From c86ce5b5b2f2e06b39d0ea099df06c4b606b9865 Mon Sep 17 00:00:00 2001 From: Pedro Arduino Date: Mon, 27 May 2024 18:34:30 -0700 Subject: [PATCH] adding updated case2 and case 4 --- source/case_2.rst | 11 +++++++++-- source/case_4.rst | 10 ++++++++-- 2 files changed, 17 insertions(+), 4 deletions(-) diff --git a/source/case_2.rst b/source/case_2.rst index 617107a..3a5bf0e 100644 --- a/source/case_2.rst +++ b/source/case_2.rst @@ -9,13 +9,20 @@ Author: Erick Martinez Introduction ------------ -This page describes basic concepts of one-dimensional ground response analysis and the usage of transfer functions. For more details, the user is encounged to read :cite:`Kramer1996`. +This page describes the basic concept of transfer functions and their use in a site response analysis. Along with this, the uncertainty in this process will be explained. For more details, the user is encouraged to read :cite:`Kramer1996`. Problem Description ------------------- -A transfer function is somewhat like a filter that is applied to an incoming wave to produce an output signal. It determines how each frequency in the input motion is amplified or suppressed, by the medium of wave travel. Considering a spring-mass system with an excitation motion at input from the foundation connected to the spring and the corresponding response motion of the connected mass in the inertial system. The response motion of the mass will be a composite factor of the elastic and the viscous damping forces which are inherently embedded in the transfer function that determines the output motion we will obtain. In our wave propagation study we also employ transfer functions as a tool to explain the factors that make our input wave motion different from our output wave obtained. Evaluating the transfer function mathematically involves converting our known input motion to a Fourier series. Each term of the Fourier series is multiplied by the transfer function to obtain the Fourier series of the output response. Resonance is a physical phenomenon that occurs when the natural frequency of vibration of particles in a body (in our case the layers) matches the frequency of the forcing function (our input motion). It is experienced as an infinite amplification of the model. +A transfer function acts as a filter that can amplify or de-amplify an incoming wave from a medium to produce the output signal in another medium. To simplify the idea of a transfer function, a spring-mass system can be used. As a motion is applied on the mass connected to the spring, a responsive outgoing wave will be propagated through the mass and the spring. This outgoing motion will be a composite factor of the stiffness and elastic damping forces found within the spring-mass system. In earth systems, this relationship between incoming and outgoing wave can be evaluated through mathematically converting an input motion, typically an acceleration-time history, to a Fourier series. In the Fourier space, the motion is then multiplied by the transfer function, resulting in the outgoing Fourier motion. This can then be converted back into various plots, such as acceleration-time history and spectral acceleration vs. period, that allow for analysis of the outgoing motion. An analysis of this ground motion can provide frequencies of interest where ground accelerations would be highest/lowest, which can aid in site response analysis and planning. + + + + +For our purposes, an earthquake motion will be applied to a rock, located at the bottom of a one-dimensional soil profile. In this example, we will analyze the amplification/deamplification effects of the ground motion caused by its propagation through the soil layer. The 10 meter soil layer has a shear wave velocity (Vs) of 500 m/s and a damping ratio of 3%. Because of the presence of uncertainty in the soil properties, the transfer function will include uncertainty in its effects. This uncertainty will be quantified through multiple runs in EE-UQ and expressed as ratios of mean velocity and acceleration, along with standard deviation and skewness. + + Solution Strategy diff --git a/source/case_4.rst b/source/case_4.rst index 4000076..c6bb240 100644 --- a/source/case_4.rst +++ b/source/case_4.rst @@ -4,18 +4,24 @@ S3hark - Site Response 2 ======================= Author: Chungen Tai +(Updated : 05/24/24) ------------------- Introduction ------------ -This page describes basic concepts of one-dimensional ground response analysis and the usage of transfer functions. For more details, the user is encounged to read :cite:`Kramer1996`. +This page shows basic concepts of one-dimensional nonlinear site response analysis by using various soil material models (ex: ElasticIsotropic, PM4Sand.).Site response analysis is commonly performed to analyze the propagation of seismic waves through soil. As shown in the below figure, one-dimensional response analyses, as a simplified method, assume that all boundaries are horizontal and that the response of a soil deposit is predominately caused by SH-waves propagating vertically from the underlying bedrock. Ground surface response is usually the major output from these analyses, together with profile plots such as peak horizontal acceleration along the soil profile. When liquefiable soils are presenting, maximum shear strain and excess pore pressure ratio plots are also important. +.. figure:: ./images/siteResponse2.png + :scale: 60 % + :align: center + :figclass: align-center Problem Description ------------------- -A transfer function is somewhat like a filter that is applied to an incoming wave to produce an output signal. It determines how each frequency in the input motion is amplified or suppressed, by the medium of wave travel. Considering a spring-mass system with an excitation motion at input from the foundation connected to the spring and the corresponding response motion of the connected mass in the inertial system. The response motion of the mass will be a composite factor of the elastic and the viscous damping forces which are inherently embedded in the transfer function that determines the output motion we will obtain. In our wave propagation study we also employ transfer functions as a tool to explain the factors that make our input wave motion different from our output wave obtained. Evaluating the transfer function mathematically involves converting our known input motion to a Fourier series. Each term of the Fourier series is multiplied by the transfer function to obtain the Fourier series of the output response. Resonance is a physical phenomenon that occurs when the natural frequency of vibration of particles in a body (in our case the layers) matches the frequency of the forcing function (our input motion). It is experienced as an infinite amplification of the model. +Treasure Island, situated atop sand fill strata overlaying Bay Mud within the San Francisco Bay, was subjected to seismic activity during the 1989 Loma Prieta Earthquake. Adjacent to Treasure Island lies Yerba Buena Island, characterized by its natural rock outcrop. Utilizing the site's soil profile and seismic data recorded on Yerba Buena Island, we endeavor to analyze the site response of Treasure Island. This entails computing parameters such as peak horizontal acceleration and shear strain distribution along the soil profile. Furthermore, we aim to investigate the influence of varying slope configurations on the site's response characteristics. + Solution Strategy