Coseismic landslides can destroy buildings, dislocate
roads, sever pipelines, and cause heavy casualties. It is thus important but
challenging to accurately map the hazards posed by coseismic landslides.
Newmark's method is widely applied to assess the permanent displacement
along a potential slide surface and model the coseismic response of slopes.
This paper proposes an improved Newmark analysis for mapping the hazards of
coseismic landslides by considering the roughness and effect of the size of the
potential slide surfaces. This method is verified by data from a case study
on the 2014
Earthquakes are recognized as one of the major causes of landslides (Keefer, 1984). Hazards caused by coseismic landslides have drawn increasing attention in recent years (e.g., Jibson et al., 1998, 2000; Khazai and Sitar, 2003; Qi et al., 2010, 2011, 2012; Chen et al., 2012; Xu et al., 2013; Yuan et al., 2014). The damage caused by seismically triggered landslides is sometimes more severe than the direct damage caused by the earthquake (Keefer, 1984). Estimating where a specific shaking is likely to induce a slope failure plays an important role in the regional assessment of coseismic landslides.
Pseudo-static analysis formalized by Terzaghi (1950), and finite-element modeling applied by Clough and Chopra (1966) have been employed to assess the seismic stability of slopes in early efforts (Jibson, 2011). Newmark (1965) first introduced a relatively simple and practical method, which is still commonly used nowadays to estimate the coseismic permanent displacements of slopes (Jibson, 2011). Studies have shown that Newmark's method yields reasonable and practical results when modeling the dynamic performance of natural slopes (Wilson and Keefer, 1983; Wieczorek et al., 1985; Jibson et al., 1998, 2000; Pradel et al., 2005). Rathje and Antonakos (2011) recently presented a unified framework for predicting coseismic permanent sliding displacement based on Newmark's method. Chen et al. (2018) used Newmark's method to calculate the minimum accelerations required for coseismic landslides in the region affected by the 2014 Ludian earthquake. Chen et al. (2019) subsequently developed an easy operation mapping method to assess hazards posed by coseismic landslides in the zone struck by the 2014 Ludian earthquake using Newmark's method.
Such applications generally start from an analysis of the dynamic stability of slopes, which is quantified as the critical acceleration. Barton model (Barton, 1973) has been widely used in rock mechanics and engineering to predict the shear strength of rock joints, which plays a crucial role in the calculation of critical acceleration. However, researchers have not adequately attended to the shear strength of rock joints during the assessment of coseismic landslides. To better estimate the dynamic stability of slopes, in this paper, we introduce the Barton model (Barton, 1973) to Newmark analysis to develop an improved modeling method for mapping the hazards posed by coseismic landslides using data from the 2014 Ludian earthquake in Yunnan Province in southwestern China. As predictions of coseismic landslides are not based on exact results, i.e., the computed permanent displacements, but are also mingled with unformalized expertise, i.e., the interpreted landslides, we present a model of inexact reasoning, i.e., the certainty factor model (CFM), that defies analysis, as an application of sets of inference rules that are expressed in predicate logic (Shortliffe and Buchanan, 1975) to produce a map of the hazards posed by coseismic landslides.
This paper briefly introduces the characteristics and spatial distribution of landslides triggered at the chosen site, describes the method of modeling used for the analysis of the stability of seismic slopes, presents the mapping procedure of the confidence level of seismic slope failure, and finally discusses the results of the assessment of seismic hazard, as well as a comparison with the conventional Newmark analysis.
The epicenter of the 2014
Map of the study area showing the inventoried landslides.
Geological map of the study area showing lithology and faults.
An inventory of 1416 landslides triggered by the 2014 Ludian earthquake
(Fig. 1) was compiled by visual inspection through comparisons between
pre-earthquake satellite images obtained from Google Earth (30 January
2014) and 0.2 m high-resolution post-earthquake aerial images (7 August
2014; data provided by the Digital Mountain and Remote Sensing Applications
Center, Institute of Mountain Hazards and Environment, Chinese Academy of
Sciences, and Beijing Anxiang Power Technology Co., ltd.). A majority of
landslides triggered by the earthquake were shallow, flow-like landslides
(shallower than 3 m), developing in particularly dense concentrations along
steeply incised river valleys. The total area of these interpreted
landslides was 7.01 km
In the context of the analysis of the dynamic stability of a slope, Newmark (1965) proposed a permanent displacement analysis that bridges the gap
between simplistic pseudo-static analysis and sophisticated but generally
impractical finite-element modeling (Jibson, 1993). Newmark's method
simulates a landslide as a rigid plastic friction block with a known
critical acceleration on an inclined plane (Fig. 3) and calculates the
cumulative permanent displacement of the block, as it is subjected to an
acceleration time history of an earthquake. Newmark (1965) showed that the
dynamic stability of a slope is related to the critical acceleration of a
potential landslide block and can be expressed as a simple function of the
static factor of safety and the geometry of the landslide (Jibson et al.,
1998, 2000):
Conceptual sliding-block model of Newmark analysis.
Natural slopes often develop a group of shallow unloading joints (Fig. 4)
parallel to the surface due to valley incisions (Gu, 1979; Hoek and Bray,
1981). Studies have shown that rock slopes behave as collapsing and sliding
failures of shallow unloading joints under strong earthquakes, and 90 % of
coseismic landslides are shallow falls and slides (Harp and Jibson, 1996;
Khazai and Sitar, 2003; Dai et al., 2011; Tang et al., 2015). According to
Qi et al. (2012), two typical kinds of landslides are triggered by
earthquakes: (a) shallow, flow-like landslides with a depth of less than 3 m in general and (b) rockfalls thrown by the shaking caused by the
earthquake that usually occur at the crest of the slope. For both types,
unstable blocks of rock are often cut and activated along the rock joints.
Therefore, the static factor of safety in terms of the critical acceleration
in these conditions is related to the peak shear strength of the rock
joints. For the purpose of regional analysis, we use a limit equilibrium
model of an infinite slope (Fig. 3) by referring to the simplification of
Newmark's method by of Jibson et al. (1998, 2000). The value of the static
factor of safety against sliding given by the ratio of resistance to the
driving forces is determined by conventional analysis without considering
accelerations, expressed as follows:
A schematic diagram showing shadow unloading joints in the slope.
For a Newmark analysis, it is customary to describe the shear strength of
rocks instead of rock joints in terms of Coulomb's constants, i.e., friction
angle (
The effective normal stress (
Hence, the static factor of safety (
Demonstration of the Newmark analysis algorithm (adapted from Wilson and Keefer, 1983; Jibson et al., 1998, 2000).
Considering that the mapped landslides greater than 1000 m
Slope map derived from the DEM of the study area.
According to Jibson et al. (1998, 2000), slopes steeper than 60
Schematic map showing the angle (
Shear strengths assigned to rock types in the study area.
Friction angle (
The digital geological map from the China Geological Survey (CGS) was
rasterized at a 30 m grid spacing to assign material properties throughout
the study area. According to the literature,
Basic friction angle (
Unit weight (
For the sake of simplicity, the thickness of the modeled block
Static factor-of-safety map of the study area.
According to Newmark (1965), a pseudo-static analysis in terms of the static
factor of safety and the slope angle was employed to calculate the critical
acceleration of a potential landslide. The map of critical acceleration
(Fig. 13) was generated by combining the static factor of safety and the
slope angle in Eq. (1). The critical accelerations were derived from the
intrinsic properties of the slope (topography and lithology), regardless of
the given shaking. Therefore, the map of critical acceleration indicated the
susceptibility of coseismic landslides (Jibson et al., 1998, 2000). The
calculated critical accelerations ranged from nearly zero in areas that were
more susceptible to coseismic landslides to greater than 1
Map showing critical accelerations in the study area.
There were 23 strong motion stations within 100 km of the epicenter of the
Ludian earthquake (Fig. 14). Each station's record contained the three
components of the peak ground acceleration (PGA), south–north direction,
east–west direction, and up–down direction, as listed in Table 2 (the
dataset was provided by the China Earthquake Data Center,
Locations of strong motion stations.
Station records of three components of peak ground acceleration.
Contour map of peak ground acceleration (PGA) produced
by the Ludian earthquake in the study area. PGA values shown are in
In case of a landslide, in practice it is impossible to conduct a rigorous
Newmark analysis when accelerometer records are unavailable. It is also
impractical and time consuming to produce a displacement in each cell during
the regional analysis. Therefore, empirical regressions (Ambraseys and Menu,
1988; Bray and Travasarou, 2007; Jibson, 2007; Saygili and Rathje, 2008;
Rathje and Saygili, 2009; Hsieh and Lee, 2011) have been proposed to
estimate Newmark displacement as a function of the critical acceleration and
peak ground acceleration or the Arias intensity. Rathje and Saygili (2009)
developed a vector model for displacement in terms of the critical
acceleration (
This model is a preferred displacement model at a site where acceleration time recordings are not available. Incorporating multiple parameters of ground motion into the analysis typically results in less variation in the prediction of displacement (Rathje and Saygili, 2009).
The Newmark displacement of each cell was calculated by combining the corresponding values of the critical acceleration, peak ground acceleration, and moment magnitude in Eq. (8). The predicted displacements ranged from 0 to 122 cm, as shown in Fig. 16.
Map showing predicted displacements in the study area.
According to Jibson et al. (1998, 2000), predicted displacements provide an
index of the seismic performance of slopes, where larger predicted
displacements relate to a greater incidence of slope failures. But the
displacements do not correspond directly to measurable slope movements in
the field. To produce a coseismic landslide hazard map, we chose a model of
inexact reasoning, the certainty factor model (CFM) created by Shortliffe
and Buchanan (1975) and improved by Heckerman (1986), to explore the
relationship between the occurrences of landslides and their predicted
displacements. The CFM was created as a numerical method, initially used in
MAYCIN, a backward-chaining expert system used in medical contexts (Shortliffe and
Buchanan, 1975), for managing uncertainty in a rule-based system. In this
model, the certainty factor (CF) represents the net confidence in a
hypothesis
Given the above definition, we produced a coseismic landslide hazard map in
terms of the certainty factors. First, displacement cells every 1 cm were
grouped into bins such that all cells with displacements between 0 and 1 cm were grouped into the first bin, those with displacements between 1
and 2 cm were grouped into the second bin, and so on. The displacements were
grouped into 123 bins, from 0 to 122 cm. We then calculated the
proportion of cells occupied by areas of landslides in each bin. This
proportion was considered the posterior probability of each bin as previously defined.
The prior probability calculated by dividing the entire landslide area by
the entire study area was the same in each bin. Finally, the values of CF
were computed in each bin by using Eq. (9) to combine the corresponding
values of the posterior and prior probabilities. The certainty factors
ranged from
As shown in the hazard map (Fig. 17), 73.2 % of landslides triggered by the Ludian earthquake were in areas with higher confidence levels with CF values greater than 0.6. The interpreted landslides were covered on the map to demonstrate their goodness of fit for the predicted confidence levels for coseismic landslides (Fig. 17).
Map showing confidence levels of coseismic landslides during the Ludian earthquake using the proposed method. Confidence levels are portrayed in terms of values of CF.
The predicted displacements represent the cumulative sliding displacements for a given time history of acceleration. Based on the statistically significant sizes of the areas, displacements less than 60 cm, which was around the middle of the range of displacement, occupied about 80 % of the study area, while displacements greater than 80 cm occupied a very small area. Jibson et al. (1998, 2000) assumed that shallow falls and slides in brittle, weakly cemented materials fail following a relatively small displacement, whereas slumps and block slides in more compliant materials likely fail following a larger displacement. That is to say, the study area was more susceptible to rockfalls and shallow, disrupted slides that fail following a relatively small displacement. By contrast, it was subjected at a lower probability to coherent, deep-seated slides that would fail following a larger displacement. Indeed, the majority of landslides triggered by the Ludian earthquake were shallow, disrupted slides and rockfalls (Zhou et al., 2016). Although a few catastrophic rock avalanches, such as the Hongshiyan landslide (Chang et al., 2017), occurred in the field, they did not produce statistically significant samples that could meaningfully contribute to the model, which is consistent with the statistical results as discussed above. Therefore, the model should relate well to typical kinds of earthquake-induced landslides in the study area, thus demonstrating its usefulness in predicting the probability of other types of landslides.
According to Jibson et al. (1998, 2000), a function of CF and Newmark
displacement would make it possible to predict the spatial variation in
coseismic landslides in any scenario of interest involving the ground
shaking. As mentioned above, 80 % of the study area featured predicted
displacements of less than 60 cm. The numbers of the Newmark displacement
cells were uneven. There were more cells in 1 cm bins for smaller
displacements and fewer cells in 1 cm bins for larger ones. This might have
affected the statistical significance of the function of CF and Newmark
displacement. Therefore, the predicted displacement cells were grouped into
bins based on quantile statistics. The breakpoints were 0, 10, 30, 39, 46,
51, 55, 59, 63, and 122. In this way, the number of cells in each bin was
equal. Figure 18 shows, for each bin, the CF value of the Newmark
displacement as plotted as a dot. As CF values ranged from
CF as a function of Newmark displacement. A dot shows the CF value of a Newmark displacement bin; the red line is the fitting curve of the data using a modified Weibull function.
When fitting the results of shear tests using Coulomb's linear relation, the shear strengths varied widely from high normal stress in the laboratory to low normal stress in the field (Barton, 1973). We introduced the Barton model to the Newmark analysis to reduce the variation in shear strength in terms of Coulomb's constants. We also considered the impact of scale effects by using Eqs. (5) and (6) to prevent Newmark's method from underestimating the shear strength of geological units in regional analysis. In addition, for the Barton model, the joint roughness coefficient (JRC) was estimated from tilt tests, or by matching Barton's joint standard roughness profiles as defined by the International Society for Rock Mechanics (ISRM, 1978). The joint wall compressive strength (JCS) was estimated by Schmidt hammer index tests. These tests helped make a quick estimate of the shear strength in situ, which can facilitate the use of Newmark's method in an emergency hazard and risk assessment after an earthquake.
It is difficult for a statically stable slope to fail under an earthquake.
Earthquakes usually cause slopes to fail in the state of limit equilibrium.
For this reason, it is important to characterize the shear strength of the
slope accurately. The shear strengths were assigned to the geological units
using the results of hundreds of shear tests reported in the references
provided in Table 1. We assigned the original shear strengths to the
geological units, instead of increasing them to render the cells statically
stable, as was done by Jibson et al. (1998, 2000). This would have changed the
statically stable level of the entire study area, especially the slopes in
the state of limit equilibrium. In addition, we considered the size effect
of the potential slide surface, which could yield a lower
We also ran a conventional Newmark analysis using the assigned strengths,
such as friction angle (
Map showing confidence levels of coseismic landslides during the Ludian earthquake using a conventional Newmark analysis. Confidence levels are portrayed in terms of values of CF.
Plots of area under the curve comparing the proposed method with the conventional Newmark's method.
Newmark's method is a useful physical model to estimate the seismic stability of natural slopes. The mapping procedure for data on the 2014 Ludian earthquake shows the feasibility of a Newmark analysis combined with Barton's shear strength criterion. Such a method has practical applications in the assessment of regional seismic hazard. We also considered the size effect of parameters of shear strength, such as the joint roughness coefficient (JRC) and the joint wall compressive strength (JCS), in regional analyses. Moreover, linking the Newmark displacements to the certainty factor model improved the utility of Newmark's method to predict the hazard posed by coseismic landslides. Finally, the results of an AUC analysis indicate that the proposed method is more reliable than the conventional Newmark method.
The digital geological map hosted by the China Geological
Survey (CGS) can be made available upon request. The pre-earthquake
satellite images are available from Google earth, a public desktop software (
SQ initiated and led this research. MZ designed the analytical framework of this study, produced maps and figures, performed the data analysis and interpretation, and wrote the paper. YZ helped interpret landslides and collect the records of the strong motion stations. SQ, ZS, and BSZ reviewed and edited the paper.
The authors declare that they have no conflict of interest.
This research was supported by the National Natural Science Foundation of China (grant nos. 41825018, 41672307, and 41807273), the Science and Technology Service Network Initiative of the Chinese Academy of Sciences (grant no. KFJ-EW-STS-094), and the China Scholarship Council (grant no. 201704910537).
This research has been supported by the National Natural Science Foundation of China (grant nos. 41825018, 41672307, and 41807273), the Science and Technology Service Network Initiative of the Chinese Academy of Sciences (grant no. KFJ-EW-STS-094), and the China Scholarship Council (grant no. 201704910537).
This paper was edited by Mario Parise and reviewed by two anonymous referees.