Coseismic landslides reveal near-surface rock strength in a high-relief, tectonically active

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1 GSA Data Repository 56 Gallen et al. Coseismic landslides reveal near-surface rock strength in a high-relief, tectonically active setting Authors: Sean F. Gallen, Marin K. Clark, Jonathan W. Godt Coseismic landslide model description. We adapt a model used by the hazard community to estimate landslide potential during an earthquake. This model is used for rapid assessment of landslide probability given a particular actual ground shaking scenario (Fig. DR) (Jibson et al., ; Godt et al., 8). Slope stability is estimated using an infinite-slope stability model and results are cast as the factor of safety (FS), which describes the ratio of shear resistance to shear stress for downslope movement. Calculation of the factor of safety requires shear strength, local topographic slope, and landslide thickness (t), in a material for which the shear strength can be defined using the internal angle of friction (ϕ) and cohesion (C). The static factor of safety FS= C t + tan(ϕ) - m ρ w g tan(ϕ) ρ r g sin(α) tan(α) ρ r g tan(α) () where g is acceleration due to gravity (9.8 m s - ), ρ r is the average density of rock and soil involved in failure, which we assume is 5 kg m -3, ρ w is the density of water, and m is the ratio of saturated thickness to total thickness. Equation () is written such that the first term represents cohesion, the second term frictional properties and the third is a pore-water pressure term that for positive-pore water pressures reduces the overall stability. Assuming the absence of positive pore-water conditions in our model runs we ignore the pore-water pressure term (m = ). The

2 pore-water pressure term is used to model transient fluctuations in slope stability, typically related to elevated surface water or ground water infiltration during storm events, and requires a significant degree of data to be implemented appropriately at the regional-scale (e.g. Godt et al., ). Regional data regarding the saturation conditions of the near-surface environment in the Longmen Shan preceding the earthquake are unavailable. Further, the climate is described as subtropical monsoon with ~8% of the annual precipitation falling between June and September (Hijmans, et al., 5), which postdates the time of the earthquake in May. In any case, exclusion of the pore-pressure term effectively means that we have incorporated that effect in our aggregate strength estimate, so that the strength represents a minimum. In other words, if there were an effect of pore fluid, our results strength estimates would be higher than reported here. We note that exclusion of this term does not mean that we neglect the long-term role of precipitation in our analysis; by spatially segregating the landscape to determine rock strength, the effects of climate-induced weathering on rock strength are implicitly considered in our estimates of rock strength. For each grid cell we solve for the static factor of safety prior to ground shaking based on the local topographic slope (α), the friction angle determined from the modal topographic slope of each geologic map unit (see below), and a range of cohesion-to-thickness ratios (.5 to 5 kpa m - ). Combining the cohesion and thickness as a ratio has the advantage of avoiding assumptions about landslide thickness in the initial modeling steps. We later use the calculated landslide thickness from our geometric criterion to determine cohesion values. Surface displacements are calculated on the basis of a simplified Newmark analysis (Newmark, 965), which considers the critical (or yield) acceleration (a c ) necessary to initiate displacement:

3 a c = (FS ) g sinα () where FS is the static factor of safety, g is gravitational acceleration and α is local topographic slope. The Newmark (965) sliding-block model provides the basis for our estimate of coseismic landslide distribution. A potential landslide is modeled as a block on a plane inclined at angle (α) that experiences a known critical acceleration (a c ) to overcome shear resistance at its base. Sliding of the block is referred to as a Newmark displacement. Newmark displacements consider only rigid-block movements (no internal deformation) and plastic deformation at its base. While other approaches consider internal deformation and elevated dynamic stresses that arise during movement, the simplified Newmark analysis has been argued to be appropriate for the regional analysis of landslides triggered by earthquakes (Wieczorek et al., 985; Jibson et al., ; Keefer, ; Godt et al., 8). A rigorous Newmark analysis calculates Newmark displacements from two integrations of the ground acceleration time history for ground accelerations that exceed the critical acceleration (Newmark, 965). Such an analysis requires a significant amount of high-quality ground acceleration data and is computationally impractical on a regional scale. The simplified Newmark analysis has been developed to overcome these limitations and typically models Newmark displacements as a non-linear function of the ratio of the critical acceleration to either peak ground acceleration (PGA) or Arias intensity (Jibson et al., ; Godt et al., 8). We use the most up-to-date function to calculate Newmark displacements as (Jibson, 7): 3

4 log D N =.5 + log [ ( - a c /PGA).34 (a c /PGA) ] ±.5 (3) Studies have shown that a critical amount of Newmark displacement is required for a slope to fail (Wieczorek et al., 985; Jibson et al., ). Most studies consider Newmark displacements greater than 5 cm as slope failures, and we use this threshold to designate "target cells" for landslides in our model (Wieczorek et al., 985; Jibson et al., ; Keefer, ; Godt et al., 8). Description of modeled landslide geometries. Newmark displacements calculated over gridbased topography do not yield a collection of cells with D n 5 cm that produce realistic landslide geometries with clearly defined boundaries. This stems from the approximations associated with a -D model of slope failure and requires that we devise a rational approach to expand failure cells to approximate the real 3-D geometry of the landslide and to generate a synthetic landslide inventory. Our approach is to use target cells as the downslope extent of the landslide and then apply a geometric criterion that will predict the area and volume of the model landslide that relates to the failure cell (Fig. A). In this way, failure of the target cell in our model acts to destabilize upslope cells beneath a failure plane generated through a geometric approximation (see below). This is analogous to undercutting a slope and is a similar approach to that used to simulate deep-seated bedrock failures in numerical models (Densmore et al., 998). Our goal was to find the most simple landslide geometry that is capable of reproducing characteristics of the observed landslides, such as landslide frequency-area statistics, total landslide volumes and the spatial distributions of landslide area and frequency. We consider a series of combinations of different landslide geometries, each constrained by different topographic boundary conditions, to explore the influence of landslide frequency-area statistics 4

5 (Fig. A). Each model assumes an initial failure plane depth of m meter at the target cell. Model a extends from the target cell to the local drainage divide in a cone shape. Model b applies to target cells that initiate in concave upward topography and are laterally confined to the concavity and extend to the local drainage divide. Model c extends a failure plane upslope at an angle equivalent to the topographic slope of the target cell. In this model, the failure plane is modeled as planar or curved concave upward (note that model c planar in figure A only considers planar failure planes, while c concave considers both planar and concave-upward failure planes). The curved failure plane generally applies to concave-upward hillslope, whereas the planar geometry generally applies to convex-upward and planar hillslopes. The resulting power-law slope is essentially identical for the planar-only geometry compared to a geometry in which we allow concave upward hillslopes to have a concave geometry (Fig. A). A failure plane is only modeled as curved if the angle between the target cell and the highest elevation cell in the landslide is greater than the topographic slope, such as in a concaveupward hillslope. If these situations are modeled with a planar slope, they produce unrealistically large and deep landslides. In order to combat this issue, we assign a curved failure geometry to concave-upward hillslopes that attempts to maintain roughly the same areal extent as a planar failure plane while simultaneously minimizing the landslide volume. The curvature of the failure plane is determined individually for each landslide. The failure plane is extended upslope at an initial angle equal to the topographic slope of the target cell and can only steepens to match the angle between the target cell and the highest elevation cell in the landslide. It was the model c concave landslide geometry that produces the best match to the observed landslide frequency-area statistics (Fig. ). This landslide geometry is used for all model runs presented in this paper. The best-fit landslide geometry (model c, concave) was used 5

6 in the brute-force search for the strength parameters that maximize the goodness-of-fit (Χ ) between the observed and modeled frequency-area distributions for each rock type (Fig. ). Generating synthetic landslide inventories. In each model run, all cells with Newmark displacements 5cm are considered target cells for potential landslides. Target cells are selected randomly throughout the landscape and landslide polygons are generated using one of the geometric criteria described above. If a target cell falls within the bounds of a previously generated landslide, it is removed from subsequent model iterations. Landslides polygons are generated until no more target cells remain in the model space. Because larger landslides are assumed to cut deeper into the Earth s surface relative to smaller ones (Hovius et al., 997; Larsen et al., ; Parker et al., ), landslides covering larger areas overtake those covering smaller areas where landslides overlap. Calculation of hillslope-scale cohesive strength. To determine the strength of each geologic map unit we initially performed a brute-force search for the best-fit combinations of the internal angle of friction and cohesion-to-landslide thickness ratio that maximize the goodness-of-fit (Χ ) between the observed and model landslide frequency area statistics (Fig. C, D). We iterated through friction angles ranging from 5 to 4 in increments and cohesion-to-thickness ratios from.5 to 5 kpa m - in.5 kpa m - increments. Approximately 6 iterations were performed on each of the geologic map units and compared to the inventory to determine the best-fit combinations of strength parameters. A range of combinations of friction angle and cohesion-tothickness ratios fits the data equally well (Fig. DR). To combat the non-uniqueness of the strength parameters, we assume a regionally uniform friction angle of 3. This value was selected because it approximates the average modal hillslope angle (3 ± 3 ) for the studied geologic map units and is a reasonable friction angle for rock or soil (Fig. DR3). Using the fixed 6

7 friction angle we solve for effective cohesion, which is the total rock strength minus the assumed frictional strength. While the actual partitioning of friction and cohesion may differ slightly from our calculations, the aggregate rock strength determined from the combination of these terms is the same as natural rock strength. Thus, effective cohesion normalized to a fixed fiction angle reflects the true relative differences in total rock strength. Of the geologic units 5 yielded best-fit cohesion-to-thickness ratios were used to determine effective cohesive strength for each of these 5 geologic map units. We conducted an additional analysis where we set cohesion to zero and solve for an effective friction angle where we iterated through friction angles ranging from to 7 in increments (Fig. DR4A). The 5 geologic map units fitted for effective friction were used in this analysis. The relative pattern of effective friction angle and effective cohesion is the same (Fig. 4; DR4). The mean (± σ) effective friction angle from this analysis is 5 ± 4. These effective friction angles would be considered high even for measurement conducted on intact rock sample (e.g. Hoek and Brown, 997), and are much greater than the model hillslope angles which are often interpreted to reflect the frictional strength of hillslopes (Fig. DR3) (c.f. Burbank et al., 997; Korup, 8). This finding suggests that cohesion is likely an important component of near-surface rock strength at the hillslope-scale, challenging the traditional view that rock strength at large spatial scales is almost entirely frictional (c.f. Burbank et al., 997; Korup, 8). The 5 geologic units that yielded statistically meaningful fits in our analysis lie mostly in the footwall of the fault rupture that had minimal observed landsliding. While our analysis does not cover the entire region effected by landsliding, the 5 units used in our final analysis cover more than 9 percent of the study and thus provide adequate spatial coverage of the study 7

8 area. The patterns of the modeled and observed landslide frequency and area densities are similar indicating model coverage indicating that 9 percent coverage of the study area is sufficient to capture regional patterns of coseismic landsliding (Fig. DR5, DR6). To determine cohesion for each geologic map unit we use our modeled landslide volumes to determine mean landslide thickness and multiply it by the best-fit cohesion-to-thickness ratio used in the factor of safety equation. The simplified geometric approximations of model landslides results in an over-estimation in modeled landslide volume relative to observed landslide inventories converted to volumes using empirically derived volume-area scaling (Larsen et al., ; Parker et al., ) (Fig. DR7). This bias stems from a grouping of landslides with areas between ~5, 5, m having depths 4 m that account for 4 percent of the total landslide population, but represent approximately percent of the total landslide volume. These modeled landslides are anomalously deep for their areal extent relative to observed landslides (Larsen et al., ). To reduce the effects of these outliers we use a logbin average of the model data to derive a model-specific volume-area scaling that is used to calculate landslide volumes based on the modeled landslide areas and is used to determine mean landslide thickness per geologic map unit (Fig. DR7). Uncertainty (± standard error) in the regression was assigned by regressing through the upper and lower 68 th percentile associated with each log-binned increment and used to assign standard errors to cohesive strength (Figs. 4A, DR7). References: 8

9 Burbank, D. W., Leland, J., Fielding, E., Anderson, R. S., Brozovic, N., Reid, M. R., and Duncan, C., 996, Bedrock incision, rock uplift and threshold hillslopes in the northwestern Himalayas: Nature, v. 379, no. 6565, p Burchfiel, B., Chen, Z., Liu, Y., and Royden, L., 995, Tectonics of the Longmen Shan and adjacent regions, central China: International Geology Review, v. 37, p Dai, F. C., Xu, C., Yao, X., Xu, L., Tu, X. B., and Gong, Q. M.,, Spatial distribution of landslides triggered by the 8 Ms 8. Wenchuan earthquake, China: Journal of Asian Earth Sciences, v. 4, no. 4, p doi:.6/j.jseaes..4. Densmore, A. L., Ellis, M. A., and Anderson, R. S., 998, Landsliding and the evolution of normal-fault-bounded mountains: Journal of Geophysical Research: v. 3, no. B7, p doi:.9/98jb5 Godt, J. W., Baum, R. L., Savage, W. Z., Salciarini, D., Schulz, W. H., and Harp, E. L., 8, Transient deterministic shallow landslide modeling: Requirements for susceptibility and hazard assessments in a GIS framework: Engineering Geology, v., no. 3â 4, p doi:.6/j.enggeo Godt, J. W., Şener-Kaya, B., Lu, N., and Baum, R. L.,, Stability of infinite slopes under transient partially saturated seepage conditions: Water Resources Research, v. 48, no. 5, p. W555. doi:.9/wr48 Hijmans, R. J., Cameron, S. E., Parra, J. L., Jones, P. G., and Jarvis, A., 5, Very high resolution interpolated climate surfaces for global land areas: International Journal of Climatology, v. 5, no. 5, p doi:./joc.76 9

10 Hoek, E., and Brown, E. T., 997, Practical estimates of rock mass strength: International Journal of Rock Mechanics and Mining Sciences, v. 34, no. 8, p doi:.6/s365-69(97)869-x Hovius, N., Stark, C. P., and Allen, P. A., 997, Sediment flux from a mountain belt derived by landslide mapping: Geology, v. 5, no. 3, p doi:.3/9-763(997)5<3:sffamb>.3.co; Jibson, R. W., 7, Regression models for estimating coseismic landslide displacement: Engineering Geology, v. 9, no. -4, p doi:.6/j.enggeo.7..3 Jibson, R. W., Harp, E. L., and Michael, J. A.,, A method for producing digital probabilistic seismic landslide hazard maps: Engineering Geology, v. 58, no. 3 4, p doi:.6/s3-795()39-9 Keefer, D.,, Investigating Landslides Caused by Earthquakes: A Historical Review: Surveys in Geophysics, v. 3, no. 6, p doi:.3/a:74784 Korup, O., 8, Rock type leaves topographic signature in landslide-dominated mountain ranges: Geophysical Research Letters, v. 35, no., p. L4. doi:.9/8gl3457 Larsen, I. J., Montgomery, D. R., and Korup, O.,, Landslide erosion controlled by hillslope material: Nature Geosci, v. 3, no. 4, p Ministry of Geology and Mineral Resources, Regional Geology of Sichuan Province: Beijing, Geological Publishing House, 78 p. Newmark, N. M., 965. Effects of earthquakes on dams and embankments. Geotechnique 5,

11 Parker, R. N., Densmore, A. L., Rosser, N. J., de Michele, M., Li, Y., Huang, R., Whadcoat, S., and Petley, D. N.,, Mass wasting triggered by the 8 Wenchuan earthquake is greater than orogenic growth: Nature Geoscience, v. 4, no. 7, p

12 Supplemental Data Tables and Figures. Supplementary Table DR. Principal component analysis of data inputs and model residuals PC* PC PC3 PC4 PC5 eigan values % trace cumulative % slope PGA rock type PDD ADD * Principal component. Landslide point density difference between modeled and observed. Landslide area density difference between modeled and observed. Figure DR. Work flow of modeling procedure to determine hillslope-scale rock shear-strength from peak ground acceleration and coseismic landslide records. Figure DR. Misfit plots (sum of Χ ) of brute-force search for model parameters of friction angle and cohesion-to-thickness ratio for the 6 rock types used in the regional analysis. See Fig. B reference on location of rock types. Figure DR3. Histograms of slope ( -bins) for the 6 rock types with near normal distributions. See Fig. C reference on location of rock types. Figure DR4. (A) Plot of best-fit effective friction for each rock-type. (B) Plot of effective cohesion calculated using a fixed friction angle of 3 (see figure 4 in main text) versus effective friction angle. Note the near perfect correlation between effective cohesion and effective friction

13 angle, as expected. Rock type descriptions (Ministry of Geology and Mineral Resources, 99; Burchfiel et al., 995): Upper Triassic: siltstone, mudstone; Triassic Flysh: Mudstones and sandstones, low metamorphic grade; Silurian: mudstone, sandstone, marl; Middle Triassic: limestone, mudstone, local evaporites; Lower Triassic: limestone, marine clastics; Devonian: Marine clastics, limestone; Cambrian: sandstone, evaporates, limestone; Proterozoic Sedimentary: marine clastics, dolostone, limestone; Upper and Lower Permian: limestone, dolostone; Carboniferous: limestone; Proterozoic Metamorphic: Amphibiolite-grade metasedimentary and meta-volcanics; Mesozoic Granite; Proterozoic Granite; undifferentiated; Pengguan Massif: Proterozoic Granite. Figure DR5. Point and area density of mapped (Dai et al., ) and modeled landslide inventories and maps showing the difference between modeled and observed data. Density maps were constructed by passing a 5km wide moving average window over the respective landslide inventory. The insets in the differences maps are histograms of the model misfits. The red dashed line is the mean misfit an the gray bars note the one standard error range. Figure DR6. 5 km wide swath profiles of landslide point and area frequency of the mapped (black) and modeled (blue) landslide inventories. Figure DR7. Coseismic landslide model volume-area statistics. Model landslide volume-area data follow a power-law trend similar to that determined from observed landslide volume-area statistics (Hovius et al., 997; Larsen et al., ). Lines indicating mean landslide depth are included for reference. The black line is a log-bin regression through the data that is used to calculate total landslide volume and mean landslide depth in an effort to reduce the effects of anomalously deep landslides highlighted in the red box. 3

14 Data inputs SRTM digital topography (~9m) PGA map Geologic map Landslide inventory Workflow Summary Select strength parameters (cohesion-to-thickness ratio, friction angle) Calculate the Factor of Safety (FS) Designate target failure cells as those with Newmark displacements > 5cm Conduct the simplified Newmark analysis Calculate the critial acceleration (a c ) Model coseismic landslides with a geometric approximation to generate modeled landslide inventory Find strength parameters that maximize the goodness-of-fit between the observed and modeled frequency-area distributions Synthesize model inventory from best-fit strength parameters Calculate cohesion (±σ) for each geologic map unit using the cohesion-to-thickness ratio and mean landslide thickness (±σ). Perform a log-binned regression through the landslide volume data to average out the effects of outliers and calculate the mean landslide depth for each geologic map unit. Figure DR

15 Cohesion-to-thickness (kpa m - ) x x x x Triassic flysh x x x x x x x x x x 4 Mesozoic granite Lower Permian Carboniferous Devonian x 4 Silurian Ordovician Cambrian Prot. sedimentary Prot. granite Upper Triassic Prot. meta Middle Triassic Pengguan Massif x LowerTriassic Upper Permian Friction angle ( ) Figure DR

16 Triassic flysh Upper Triassic Middle Triassic LowerTriassic normalized frequency Mesozoic granite Lower Permian Carboniferous Devonian Silurian Ordovician Cambrian Prot. sedimentary Prot. granite 4 6 Prot. meta. 4 6 Pengguan Massif 4 6 Upper Permian topographic slope ( ) Figure DR3

17 effective friction angle ( ) clastics Triassic flysh Upper Triassic Silurian mixed CO 3 meta.& ign. clastics and CO 3 Middle Triassic LowerTriassic Devonian Cambrian Prot. sed. Upper Permian Lower Permian Carboniferous Prot. meta. Mesozoic granite Prot. granite Pengguan Massif A effective friction angle ( ) 6 B r = effective cohesion (kpa) Figure DR4

18 Observed 5 3 E N 5 km 4 E 5 5 E 4 E 5 E Normalized misfit (percent) N < -5 > 5 frequency Landslides per km N 5 km normalized misfit (percent) Normalized misfit (percent) N < -5 > E 3 E 4 E Figure DR5 x 5 3 E 5 N mean ± σ: -3.6±.7%.6 5 E 4 5 km 3 N 4.3 frequency 38.4 % landslide area per km % landslide area per km 3 N 4 E N -.±.% 3 E 5 3 N 5 3 N 5 km 5 km 4 mean ± σ: x 5.4 Landslides per km 3 N. Area density 3 E 3 N 5 km 5 E 3 N Point density 4 E Difference 3 N 3 E Modeled 4 E 6 6 normalized misfit (percent) 5 E

19 E 4 E 6 E 3 N Swaths N Landslide Frequency km Landslide Area swath # x 5 swath # swath # x 6 swath # Number of landslides swath # swath # swath # 5 Area covered by landslides (m ) swath # 3 x 6 5 x swath # x 6 swath # swath # x 6 swath # distance (km) 5 5 distance (km) Figure DR6

20 8 Anomalously deep landslides: area 5, - 5, m, 4% of landslides, ~% of landslide volume. 4 m m Landslide volume (m 3 ) m Total volume sum = 8.98 km 3 Log-bin volume = 4.8 (+.73/-.7) km 3 V = αa γ Where, V is volume, A is area and α and γ are the scaling constant and power-law exponent, respectively. V =.9(+./-.3)A.59(+.5/-.6) Landslide area (m ) Figure DR7