Lateral structure-foundation interaction of structures with base masses

1972 ◽  
Vol 62 (2) ◽  
pp. 453-470
Author(s):  
R. J. Scavuzzo ◽  
D. D. Raftopoulos ◽  
J. L. Bailey
Keyword(s):  
Integral Equation ◽  
Free Field ◽  
Response Spectra ◽  
Elastic Half Space ◽  
Two Dimensional ◽  
Transient Solution ◽  
Volterra Type ◽  
Seismic Motion ◽  
Lateral Structure ◽  
Inertia Forces

abstract The interaction of lateral inertia forces of an N-mass structure with a base mass and lateral seismic motion of the foundation is formulated as an integral equation of the Volterra type. Flexibility of the foundation is based on the transient solution of a two-dimensional elastic half-space. Interaction effects are evaluated by comparing the response spectra of the free-field motion to that of the foundation motion. Results show that changes in the response spectra are significant for heavy, stiff structures such as a reactor-containment vessel.

Can We Trust High-Frequency Content in Strong-Motion Database Signals? Impact of Housing, Coupling, and Installation Depth of Seismic Sensors

2020 ◽  
Vol 91 (4) ◽  
pp. 2192-2205 ◽  
Author(s):  
Fabrice Hollender ◽  
Zafeiria Roumelioti ◽  
Emeline Maufroy ◽  
Paola Traversa ◽  
Armand Mariscal
Keyword(s):  
Ground Motion ◽  
High Frequency ◽  
Free Field ◽  
Strong Motion ◽  
Response Spectra ◽  
High Frequencies ◽  
Field Recording ◽  
Seismic Motion ◽  
Free Data ◽  
Installation Depth

Abstract Seismic hazard studies provide indicators of seismic motion that are expressed for “free-field,” that is, representative of the ground motion exactly at the free surface, without disturbances due to interactions between soil and buildings or other structures. Most of these studies are based on ground-motion prediction equations, which are, themselves, formulated to predict free-field motion, as they are derived from similarly free data. However, is this really the case? In this study, we use several examples to illustrate how small structures hosting permanent strong-motion stations (often anchored on small concrete slabs) generate soil–structure interaction effects that can amplify the high-frequency part of the earthquake signal (>10  Hz) by up to a factor of 2–3 for stations on soils. We also show that the installation depth of a station, even if very shallow (i.e., a few meters), can change the recorded response, mainly by deamplifying the signal in high frequencies (>10  Hz) by a factor up to 0.3. Such effects imply that there are actual differences between recorded and true free-field signals. Depending on the housing conditions, these effects can have significant impact on response spectra at high frequencies, and on measurements of the κ parameter. It is, thus, becoming clear that such effects should be taken into account in studies involving high-frequency seismic motion. To do so, scientists need a detailed description of the conditions of installation and housing of seismological and accelerometric stations, which often lacks from the metadata distributed through the various, commonly used web services. Increasing such information and facilitating the access to it would allow the identification of stations that are problematic and of those that are truly close to free-field recording conditions. In a subsequent step, it would be important to quantify the modification curve of the response of stations that experience such effects.

scholarly journals On local and integrated stress-tensor commutators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys
Keyword(s):  
Stress Tensor ◽  
Free Field ◽  
Virasoro Algebra ◽  
Light Sheet ◽  
Operator Product ◽  
Local Form ◽  
Two Dimensional ◽  
Conformal Embedding ◽  
General Aspects ◽  
The Right

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

scholarly journals Nonlinear two-dimensional free surface solutions of flow exiting a pipe and impacting a wedge

2021 ◽  
Vol 126 (1) ◽  
Author(s):  
Alex Doak ◽  
Jean-Marc Vanden-Broeck
Keyword(s):  
Surface Tension ◽  
Integral Equation ◽  
Free Surface ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Two Dimensional ◽  
Numerical Schemes ◽  
Additional Advantage ◽  
Infinite Wedge ◽  
Good Agreement

AbstractThis paper concerns the flow of fluid exiting a two-dimensional pipe and impacting an infinite wedge. Where the flow leaves the pipe there is a free surface between the fluid and a passive gas. The model is a generalisation of both plane bubbles and flow impacting a flat plate. In the absence of gravity and surface tension, an exact free streamline solution is derived. We also construct two numerical schemes to compute solutions with the inclusion of surface tension and gravity. The first method involves mapping the flow to the lower half-plane, where an integral equation concerning only boundary values is derived. This integral equation is solved numerically. The second method involves conformally mapping the flow domain onto a unit disc in the s-plane. The unknowns are then expressed as a power series in s. The series is truncated, and the coefficients are solved numerically. The boundary integral method has the additional advantage that it allows for solutions with waves in the far-field, as discussed later. Good agreement between the two numerical methods and the exact free streamline solution provides a check on the numerical schemes.

Concurrent Design Forces in Structures under Three-Component Orthotropic Seismic Excitation

2002 ◽  
Vol 18 (1) ◽  
pp. 1-17 ◽  
Author(s):  
K. Anastassiadis ◽  
I. E. Avramidis ◽  
P. Panetsos
Keyword(s):  
Ground Motion ◽  
Design Procedure ◽  
Strong Motion ◽  
Response Spectra ◽  
Concurrent Design ◽  
Motion Model ◽  
Specific Point ◽  
Extreme Stress ◽  
Seismic Motion

According to the model of Penzien and Watabe, the three translational ground motion components on a specific point of the ground are statistically noncorrelated along a well-defined orthogonal system of axes p, w, and v, whose orientation remains reasonably stable over time during the strong motion phase of an earthquake. This orthotropic ground motion is described by three generally independent response spectra Sa, Sb, and Sc, respectively. The paper presents an antiseismic design procedure for structures according to the above seismic motion model. This design includes a) determination of the critical orientation of the seismic input, i.e., the orientation that gives the largest response, b) calculation of the maximum and the minimum values of any response quantity, and c) application of either the Extreme Stress Method or the Extreme Force Method for determining the most unfavorable combinations of several stress resultants (or sectional forces) acting concurrently at a specified section of a structural member.

EXISTENCE OF SOLUTION FOR A VOLTERRA TYPE INTEGRAL EQUATION USING DARBO-TYPE F-CONTRACTION

2021 ◽  
Vol 10 (6) ◽  
pp. 2687-2710
Author(s):  
F. Akutsah ◽  
A. A. Mebawondu ◽  
O. K. Narain
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Existence Of Solution ◽  
Volterra Type ◽  
Complete Metric Spaces ◽  
Type Integral ◽  
New Type

In this paper, we provide some generalizations of the Darbo's fixed point theorem and further develop the notion of $F$-contraction introduced by Wardowski in (\cite{wad}, D. Wardowski, \emph{Fixed points of a new type of contractive mappings in complete metric spaces,} Fixed Point Theory and Appl., 94, (2012)). To achieve this, we introduce the notion of Darbo-type $F$-contraction, cyclic $(\alpha,\beta)$-admissible operator and we also establish some fixed point and common fixed point results for this class of mappings in the framework of Banach spaces. In addition, we apply our fixed point results to establish the existence of solution to a Volterra type integral equation.

Sensitivity analysis of geotechnical site conditions effect on the seismic response of a saturated inhomogeneous poroviscoelastic soil profile

2018 ◽  
Vol 15 (6) ◽  
pp. 661-677 ◽  
Author(s):  
Toufiq Ouzandja ◽  
Mohamed Hadid
Keyword(s):  
Soil Properties ◽  
Seismic Response ◽  
Pore Water ◽  
Soil Profile ◽  
Water Saturation ◽  
Free Field ◽  
Response Spectra ◽  
Response Analysis ◽  
Content Type ◽  
Linear And Nonlinear

Purpose This paper aims to present the investigation of the linear and nonlinear seismic site response of a saturated inhomogeneous poroviscoelastic soil profile for different soil properties, such as pore-water saturation, non-cohesive fines content FC, permeability k, porosity n and coefficient of uniformity Cu. Design/methodology/approach The inhomogeneous soil profile is idealized as a multi-layered saturated poroviscoelastic medium and is characterized by the Biot’s theory, with a shear modulus varying continuously with depth according to the Wichtmann’s model. Seismic response analysis has been evaluated through a computational model, which is based on the exact stiffness matrix method formulated in the frequency domain assuming that the incoming seismic waves consist of inclined P-SV waves. Findings Unlike the horizontal seismic response, the results indicate that the vertical one is strongly affected by the pore water saturation. Moreover, in the case of fully saturated soil profile, the same vertical response spectra are found for the two cases of soil behavior, linear and nonlinear. Originality/value This research is a detailed study of the geotechnical soil properties effect on the bi-directional seismic response of saturated inhomogeneous poroviscoelastic soil profile, which has not been treated before; the results are presented in terms of the peak acceleration ratio, as well as the free-field response spectra and the spectral ratio (V/H).

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