The Canterbury Earthquake Sequence (CES) of 2010–2011 on the previously unmapped Greendale and Christchurch fault traces to the west and east of Christchurch produced seismic moments up to Mw 7.1 and high peak ground accelerations (≥1 g) (Holden, 2011; Cousins and McVerry, 2010; Bannister and Gledhill, 2012; Wood et al., 2010; Beavan et al., 2011; Fry et al., 2011a, b; Kaiser et al., 2012). These large, shallow (< 15 km) ruptures triggered large slope failures on the Port Hills, of which rockfalls were the most abundant type and posed the most risk (Massey et al., 2014b). More than 6000 individual boulders were mobilized, many of which impacted houses and affected the livelihoods of people within the impacted area. Rockfall is most likely to occur in closely jointed or weakly cemented material on slopes of ≥40∘ (Keefer, 1984). The columnar jointed lava of the Port Hills is generally dominated by three to four joint sets (Brideau et al., 2012) which vary somewhat between sites, attributed to variations in the paleotopography (Massey et al., 2014b). Scoria layers are interbedded with lava in some sites, and these have more widely spaced discontinuities than the lava (Massey et al., 2014b). Rockfall data were collected by a rapid-response group immediately following events of the CES and resulted in a repository of data including 5 719 boulder locations (Massey et al., 2014b), with their associated earthquake event and boulder dimensions (Fig. 1).

Loess is defined as a loosely deposited aeolian soil of predominantly silt-sized particles. Loess often displays high enough strength and cohesion to allow deposits to be meta-stable in a near-vertical exposure in dry conditions. When dry, the high cohesion of loess has been attributed to several possible mechanisms, including clay cohesion, calcite bonding, and soil suction (e.g. Goldwater, 1990). Post-depositional flocculation of cohesive clay grains to the larger silt- and sand-sized grains causes the irregular formation of clay “bridges” between larger grains. As the larger grains within the soil do not touch, the mechanical behaviour of the material is dominated by the bonds between the larger grains (Gao, 1988; Lutenegger and Hallberg, 1988; Derbyshire and Mellors, 1988). Due to the cohesion between clay particles and negative pore pressure above any water table, loess generally displays a high dry shear strength; up to 180 kPa has been reported in Christchurch in loess of < 10 % moisture content (Mcdowell, 1989). However, loess has been observed to lose significant strength and cohesion upon wetting, with cohesion and friction angle generally decreasing with increasing moisture content (Kie, 1988; Mcdowell, 1989; Della Pasqua et al., 2014; Carey et al., 2014). Wetting of the clay bridges and an increase in pore pressure reduces the shear strength of the material (Gao, 1988; Lutenegger and Hallberg, 1988; Derbyshire and Mellors, 1988; Della Pasqua et al., 2014; Carey et al., 2014).

The Port Hills loess is a cohesive predominantly silty soil with minor clay content. Strength parameters of the soil are largely controlled by the moisture content as repeatedly shown in testing (e.g. Tehrani, 1988; Mcdowell, 1989; Goldwater, 1990; White, 2016; Della Pasqua et al., 2014; Carey et al., 2014). A review of these studies (Massey et al., 2014a) shows that it displays high cohesion at moisture contents of < 10 %, while cohesion values are very sensitive to changes in the moisture content between 10 % and 20 % tests. Carey et al. (2014) found that at 3 % moisture content the loess has cohesion of 45 kPa and a friction angle of 48∘. Comparatively at 16 % moisture content the soil displayed cohesion of 25 kPa and a friction angle of 28∘. At moisture contents less than 15 % the soil can display a brittle deformation style. The measured plastic limit for the Port Hills loess is a moisture content ranging from 16 % to 20 %, with a plasticity index of between 4 and 8.8, and liquid limit ranging between 22 % and 28 %, above which the material deforms as a fluid (Hughes, 2002).

Boulder deposit locations were measured in the field using a handheld GPS. Boulder size (lengths along three axes) and shape were recorded for most mapped boulders. New rockfall deposits were easily distinguished from paleo-boulders by fresh rock surfaces and their location on top of the substrate. Impact scars on the substrate were mapped at both Rapaki Bay and Mt Vernon with lengths (axis parallel to boulder travel direction) and depths of 140 scars recorded. Additional mapped earthquake boulder data were contributed by the Port Hills Geotechnical Group – only boulder deposit locations were used from this data set. In total 336 boulders were mapped at Rapaki Bay.

To assess soil moisture conditions at the time of the earthquake, weather data were accessed through the National Climate Database (CliFlo; http://www.cliflo.niwa.co.nz, last access: 11 January 2019) from the Governors Bay station, 3.5 km south-west of the site and also south-east-facing (Fig. 1). The Governors Bay rainfall data are presented in Table 1. Moisture content of the soil at Rapaki Bay was not tested at the time of the earthquake and instead inferred from published testing of 14 Port Hills loess samples in January and February 2013 and 2014 (taken from the northern side of the Port Hills: Lucas Lane, Maffeys Road, Redcliffs, Deans Head, Clifton Hill, Richmond Hill, and Wakefield Avenue; Carey et al., 2014).

We conducted moisture content and direct shear tests on 36 disturbed hand auger and borehole samples of Port Hills loess and loess–colluvium from 17 Ramahana Road and Centaurus Park (Fig. 1). Unfortunately no sub-surface investigations could be undertaken at Rapaki Bay, and as such testing was carried out on samples taken on similar soil types from a site investigation that was underway at the time of the study (White, 2016). Samples were taken from a range of soil profile depths (Table 2) and as such reflect a range of clay and natural moisture content and therefore mechanical properties. Testing was in accordance with ISO/TS 17892-10:2004 Direct shear tests and NZS 4402:1996 Test 2.1 Determination of the water content. Samples selected displayed a spread of both clay contents (Table 2; 5 %–19 %) and natural moisture contents below, near, and above their 16 %–19 % plastic limit (Table 2; 8 %–22 %). The samples were reconsolidated by means of tamping, using a standard Proctor test within the shear-box test sample rings. A total of 25 blows from the hammer were used to compact the soil directly into the shear-box test sample ring, and the method was repeated with a fresh sample if the blows from the hammer caused the soil to be compacted to below or > 5 mm above the height of the sample ring. The method was considered satisfactory; however there was an unavoidable amount of variation in the density of the samples: the dry density varied between 1658 and 1954 kg m-3, with an average of 1750 kg m-3. This variation can be attributed to the variable moisture contents of the soils that were compacted, which would have allowed greater or lesser compaction depending on the optimum moisture content for compaction and the soil's particle-size distribution. The samples were subjected to 20, 50, and 100 kg applied weight (corresponding to 26, 64, and 126 kPa normal stress and overburden depths of 1.45, 3.64, and 7.28 m respectively with consideration of the average sample density (1750 kg m-3)) and sheared at a constant rate.

We conducted rockfall experiments, which involved the triggering and recording of 20 boulders at Mt Vernon. The boulders were jacked from the bedrock along cooling joints by inflation of air compression bladders. Each boulder was measured for size and shape, dislodged, captured by video during travel, and impact trail (lines of impact scars) and deposit location were mapped. Locations were recorded with a handheld GPS and dGNSS. As most boulders fragmented on initial impact, all fragments were mapped as boulder deposits – therefore 70 deposited boulder locations were mapped, including pieces from the initial triggering of only 20 boulders. A total of 19 impact scars were mapped and measured.

A total of 13 soil samples were taken at Mt Vernon at the time of the experiments and analysed according to NZS 4402:1996 Test 2.1 Determination of the water content to obtain the natural moisture content. Samples were collected as 30 cm tube samples from the base of 13 impact scars equally distributed down the slope.

RAMMS::Rockfall is a rigid-body three-dimensional rockfall simulation programme (Leine et al., 2013). It was chosen as an appropriate tool because (1) it allows the user to create a boulder population of varying sizes and shapes modelled on point clouds of real boulders and (2) the parameters that control different aspects of the terrain–boulder interaction process can be sensitively adjusted by the user.

In conventional rockfall models, rock interaction with the substrate is represented by coefficients of restitution, a ratio that defines the change in velocity after impact in both normal and tangential directions (e.g. Volkwein et al., 2011). In RAMMS the process of boulder interaction with a substrate is represented as a function of “slippage” through near-surface material, a complex interaction with the substrate that includes sliding of a block through material until maximum frictional resistance is reached, and angular momentum generated by contact forces cause the block to be launched from the ground (Glover, 2015; Leine et al., 2013). The slippage can be parameterized (Table 3) for hard surfaces (e.g. rock) by decreasing the distance over which impact occurs and its time duration, to better reflect the instantaneous rebound observed in rock–rock interactions.

A robust RAMMS calibration exercise was performed for the Rapaki Bay data set (Borella et al., 2016; this paper) and checked against other dry condition data sets generated from the same earthquake sequence in other locations on the Port Hills (Vick et al., 2015). The modelling inputs included a representative sample of 21 mapped boulders with real shapes and sizes, a 3 m digital elevation model (DEM; 2013 lidar), and a terrain map delineated by changes in ground cover (outcropping rock, loess–colluvium, and loess). Following a recent RAMMS update (Bartelt et al., 2016) this calibration exercise was repeated (this paper) to confirm relevance of the results.

Modelling of Mt Vernon boulder runouts was performed using the dry calibrated parameters. A second set of parameters was created to reflect the wet soil conditions assessed by the natural moisture content testing. This was done by modifying the original dry calibrated parameters to incorporate more soil damping as the boulder interacts with the soil (Table 3). RAMMS parameters were adjusted incrementally until modelled runout paths showed a similar spatial distribution to that of the experimental boulder runouts. For each iteration of the model, parameters were adjusted to more closely represent wet conditions: the parameter κ was decreased by 16 % for loess–colluvium and 54 % for loess, to reflect the longer slip distance through the soil (1/κ= impact length); the parameter β was decreased by 16 % for loess–colluvium and 33 % for loess, to reflect the longer impact time (1/β= impact time); the μ values were lowered by 33 % for both soil substrates to reflect the decreased friction applied to the boulder over the period of the impact; the drag coefficient was increased by 40 % for both soils, to represent the general greater drag on the boulder due to decreased soil hardness. These adjustments to the parameters were considered suitable when the runout envelopes of both the experimental rockfall and the modelled rockfall were closely aligned, rather than changing the parameters by a specific predetermined value.

Inputs to the Mt Vernon model included a representative sample of five model boulders, which were based on the measured size and shape of the boulders used in the field experiments. A 3 m DEM (derived from the 2013 lidar) was used as the basis for the simulations, and a terrain map delineating field mapped changes in ground cover (outcropping rock, loess–colluvium, and loess) was used to proportion the locations of the various terrain material types across the slope.

The boulder density for both modelling exercises was 2700 kg m-3, based on previous laboratory density testing of similar rock by others (Mukhtar, 2014).

Soil moisture tests from the Mt Vernon site in May 2014 showed water contents of between 28 % and 62 %. A prolonged rainy period preceded the experiments, with rainfall totals of 267, 263, and 44 mm recorded in March, April, and May, respectively (the average totally monthly rainfall recorded since 1989 at the same weather station is 125, 144, and 88 mm for March, April, and May respectively, Fig. 3a, b; Table 1).

Testing conducted by Carey et al. (2014) in January and February 2013 and 2014 (when recorded rainfall for December, January, and February was 65, 46, and 29 and 105, 33, and 48 mm for each year respectively) showed moisture contents ranging from 3.5 % to 11 %. The Rapaki Bay rockfalls occurred during typical dry summer conditions, when rainfall totals of 58, 50, and 38 mm were recorded for December, January, and February, respectively (Fig. 3a and b).

Our direct shear testing of loess samples showed a low moisture content (< 10 %) of the loess resulted in high cohesion (> 35 kPa) for all clay content variations (Fig. 4). Increased moisture content correlated with decreased cohesion; samples with 16 %–17 % moisture displayed cohesion of 6–16 kPa for all clay contents. Moisture contents of > 19 %, above the liquid limit of the soil, displayed < 5 kPa for all percentages of clay contents tested. The spread of the cohesion data is large (±14.5 kPa) for varying clay contents at lower moisture contents, noticeable (±5 kPa) for intermediate moisture content, and low (±1.5 kPa) for high moisture content. High clay contents correspond to higher cohesion values at low and intermediate moisture content, but the effect of clay content is negligible at high moisture contents.

Mapped impact scars in the soil display a wedge-like form, with a clear boulder penetration point at the upslope end and a widening outwards and downslope and an area of compression (where soil has been compacted and pushed up) with some excavated and overturned soil on the downslope end (Fig. 6). Impact scar dimensions at both sites when compared (P=0.035) showed variation in minimum, average, and maximum depth : length ratio: 0.05, 0.29, and 0.4 at Rapaki Bay and 0.125, 0.22, and 0.43 at Mt Vernon respectively (Fig. 5). Although both data sets display similar maximum depth : length ratios, the distribution of the values within the Mt Vernon data set (wet conditions) generally shows a higher depth : length ratio. Scars that show a greater depth : length ratio are a result of impact of boulders which achieve depth in a shorter space during slippage/contact with the ground (Fig. 6a and b). The Rapaki Bay impact scars show a generally lower depth : length ratio, indicative of shallower slippage through the soil during contact with the ground.

Modelling was performed at Rapaki Bay to ensure that results were the same/similar following RAMMS updates since the publication of the original calibration (Borella et al., 2015). The RAMMS simulation of boulders at Rapaki Bay still compares favourably with the runout envelope of mapped boulders (Fig. 7). Mapped and simulated boulder distribution within the envelope was compared: the largest proportion of boulders from both data sets were deposited in the upper slope (33∘ shadow angle) and the middle–lower slope (26∘ shadow angle). Both data sets showed a maximum runout within the 22∘ shadow zone. The distributions of the data sets were both constrained by lateral ridges and a creek at the toe. A large proportion of the boulders from both data sets were channelled into a gully running parallel with the slope direction.

A RAMMS simulation of Mt Vernon boulder motions was performed using the dry calibration parameters. The runout envelope of the simulated boulders compares unfavourably to the envelope from the experimental rockfall rolling (Fig. 8). Runout of the simulated boulders is 175 m further downslope. The topography is more constrained than Rapaki Bay, with a channelization effect that means lateral dispersion was not large; however the simulated rockfall showed a divergence of boulder paths into a neighbouring gully, behaviour that was not observed during the field experiments.

An adjustment of parameters from the original values, to reflect wetter soil conditions (Table 4), resulted in a better match between the field experiment and runout simulation envelopes (Fig. 8).