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# Coseismic landslide hazard modeling methodologies - 2.c Methods and Analysis: Capacity-Demand

2.c Capacity-Demand Analysis

Capacity-demand analysis of slope stability relies on the Newmark (1965) sliding block model, and determines the probability that a specified amount of seismic shaking will be exceeded, resulting in displacement. Newmark’s model is a simple way to predict coseismic displacement in a specified shaking scenario. The mechanical processes behind Newmark displacement rely on the exceedence of frictional forces holding a block on an inclined surface; it relies on slope geometry, pore-pressure, and mechanical soil properties (Romeo et al., 2000).

2.c.I Application: Romeo et al., 2007

Romeo et al. (2007) utilized a capacity-demand analysis to estimate the probability of landslide risk by integrating the slope performance following a seismic event. Landslide risk is assessed both deterministically (landslide hazard assessment for largest plausible earthquake scenario) and probabilistically (assessment of slope failure in a given time period) using the capacity-demand method. Deterministic modeling aids in emergency planning and warning systems, and probabilistic scenarios help with land development.The capacity-demand equation Romeo et al. (2007) used is as follows:

Where Dc is the critical displacement ( >10cm)

Y is intensity, or strength of ground motion measured using Arias intensity

P is the exceeded at a mean annual rate

Figure 2. Taken directly from Romeo et al. (2007). Depicts Newmark sliding block analysis incorporation with capacity-demand equations. Earthquake intensity (Y in Equation 2) is calculated as Arias intensity in the sliding block model. Coseismic displacement is calculated, displacements greater than 10cm are critical.

2.c.II Methodologies: The following procedures follow protocol of Romeo et al., 2007.

In order to perform landslide hazard assessment, landslide inventory maps, geotechnical properties of existing landslides, a digital terrain model (DTM), and groundwater levels were incorporated into the model. After incorporation of these inputs, limit-equilibrium slope stability analysis was used to compute the static factor of safety.

Using Newmark’s sliding block model, seismic slope performance was evaluated by computing the threshold critical acceleration necessary for slope failure. Then, probabilistic and deterministic seismic hazard analyses were performed, characterizing slope performance in multiple shaking scenarios. This analysis demonstrated the functionality of Newmark methodology in predicting landslide displacement given a specified shaking event.

Romeo et al. (2007) tested the capacity-demand model in southern California using the 1994 M6.7 Northridge earthquake as a case study. The data for the Northridge earthquake is comprised of a comprehensive landslide inventory, records of ground motion, detailed geologic maps, geotechnical properties of lithologic units, and slopes derived from a DEM. Data analysis in the capacity-demand model of Newmark displacement predicts the spatial distribution of coseismic landslides.  The model of failure determined by Romeo et al. (2007) is as follows:

3)             P(f)=0.335[1-exp(-0.048Dn1.565)]

Where P(f) is the proportion of landslide cells

Dn is the Newmark displacement (>10 cm)

2.c.III Analysis

The results show, based on slope performance, that the equation is not valid on a global scale, rather it is only valid in Northridge, California where it was calibrated. The capacity-demand model needs to be expanded by means of further variable incorporation for proper assessment of earthquake induced landslide hazard, both probabilistically and deterministically, in order to aid in emergency planning and warning system development.