scholarly journals On the fundamental resonant mode of inhomogeneous soil deposits

2019 ◽  
Author(s):  
Joaquin Garcia-Suarez ◽  
Domniki Asimaki
Keyword(s):  
Fundamental Frequency ◽  
Numerical Solutions ◽  
Ground Deformation ◽  
Site Response ◽  
Seismic Hazard Assessment ◽  
Resonant Mode ◽  
Single Degree Of Freedom ◽  
Shallow Layer ◽  
Soil Deposits ◽  
Definition Of

The problem of estimating seismic ground deformation is central to state-of-practice procedures of designing and maintaining infrastructure in earthquake-prone areas. Particularly, the problem of estimating the displacement field in a soft shallow layer overlying rigid bedrock induced by simple SH wave excitation has been favored by engineers due to its simplicity combined with inherent relevance for practical scenarios. We here derive analytical, accurate estimates for both the fundamental frequency and the amplitude of the first resonant mode of such systems by applying an intuitive argument based on resonance of single-degree-of-freedom systems. Our estimates do not presuppose a continuous velocity distribution, and can be used for fast assessment of site response in seismic hazard assessment and engineering design. On the basis of the said estimates of fundamental frequency and amplitude, we next propose a novel definition of ``equivalent homogeneous shear modulus’’ of the inhomogeneous deposit; and we show that the response of the fundamental mode of these systems is governed by the mechanical properties of the layers closer to the bedrock. We finally discuss the validity of our argument, and evaluate the accuracy of our results by comparison with analytical and numerical solutions.

scholarly journals Energy Minimization Scheme for Split Potential Systems Using Exponential Variational Integrators

2021 ◽  
Vol 2 (3) ◽  
pp. 431-441
Author(s):  
Odysseas Kosmas
Keyword(s):  
Numerical Solutions ◽  
Oscillatory Behavior ◽  
Lagrangian Function ◽  
Computational Time ◽  
Variational Integrators ◽  
Weighted Sum ◽  
Lagrange Equations ◽  
Exponential Functions ◽  
Intermediate Time ◽  
Definition Of

In previous works we developed a methodology of deriving variational integrators to provide numerical solutions of systems having oscillatory behavior. These schemes use exponential functions to approximate the intermediate configurations and velocities, which are then placed into the discrete Lagrangian function characterizing the physical system. We afterwards proved that, higher order schemes can be obtained through the corresponding discrete Euler–Lagrange equations and the definition of a weighted sum of “continuous intermediate Lagrangians” each of them evaluated at an intermediate time node. In the present article, we extend these methods so as to include Lagrangians of split potential systems, namely, to address cases when the potential function can be decomposed into several components. Rather than using many intermediate points for the complete Lagrangian, in this work we introduce different numbers of intermediate points, resulting within the context of various reliable quadrature rules, for the various potentials. Finally, we assess the accuracy, convergence and computational time of the proposed technique by testing and comparing them with well known standards.

Simplified Criteria to Select Ground Response Analysis Methods for Seismic Building Design: Equivalent Linear versus Nonlinear Approaches

2021 ◽  
Author(s):  
Mauro Aimar ◽  
Sebastiano Foti
Keyword(s):  
Seismic Waves ◽  
Site Response ◽  
Building Design ◽  
Soil Conditions ◽  
Response Analysis ◽  
Depth Range ◽  
Ground Response Analysis ◽  
Equivalent Linear ◽  
Acceleration Time Histories ◽  
Soil Deposits

ABSTRACT The possible amplification of seismic waves in soil deposits is crucial for the seismic design of buildings and geotechnical systems. The most common approaches for the numerical simulation of seismic site response are the equivalent linear (EQL) and the nonlinear (NL). Even though their advantages and limitations have been investigated in several studies, the relative field of applicability is still under debate. This study tested both methods over a wide population of soil models, which were subjected to a set of acceleration time histories recorded from strong earthquakes. A thorough comparison of the results of the EQL and the NL approaches was carried out, to identify the conditions in which the relative differences are significant. This assessment allowed for the definition of simplified criteria to predict when the two schemes are or are not compatible for large expected shaking levels. The proposed criteria are based on simple and intuitive parameters describing the soil deposit and the ground-motion parameters, which can be predicted straightforwardly. Therefore, this study provides a scheme for the choice between the EQL and the NL approaches that can be used even at the preliminary design stages. It appears that the EQL approach provides reliable amplification estimates in soil deposits with thickness up to 30 m, except for very deformable soils, but this depth range may be extended at long vibration periods. This result reveals a good level of reliability of the EQL approach for various soil conditions encountered in common applications, even for high-intensity shaking.

scholarly journals A hybrid model for mapping simplified seismic response via a GIS-metamodel approach

2014 ◽  
Vol 14 (7) ◽  
pp. 1703-1718 ◽  
Author(s):  
G. Grelle ◽  
L. Bonito ◽  
P. Revellino ◽  
L. Guerriero ◽  
F. M. Guadagno
Keyword(s):  
Seismic Hazard ◽  
Seismic Response ◽  
Hybrid Model ◽  
Computational Models ◽  
Site Response ◽  
Seismic Hazard Assessment ◽  
Physical Parameters ◽  
Seismic Zone ◽  
Acceleration Response ◽  
Good Correspondence

Abstract. In earthquake-prone areas, site seismic response due to lithostratigraphic sequence plays a key role in seismic hazard assessment. A hybrid model, consisting of GIS and metamodel (model of model) procedures, was introduced aimed at estimating the 1-D spatial seismic site response in accordance with spatial variability of sediment parameters. Inputs and outputs are provided and processed by means of an appropriate GIS model, named GIS Cubic Model (GCM). This consists of a block-layered parametric structure aimed at resolving a predicted metamodel by means of pixel to pixel vertical computing. The metamodel, opportunely calibrated, is able to emulate the classic shape of the spectral acceleration response in relation to the main physical parameters that characterize the spectrum itself. Therefore, via the GCM structure and the metamodel, the hybrid model provides maps of normalized acceleration response spectra. The hybrid model was applied and tested on the built-up area of the San Giorgio del Sannio village, located in a high-risk seismic zone of southern Italy. Efficiency tests showed a good correspondence between the spectral values resulting from the proposed approach and the 1-D physical computational models. Supported by lithology and geophysical data and corresponding accurate interpretation regarding modelling, the hybrid model can be an efficient tool in assessing urban planning seismic hazard/risk.

scholarly journals Seismogenic nodes as a viable alternative to seismogenic zones and observed seismicity for the definition of seismic hazard at regional scale

2019 ◽  
Vol 41 (4) ◽  
pp. 289-304 ◽  
Author(s):  
Paolo Rugarli ◽  
Franco Vaccari ◽  
Giuliano Panza
Keyword(s):  
Seismic Hazard ◽  
Safety Factor ◽  
Seismic Moment ◽  
Regional Scale ◽  
Seismic Hazard Assessment ◽  
Hazard Maps ◽  
Earthquake Catalogues ◽  
Definition Of ◽  
Partial Factor ◽  
Seismogenic Nodes

A fixed increment of magnitude is equivalent to multiply the seismic moment by a factor γEM related to the partial factor γq acting on the seismic moment representing the fault. A comparison is made between the hazard maps obtained with the Neo-Deterministic Seismic Hazard Assessment (NDSHA), using two different approaches: one based on the events magnitude, listed in parametric earthquake catalogues compiled for the study areas, with sources located within the seismogenic zones; the other uses the seismogenic nodes identified by means of pattern recognition techniques applied to morphostructural zonation (MSZ), and increases the reference magnitude by a constant amount tuned by the safety factor γEM.Using γEM=2.0, in most of the territory the two approaches produce totally independent, comparable hazard maps, based on the quite long Italian catalogue. This represents a validation of the seismogenic nodes method and a tuning of the safety factor γEM at about 2.

Impact of a Mass on a Damped Elastically Supported Beam

1948 ◽  
Vol 15 (2) ◽  
pp. 125-136
Author(s):  
W. H. Hoppmann
Keyword(s):  
Differential Equation ◽  
Elastic Foundation ◽  
Forced Vibration ◽  
Numerical Solutions ◽  
Coefficient Of Restitution ◽  
Tabular Form ◽  
Single Degree Of Freedom ◽  
Simply Supported ◽  
Single Degree ◽  
Elastically Supported

Abstract In this paper a study is made of the problem of the central impact of a mass on a simply supported beam on an elastic foundation with considerations of internal and external damping. The differential equation for the forced vibration of the beam is developed. It is solved for the case in which the force is a function of time and is concentrated at the center of the beam. Formulas are obtained for the deflections. An expression is developed for the coefficient of restitution which is essential in determining the deflections and the strains. Criteria are devised for determining the cases in which the beam may be considered as a single-degree-of-freedom system when damping and an elastic foundation are considered. The importance of these criteria is discussed. A numerical example illustrating the theory developed in the paper is worked out in detail. Results of computations for several numerical solutions are given in tabular form.

scholarly journals On the fundamental resonant mode of inhomogeneous soil deposits

2020 ◽  
Vol 135 ◽  
pp. 106190 ◽  
Author(s):  
Joaquin Garcia-Suarez ◽  
Domniki Asimaki
Keyword(s):  
Resonant Mode ◽  
Soil Deposits

scholarly journals An updated and unified earthquake catalog from 1787 to 2018 for seismic hazard assessment studies in Mexico

2019 ◽  
Vol 6 (1) ◽  
Author(s):  
Rashad Sawires ◽  
Miguel A. Santoyo ◽  
José A. Peláez ◽  
Raúl Daniel Corona Fernández
Keyword(s):  
Seismic Hazard ◽  
Hazard Assessment ◽  
Seismic Hazard Assessment ◽  
Large Earthquake ◽  
Seismic Source ◽  
Earthquake Catalog ◽  
Magnitude Conversion ◽  
Seismic Source Models ◽  
Source Models ◽  
Definition Of

Abstract Here we present a new updated and unified Poissonian earthquake catalog for Mexico. The details about the catalog compilation, the removal of duplicate events, unifying the magnitude scales, removal of dependent events through the declustering process and its completeness analysis are presented. Earthquake and focal mechanism data have been compiled from various local, regional and international sources. Large earthquake events (MW ≥ 6.5) have been carefully revised for their epicentral locations and magnitudes from trusted publications. Different magnitude-conversion relationships, compatible with available local and regional ones, has been established to obtain unified moment magnitude estimates for the whole catalog. Completeness periods for the declustered catalog were estimated for the definition of appropriate seismic source models for the whole territory. The final unified Poissonian earthquake catalog spans from 1787 to 2018, covering a spatial extent of 13° to 33°N and 91° to 117°W. This catalog is compatible with other published catalogs providing basis for new analysis related to seismicity, seismotectonics and seismic hazard assessment in Mexico.

scholarly journals Integration of Site Effects into Probabilistic Seismic Hazard Assessment (PSHA): A Comparison between Two Fully Probabilistic Methods on the Euroseistest Site

Geosciences ◽  
2018 ◽  
Vol 8 (8) ◽  
pp. 285 ◽  
Author(s):  
Claudia Aristizábal ◽  
Pierre-Yves Bard ◽  
Céline Beauval ◽  
Juan Gómez
Keyword(s):  
Seismic Hazard ◽  
Site Effects ◽  
Site Response ◽  
Seismic Hazard Assessment ◽  
Probabilistic Seismic Hazard Assessment ◽  
Site Specific ◽  
Hazard Curve ◽  
Non Linear ◽  
Time Histories ◽  
Stochastic Time

The integration of site effects into Probabilistic Seismic Hazard Assessment (PSHA) is still an open issue within the seismic hazard community. Several approaches have been proposed varying from deterministic to fully probabilistic, through hybrid (probabilistic-deterministic) approaches. The present study compares the hazard curves that have been obtained for a thick, soft non-linear site with two different fully probabilistic, site-specific seismic hazard methods: (1) The analytical approximation of the full convolution method (AM) proposed by Bazzurro and Cornell 2004a,b and (2) what we call the Full Probabilistic Stochastic Method (SM). The AM computes the site-specific hazard curve on soil, HC(Sas(f)), by convolving for each oscillator frequency the bedrock hazard curve, HC(Sar(f)), with a simplified representation of the probability distribution of the amplification function, AF(f), at the considered site The SM hazard curve is built from stochastic time histories on soil or rock corresponding to a representative, long enough synthetic catalog of seismic events. This comparison is performed for the example case of the Euroseistest site near Thessaloniki (Greece). For this purpose, we generate a long synthetic earthquake catalog, we calculate synthetic time histories on rock with the stochastic point source approach, and then scale them using an adhoc frequency-dependent correction factor to fit the specific rock target hazard. We then propagate the rock stochastic time histories, from depth to surface using two different one-dimensional (1D) numerical site response analyses, while using an equivalent-linear (EL) and a non-linear (NL) code to account for code-to-code variability. Lastly, we compute the probability distribution of the non-linear site amplification function, AF(f), for both site response analyses, and derive the site-specific hazard curve with both AM and SM methods, to account for method-to-method variability. The code-to-code variability (EL and NL) is found to be significant, providing a much larger contribution to the uncertainty in hazard estimates, than the method-to-method variability: AM and SM results are found comparable whenever simultaneously applicable. However, the AM method is also shown to exhibit severe limitations in the case of strong non-linearity, leading to ground motion “saturation”, so that finally the SM method is to be preferred, despite its much higher computational price. Finally, we encourage the use of ground-motion simulations to integrate site effects into PSHA, since models with different levels of complexity can be included (e.g., point source, extended source, 1D, two-dimensional (2D), and three-dimensional (3D) site response analysis, kappa effect, hard rock …), and the corresponding variability of the site response can be quantified.

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