Reply to Comment by J. Zhang and N. Makris on “Estimates of the Ground Accelerations at Point Reyes Station during the 1906 San Francisco Earthquake” by A. Anooshehpoor, T. H. Heaton, B. Shi, and J. N. Brune

Contrary to the comments by Zhang and Makris (hereafter, ZM), our equations of motion governing the rocking response of a rectangular block subjected to a full-sine acceleration pulse are correct. Therefore, the first part of ZM's discussion, which is based primarily upon the assumption that the equations of motion in our article were incorrect, is inappropriate. In the second part of the discussion, ZM present new results for mode 2, toppling without impact. We did not consider this mode because it was not relevant to the Point Reyes train, which by eyewitness accounts, had overturned after experiencing one impact. However, as explained in this reply, toppling with no impact is never the minimum condition for overturning, and would in general involve very large horizontal accelerations, especially at frequencies where mode 2 is the only overturning mode

Precarious Rock Methodology for Seismic Hazard: Physical Testing, Numerical Modeling, and Coherence Studies

The precarious rock methodology used for seismic hazard assessment includes location, age dating, field measurements of the quasi-static toppling acceleration of balanced rocks, and study of their dynamic response to realistic strong motion seismograms using numerical modeling. The work scope is contained in the task description issued by the DOE to the Seismology Laboratory of the University of Nevada, Reno and is itemized in section 2.3 below. In addition, measurement of the coherence of seismic energy at high frequencies, critical to the understanding of the variability of high frequency ground motions at the repository level, will be estimated based on data collected in limited scope portable instrument deployments. Existing high-frequency geophones that remain in place from earlier geophysical experiments will be used

Estimates of the ground accelerations at Point Reyes Station during the 1906 San Francisco earthquake

We have developed an analytical solution for the rocking and overturning response of a two-dimensional, symmetric rigid block subject to a full sine wave of horizontal ground acceleration. We use this solution to provide lower-bound estimates of the peak ground acceleration at Point Reyes Station, California, during the 1906 San Francisco earthquake that toppled the San Francisco-bound train. Our results, for a 3% damping ratio, indicate that for a single cycle of a sine wave the minimum toppling accelerations at 1, 1.5, and 2 Hz are 0.35g, 0.5g, and 1.05g, respectively. For more realistic accelerograms the toppling accelerations are about 1.1g (complex synthetic) and 0.76g (Lucerne record of the 1992 Landers earthquake)

Rocking and kinematic approaches for rigid block analysis of masonry walls: state of the art and recent developments

The assessment of the rocking and overturning response of rigid blocks to earthquakes is a complex task, due to its high sensitivity to the input motion, variations in geometry and dissipation issues. This paper presents a literature review dealing with classical and advanced approaches on rocking motion with particular reference to masonry walls characterized by a monolithic behavior. Firstly, the pioneering work of Housner based on the concept of the inverted pendulum is discussed in terms of the most significant parameters, i.e., the size and slenderness of the blocks, the coefficient of restitution and ground motion properties. Free and restrained rocking blocks are considered. Then, static force-based approaches and performance-based techniques, mostly based on limit analysis theory, are presented to highlight the importance of investigating the evolution of the rocking mechanisms by means of pushover curves characterized by negative stiffness. From a dynamic perspective, a review of probabilistic approaches is also presented, evaluating the cumulative probability of exceedance of any response level by considering different earthquake time histories. Some recent simplified approaches based on the critical rocking response and the worst-case scenario are illustrated, as well.The authors acknowledge the sponsorship of the Italian Civil Protection, through the RELUIS Project-Line: Masonry Structures (2017).info:eu-repo/semantics/publishedVersio

Self healing slip pulses along a gel/glass interface

We present an experimental evidence of self-healing shear cracks at a gel/glass interface. This system exhibits two dynamical regimes depending on the driving velocity : steady sliding at high velocity (> Vc = 100-125 \mu m/s), caracterized by a shear-thinning rheology, and periodic stick-slip dynamics at low velocity. In this last regime, slip occurs by propagation of pulses that restick via a ``healing instability'' occuring when the local sliding velocity reaches the macroscopic transition velocity Vc. At driving velocities close below Vc, the system exhibits complex spatio-temporal behavior.Comment: 4 pages, 6 figure

Southern Great Basin Seismic Network Operations

QAP-3.0 (Scientific Investigation Control) of the University and Community College System of Nevada (UCCSN) Quality Assurance (QA) program requires that, prior to initiating work, a Scientific Investigation Plan (SIP) must be prepared and approved. This SIP is intended to cover the seismic monitoring task performed by the Nevada Seismological Laboratory (NSL). The purpose of this SIP is to describe the high-level planning for the overall task such that it can be referred to by individual scientific notebooks. Due to the continuation nature of this task, this SIP contains language that may be considered generic so that new subtasks can be initiated within an established framework without revision of this SIP. The work described in this SIP, except as noted, is subject to UCCSN QA program requirements

Studies on "precarious rocks" in the epicentral area of the AD 1356 Basle earthquake, Switzerland

For the first time precarious rocks have been analysed in the epicentral area of the AD 1356 Basle earthquake in northern Switzerland. Several cliff sites in flat-lying, thickly bedded Upper Jurassic coral limestones in the Jura Mountains were investigated. Seven blocks are regarded as precarious with respect to earthquake strong ground motions. The age of these precarious rocks could not be determined directly as for instance by radiometric dating methods; however, based on slope degradation processes it can be concluded that the formation of these blocks predates the AD 1356 Basle earthquake. The acceleration required to topple a precarious rock from its pedestal is estimated using geometrical data for individual block sections and earthquake strong-motion records from stations on rock sites in the European Strong-Motion Database as input data for the computer program ROCKING V1.0 from the Seismological Laboratory, University of Nevada, Reno. The calculations indicate that toppling of a precarious rock largely depends on earthquake strength but also on the frequency spectrum of the signal. Although most investigated precarious rocks are surprisingly stable for ground motions similar to those expected to have occurred during the AD 1356 Basle earthquake, at least two blocks are clearly precariously balanced, with peak toppling accelerations lower than 0.3 g. Possible reasons why these blocks did not topple during the AD 1356 Basle earthquake include incomplete separation from their base, sliding of precarious rocks, their size, lower than assumed ground accelerations and/or duration of shaking

Precarious rock methodology for seismic hazard: Physical testing, numerical modeling and coherence studies

This report covers the following projects: Shake table tests of precarious rock methodology, field tests of precarious rocks at Yucca Mountain and comparison of the results with PSHA predictions, study of the coherence of the wave field in the ESF, and a limited survey of precarious rocks south of the proposed repository footprint. A series of shake table experiments have been carried out at the University of Nevada, Reno Large Scale Structures Laboratory. The bulk of the experiments involved scaling acceleration time histories (uniaxial forcing) from 0.1g to the point where the objects on the shake table overturned a specified number of times. The results of these experiments have been compared with numerical overturning predictions. Numerical predictions for toppling of large objects with simple contact conditions (e.g., I-beams with sharp basal edges) agree well with shake-table results. The numerical model slightly underpredicts the overturning of small rectangular blocks. It overpredicts the overturning PGA for asymmetric granite boulders with complex basal contact conditions. In general the results confirm the approximate predictions of previous studies. Field testing of several rocks at Yucca Mountain has approximately confirmed the preliminary results from previous studies, suggesting that the PSHA predictions are too high, possibly because the uncertainty in the mean of the attenuation relations. Study of the coherence of wavefields in the ESF has provided results which will be very important in design of the canisters distribution, in particular a preliminary estimate of the wavelengths at which the wavefields become incoherent. No evidence was found for extreme focusing by lens-like inhomogeneities. A limited survey for precarious rocks confirmed that they extend south of the repository, and one of these has been field tested

On slip pulses at a sheared frictional viscoelastic/ non deformable interface

We study the possibility for a semi-infinite block of linear viscoelastic material, in homogeneous frictional contact with a non-deformable one, to slide under shear via a periodic set of ``self-healing pulses'', i.e. a set of drifting slip regions separated by stick ones. We show that, contrary to existing experimental indications, such a mode of frictional sliding is impossible for an interface obeying a simple local Coulomb law of solid friction. We then discuss possible physical improvements of the friction model which might open the possibility of such dynamics, among which slip weakening of the friction coefficient, and stress the interest of developing systematic experimental investigations of this question.Comment: 23 pages, 3 figures. submitted to PR

Earthquakes: from chemical alteration to mechanical rupture

In the standard rebound theory of earthquakes, elastic deformation energy is progressively stored in the crust until a threshold is reached at which it is suddenly released in an earthquake. We review three important paradoxes, the strain paradox, the stress paradox and the heat flow paradox, that are difficult to account for in this picture, either individually or when taken together. Resolutions of these paradoxes usually call for additional assumptions on the nature of the rupture process (such as novel modes of deformations and ruptures) prior to and/or during an earthquake, on the nature of the fault and on the effect of trapped fluids within the crust at seismogenic depths. We review the evidence for the essential importance of water and its interaction with the modes of deformations. Water is usually seen to have mainly the mechanical effect of decreasing the normal lithostatic stress in the fault core on one hand and to weaken rock materials via hydrolytic weakening and stress corrosion on the other hand. We also review the evidences that water plays a major role in the alteration of minerals subjected to finite strains into other structures in out-of-equilibrium conditions. This suggests novel exciting routes to understand what is an earthquake, that requires to develop a truly multidisciplinary approach involving mineral chemistry, geology, rupture mechanics and statistical physics.Comment: 44 pages, 1 figures, submitted to Physics Report