SCEC Award Number 11206 View PDF
Proposal Category Individual Proposal (Integration and Theory)
Proposal Title 3-D Modeling of the Rocking of Precariously Balanced Rocks
Investigator(s)
Name Organization
Swaminathan Krishnan California Institute of Technology
Other Participants Graduate Student: Swetha Veeraraghavan
SCEC Priorities B2, B4, B6 SCEC Groups GMP, SHRA
Report Due Date 02/29/2012 Date Report Submitted N/A
Project Abstract
 There are several precariously balanced rocks (PBRs) in western US located on hill-sides and cliffs.
Analyzing the toppling behavior of these rocks can provide limits on the largest ground motions (of the type that the rocks are sensitive to) that could have occurred at the rock sites in the time that they have been precarious. Such analyses can not only provide important data to constrain ground motion simulations, but also help characterize seismic hazard in a region. Brune and his colleagues
have identified and cataloged thousands of these rocks. They have also conducted dynamic analyses of several rocks to develop overturning fragilities, but with
simplistic idealizations and assumptions such as a rectangular shape for the rocks, two-point rocking, sliding does not occur, etc. Recently, Hudnut et al.
have used terrestrial laser scanning (TLS) techniques to image these rocks in three dimensions taking special care to capture the rock-pedestal interface.

We conducted some preliminary theoretical analysis of the Echo Cliff PBR by idealising the shape of the rock to resemble a rectangle with a curved base. The shape of the toppling regime of the rock-like block (as can be seen from the PGV vs T graphs) matches well with the results obtained by Brune for rocks of dimensions similar to that of the Echo Cliff PBR. We modified the curvature of the rock to analyze the effect of change in basal shape. Our results indicate that the toppling regime of the rock is highly sensitive to the basal geometry. Therefore, it is imperative to model
the rock-pedestal interface accurately and a simplistic two point contact model will not be accurate. We then created a 3D Finite Element Mesh of the rock using Matlab and tried to analyze the full 3-D rocking response using LS-DYNA3D. We modeled the rock and pedestal separately and connected them using a contact interface. Since the contact interface in LS-DYNA is based on penalty stiffness method, we
had to calibrate the contact parameters like contact stiffness, contact damping etc to arrive at the correct response even for the
simple case of Housner's block. Calibrating the contact parameters for each rock is not feasible. Therefore, we are now developing an alternate methodology using rigid body mechanics for rocking body analysis to overcome the difficulties associated with the finite-element implementation. The rigid body mechanics algorithm
works on the simple principles of force and moment balance using the fact that a rigid body can only translate and rotate and cannot deform. We are currently coding the rigid body algorithm. We will validate the numerical methodology by comparing its results with the Housner's block results as well as results obtained from the idealized rock with curved base. We would then analyze the Echo Cliff PBR under
a suite of idealized motions using the newly developed methodology. Then we would proceed to analyse the rocking response of several precariously balanced rocks in southern California to help characterize seismic hazard in the region as well as lend a measure of credibility to the rupture-to-rafters simulations.
Intellectual Merit Two of SCEC's key research objectives are to improve ground motion simulation methodologies and to characterize seismic hazard to southern California. Analyzing precariously balanced rocks can give us physical constraints on historical ground motions that may have occurred in the region and at the same time provide us with important information for Uniform California Earthquake Rupture Forecasting. The 3-D PBR analyses with precise modeling of the rock-pedestal contact interface that we are conducting represents a significant advancement to the state-of-the-art which comprises of 2-D modeling of idealized shapes rocking under a 2-point contact.
Broader Impacts The graduate student researcher, Swetha Veeraraghavan, is a brilliant woman who has independently developed the rigid body analysis technique that we expect will enable us to finally analyze Brune's PBR catalog in a deeply quantitative way. Swetha has benefited tremendously from SCEC funding and has grown leaps and bounds intellectually. I fully expect her to make tremendous contributions to dynamics and its applications to several fields in her career. The continuing funding from SCEC is enabling her to evolve into an excellent scientist, engineer, and researcher.
Exemplary Figure Figure 2.2