentcliff displacements and cracking also affected cliff perfor-mance in subsequent earthquakes.

The accumulating damage from the 2010–2011 Canterburyearthquakes on the rock masses forming the cliffs was clearlyvisible in cliff outcrops around the Port Hills. During the 4September 2010 Darfield earthquake, only minor volumes ofdebris (between 5–60 m3) were measured as fallen from the cliffsin this study (Massey et al. 2014b, 2014c, 2014d, 2014e). Thevolumes of debris falling from the same cliffs in response tothe 16 April and 23 December 2011 earthquakes were much higher(between 70–1500 m3) than the volumes that fell on the 4September 2010 earthquake, even though observed PGAs andPGVs in the Port Hills at the same instrument sites were similar.This is thought to be because the 16 April and 23 December 2011earthquakes occurred after the 22 February and 13 June 2011earthquakes, which each caused significant and widespread dam-age (shear and dilation of rock joints and the formation of newones) to the cliffs. Experimental studies on the mechanical be-havior of rock joints show that shear and dilation of rock joints

decreases the shear strength of the rock mass (e.g., Oh et al.2015). Such effects on cliff stability were modeled by reducing theshear strengths of the rock types—using the Geological StrengthIndex (Hoek 1999)—to reflect the observed rock mass crackingand deformation to the cliffs caused by the main earthquakes.Results suggest that if the same earthquakes were to occur in thefuture they would initiate larger permanent displacements andwould likely trigger larger volumes of debris at the sites understudy.

ConclusionsCliffs lower than 10 m in height and inclined at angles >65°generally remained stable during the strong shaking, with onlyisolated release of a few individual boulders. Cliffs higher than10 m (up to the maximum cliff height of about 100 m and inclinedat angles >65°) performed increasingly worse, with many debrisavalanches falling from them.

The mean KMAX/AFF amplification ratio—where KMAX is thepeak of the average acceleration versus time plot calculated for agiven number of characteristic slide surfaces—for all sites was 1.6(range of 1.1–3.8), regardless of slope height, and most of thesimulated permanent displacements were attributable to one ortwo peak amplitudes—in the simulated average acceleration ver-sus time plots—rather than cumulative displacements caused bymany lower amplitude peaks.

Field data and two-dimensional seismic site responsemodeling results showed that amplification of shaking didnot necessarily increase linearly with increasing cliff height.Instead, our results showed that accelerations in the slope wereamplified mainly by site-specific material impedance contrasts,where material modulus, strength, and shear-wave velocitycontrasts led to acceleration contrasts in the cliffs, and alsocontrolled the cliff stability. In general, the simulated maxi-mum out-of-slope horizontal accelerations tended to increasewith height above the slope toe. The acceleration profiles,however, were not smooth, but instead reflected variations inthe geology caused by contrasting material modulus anddamping characteristics. The modeled maximum amplificationratios occurred around the sharp breaks in slope at the cliffcrests, and within the lower velocity basalt and trachy-basaltbreccia, especially when underlain in the cliff by higher veloc-ity basalt and trachy-basalt lavas.

The spectral ratios from the Port Hills cliffs indicated that eachsite had its own characteristic period of vibration that reflected thelocal geology, material contrasts and topography. The relativecontributions from topography and geology to amplification couldnot be decoupled in the simulations and were thought to beinherently related. However, H/V spectral ratios from field obser-vations suggested “ridge scale” amplification occurred at frequen-cies of 1–2 Hz, and localized “cliff scale” amplification occurred atfrequencies >2–5 Hz.

AcknowledgmentsThe authors acknowledge the New Zealand Natural HazardsResearch Platform which funded this research, ChristchurchCity Council for access to information and Philip Carthew(GNS Science) for graphics support. The authors would like

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to thank Stuart Read and Graeme McVerry (GNS Science) forreviewing previous drafts of this manuscript and the twoanonymous peer reviewers for their constructive reviewcomments.

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C. Massey ()) : F. Della Pasqua : C. Holden : A. Kaiser : M. J. McSaveney :G. ArchibaldGNS Science,Lower Hutt, New Zealande-mail: c.massey@gns.cri.nz

L. RichardsRock Engineering Consultant, The Tree House,Akaroa, New Zealand

J. WartmanThe University of Washington,Seattle, WA, USA

M. YettonGeotech Consulting,Ltd., Christchurch, New Zealand

L. JankuUniversity of Canterbury,Christchurch, New Zealand

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