diff --git a/source/case_4.rst b/source/case_4.rst index 5107802..63c7c2e 100644 --- a/source/case_4.rst +++ b/source/case_4.rst @@ -1,148 +1,324 @@ .. _case_4: S\ :sup:`3` hark - Site Response 2 -================================== +=================================== Author: Chungen Tai -(Updated : 05/24/24) -------------------- + + Introduction ------------ -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. +This page shows basic concepts of one-dimensional nonlinear site response analysis by using various soil material models (ex: Elastic, PM4Sand.) and the lateral spreading. -.. figure:: ./images/siteResponse2.png - :scale: 60 % - :align: center - :figclass: align-center Problem Description ------------------- -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. +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/case4_siteResponse.png + :scale: 60 % + :align: center + :figclass: align-center + Figure 1. Site Response Analysis Solution Strategy ----------------- -#. Open the Dr. Layer program. By default we get twelve layers. The top six layers are hardwired into the system with a velocity of specified as very fast. The bottom six layers are hardwired with a velocity of very slow. +OpenSees +~~~~~~~~~~~~~~~~~ +OpenSees (Open System for Earthquake Engineering Simulation) is an open-source software framework used for simulating the response of structural and geotechnical systems to earthquakes and other loading conditions. It is widely used in research and practical applications for the analysis and design of structures subjected to dynamic loading. S3hark created a GUI to help user doing nonlinear site response analysis easily. + -#. Select all the layers to all have very slow values using the select all option. +Soil model +~~~~~~~~~~~~~~~~~ +PM4Sand Model +~~~~~~~~~~~~~~~~~ +PM4Sand is a constitutive model used in geotechnical engineering to simulate the behavior of sand under various loading conditions, including seismic events. Developed by Boulanger and Ziotopoulou, this model captures the complex behaviors of sand such as cyclic mobility, dilatancy, and liquefaction. It's particularly useful in finite element analysis for evaluating the performance of soil-structure systems during earthquakes. PM4Sand is known for its ability to represent the stress-strain behavior of sandy soils accurately, aiding in the design and analysis of foundations, slopes, and embankments in seismic regions. The model parameters are grouped into two categories: a primary set of six parameters (three properties, two flags, and atmospheric pressure) that are most important for model calibration, and a secondary set of parameters that may be modified from their default values in special circumstances. The three primary input properties are the sand’s apparent relative density :math:`D_R`, the shear modulus coefficient :math:`G_o`, and the contraction rate parameter :math:`h_po`. +Apparent relative density (:math:`D_R`) can be calculated by correlation to penetration resistance.Commonly estimated based on CPT or SPT penetration resistances, such as the following relationships used by Idriss and Boulanger (2008): -#. On the top left hand corner of the menu box choose the plot box tool and apply a plot box at the top of the layers. Do the same at four arbitrary points along the soil layers. Note the height (:math:`H`) you place the plots. +.. math:: + + D_R = \frac{(N_1)_{60}}{C_d} + +Where - +:math:`D_R` = Apparent Relative density (%) -#. Push the time increment button for about 1 minute. +:math:`C_d` = 46 (Idriss and Boulanger ,2008) -#. Obtain the angular frequency :math:`(2p/T)`, where :math:`T` is the period i.e. time it takes to complete one revolution. -#. Obtain the maximum displacements from the plots by clicking on the crest of the curves with your cursor. +Shear modulus coefficient is the primary variable controlling the small strain shear modulus, G_max. Should be chosen to match estimated or measured shear wave velocities. + +The shear modulus \( G_{max} \) can be described by the following equations: .. math:: - TF = \frac{1}{\cos(\frac{wH}{v_s})} + + G_{max} = \rho V_s^2 + +Usign following equation to calculate :math:`G_0` - AF = \frac{1}{|\cos(\frac{wH}{v_s})|} +.. math:: + G_{max} = G_0 p_a \left(\frac{p}{p_a}\right)^{0.5} -Where +Contraction rate parameter :math:`h_{po}` is one of primary variable that adjusts contraction rates and hence can be adjusted to obtain a target cyclic resistance ratio, as commonly estimated based on CPT or SPT penetration resistances and liquefaction correlations. -:math:`w` = Angular frequency (2pf) + -:math:`H` = distance between any two points in the layers under consideration. -:math:`V` = Velocity of wave travel within the soil layer. +Elasticisotropic Model +~~~~~~~~~~~~~~~~~~~~~~~ -:math:`TF` = Transfer function +In the context of geotechnical engineering and computational modeling, the "elastic model" refers to a mathematical representation of soil or rock behavior under loading conditions, where the material responds to stress with a proportional strain, following Hooke's Law. This model assumes that the material returns to its original shape once the load is removed, provided the stress is within the elastic limit.We can get the shear modulus from shear wave velocity, and then use the following equation convert to elastic modulus, -:math:`AF` = Amplification function +.. math:: + + E= (2G)(1+\nu) + + +Where +:math:`\nu` = Poisson’s ration (default is 0.3) -Dr. Layer's operation is controlled via menu commands (with associated keyboard accelerators), manipulation tools, scaling buttons, the load tool bar, and time control buttons. The program displays the results of its calculations visually in the form of animated displacements, and also in the form of dynamically generated time history plots. There are also mechanisms for getting numerical values. -.. figure:: ./images/case1.png - :scale: 30 % + +Lateral Spreading +~~~~~~~~~~~~~~~~~ + +Lateral spreading refers to the horizontal movement of soil, typically caused by liquefaction during an earthquake. When an earthquake occurs, seismic waves can cause loose, water-saturated, granular soils to temporarily lose their strength and behave like a liquid. This process is known as liquefaction. Once liquefaction occurs, the affected soil can flow or spread laterally, especially if there is a slope or free face (like a riverbank or retaining wall) nearby. Lateral spreading can cause significant ground displacement and can lead to damage of structures, utilities, and infrastructure. In this example, we will focus on the lateral movement cause by different slope angles. + +.. figure:: ./images/case4_lateralspreading.png + :scale: 60 % :align: center :figclass: align-center + + Figure 2. Lateral spreading + + SimCenter Tool Used ------------------- -blablabla +S\ :sup:`3` hark is the acronym of site-specific seismic hazard analysis and research kit. This tool focuses on simulating wave propagation along soil depth using finite element (FE) method. The intended audience for s3hark is researchers and practitioners interested in performing site-specific analysis of soil in response to earthquakes, and educators interested in teaching site response analysis in their classes. The tool provides a friendly interface for users to input and modify soil layers using tables, while the built soil profile and the FE mesh being visualized simultaneously. Results including acceleration, velocity, displacement, pore pressure, spectral acceleration, etc., are visualized for the soil profile and for each node as well, from which the user can comprehend the wave propagation and liquefaction status along the soil depth. -.. list-table:: Title - :widths: 25 25 50 - :header-rows: 1 +Features of S\ :sup:`3` hark include: + +#. 2D and 3D elements for dynamic analysis of fluid saturated porous media + +#. Advanced linear / nonlinear soil material models + +#. Total stress / effective stress analysis + +#. Bi-directional motions + +#. Flat / slope free field analysis + +#. Finite rigidity of the bedrock - * - Heading row 1, column 1 - - Heading row 1, column 2 - - Heading row 1, column 3 - * - Row 1, column 1 - - - - Row 1, column 3 - * - Row 2, column 1 - - Row 2, column 2 - - Row 2, column 3 +Click on the icon of S\ :sup:`3` hark to open the application. Figure 3 illustrates the main window. It is split into the following areas: -Time can be controlled using either the keyboard or the time control buttons: +.. figure:: ./images/case4_window.png + :scale: 20 % + :align: center + :figclass: align-center + + Figure 3. S\ :sup:`3` hark HARK Main Window + + + + + +#. Soil Column Graphic: The first graphic on the left of the panel shows a visualization of the soil column. + +#. FE Mesh Graphic: The second graphic on the left shows the finite element mesh and profile plots. Selecting any of the tabs on the right inside this graphic (i.e, PGA, γmax,maxDisp, maxRu, maxRuPWP) will show various results from the simulation at the mesh points. + +.. figure:: ./images/case4_plot.png + :scale: 50 % + :align: center + :figclass: align-center + + Figure 4. S\ :sup:`3` hark HARK FE Mesh Graphic + + +#. Operations Area: The right side of this area shows some information (e.g., total height and number of soil layers), includes the Ground Water Table (GWT) input field, and plus and minus buttons. If the user presses the plus button, a layer is added below the selected layer. If the minus button is pressed the selected layer is removed. The GWT input field allows the user to specify the level of the ground water table. + +#. Soil Layer Table: This table is where the user provides the characteristics of the soil layer, such as layer thickness, density, Vs30, material type, and element size in the finite element mesh. + +#. Tabbed Area: This area contains the three tabbed widgets described below. + + #. Configure Tab: This tab allows the user to specify the path to the OpenSees executable and to a ground motion file. -* To run time **forward**: Press and hold the 'g' key or click and hold the time forward button: . + #. Layer Properties Tab: This tab allows the user to enter additional material properties for the selected soil layer. -* To reset time to **zero**: Type the '0' key or click on the time reset button: . + #. Response Tab: Once the site response analysis has been performed, this tab provides information about element and nodal time varying response quantities. + +.. figure:: ./images/case4_response.png + :scale: 50 % + :align: center + :figclass: align-center + + Figure 5. S\ :sup:`3` hark HARK Response Tab + + +#. Analyze Button: This button shall be used to run the simulation locally. A progress bar will show the status of the analysis. This allows the user to review the ground motion predicted at the surface -* The current analysis time is **displayed** in the feedback pane at the bottom of the screen. -* The analysis time step size can be controlled via the Time Step menu (there are combinations of material properties and time steps that intentionally lead to unstable results, so beware). -* The display time step can be controlled via the Animation Speed menu. Internally, this command controls how many analysis time steps are computed between screen updates. Example Application ------------------- +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 peak horizontal displacement along the soil profile. Furthermore, we aim to investigate the influence of lateral spread in varying slopes on the site's response characteristics. +For lateral spreading, we change the slope :math:`\alpha` as 0, 2, 5 to see the influence of it. + -Dr. Layer's tool palette is illustrated below (Windows version: the Mac version is similar but grouped a bit differently): +Analysis Processes +~~~~~~~~~~~~~~~~~~~~~~~~ +There is the analysis process of site response analysis: - +#. Input the earthquake motions: Covent the earthquake motion record into '.json' file. Then, input the path into 'Configure Layer'. -* The **Arrow Tool** is used to select and manipulate objects. +#. Input ths soil parameters: This is the most important step in site response analysis. The soil parameters are obtained from theory or investigation reports. Then, type all of the soil parameters into the 'Soil Layer Table'. -* The **Panner** and **Camera Orbit Tools** are used to change the viewing point and camera orientation via clicking and dragging. +#. Click "analysis" bottom: Click the button to run the analysis. The program will notify you when it is finished. -* The **Plot Box Tool** is used to create one of the various types of plot boxes: +Earthquake motion +~~~~~~~~~~~~~~~~~ +The motion recorded at Yerba Buena Island from the Loma Prieta earthquake is used in this sample. Figure 6 shows the acceleration, velocity, and displacement of this motion. + +.. figure:: ./images/case4_YERBAISL2_Records.png + :scale: 50 % + :align: center + :figclass: align-center - * **Displacement Time History plots** are created by clicking on the relevant layer. The top node in the layer is used as the plotting target. + Figure 6. Input ground motion (acceleration, velocity, and displacement) - * **Fast Fourier Transform (FFT) plots** of a displacement history can be created by clicking on the time history plot. +Figure 7 illustrates the spetrum of this motion. - * **Stress-strain plots** can be created by control-clicking (i.e., holding down the control key while clicking) on the desired layer. +.. figure:: ./images/case4_YERBAISL2_RSpectra.png + :scale: 50 % + :align: center + :figclass: align-center + Figure 7. Input ground motion spetrum (acceleration, velocity, and displacement) - These controls are self-explanatory in regards to their functions. Note the following, however: -.. note:: - The scaling buttons will continue to scale as long as they are held down. It is not necessary to click multiple times to get this effect. +Soil condition +~~~~~~~~~~~~~~~~~ +The following table shows the soil parameters in this site. Using PM4Sand to stimulate sand , and using Elasticisotropic to model clay. -Remarks -------- -* To adjust the **plotting scales**, use the small expansion/contraction triangular buttons on the plot for the horizontal scale, and the plot scale buttons on the `Scale Button Toolbar <#scaling-buttons>`_ for the vertical scale. +.. list-table:: Table1. Soil Profile Parameters + :widths: 20 20 20 20 20 20 20 20 + :header-rows: 1 -.. note:: - You will notice that all plots scale together. This is so that plots of a given type can be compared visually without any misleading differences in scale factors. + * - Layers + - Thickness(m) + - :math:`V_s (m/s)` + - :math:`\rho (kg/m^3)` + - :math:`G_o(kPa)` + - :math:`E (kPa)` + - :math:`D_R` (%) + - Model + * - SAND1 + - 15 + - 175.3 + - 2.01 + - 0.69 + - -- + - 0.33 + - PM4Sand + * - CLAY1 + - 14 + - 198.8 + - 1.68 + - -- + - 172.8 + - -- + - Elasticisotropic + * - SAND2 + - 12 + - 300 + - 2.08 + - 1.33 + - -- + - 0.77 + - PM4Sand + * - CLAY2 + - 32 + - 280 + - 2.08 + - -- + - 423.8 + - -- + - Elasticisotropic + * - SAND3 + - 8 + - 380 + - 2.08 + - 1.46 + - -- + - 0.62 + - PM4Sand + * - CLAY3 + - 8 + - 300 + - 2.08 + - -- + - 486.6 + - -- + - Elasticisotropic + * - WRock + - 5 + - 600 + - 2.16 + - -- + - 2022.8 + - -- + - Elasticisotropic + * - Rockbed + - -- + - 1830 + - 2.24 + - -- + - 19526.7 + - -- + - Elasticisotropic + + +Result +~~~~~~~~~~~~~~~~~~ + +The following plots show maximun displacement in different slope angles. + + +Displacement +~~~~~~~~~~~~~~~~~ + +Figure 8 shows the result of maximun displacement, we can see that the displacement on the surface increases with increasing the slope. + + +.. figure:: ./images/case4_d.png + :scale: 50 % + :align: center + :figclass: align-center -* To adjust the **horizontal offset** of a plot, click in the plot and drag horizontally to scroll back and forth. + Figure 8. The maximum displacement in different slope -.. note:: - In general, plots will automatically scroll as necessary as time is running. Once you have manually scrolled a plot, though, the automatic scrolling will cease until time is reset to zero. -* Plot boxes can be added or removed at any time, but they only accumulate data beginning from the time they are installed, with the exception of FFT plots, which always plot the according to the data accumulated in the target time history. FFT plots can use up to the first 1024 points in a time history. +Figure 9 illustrates the relationships between slope and the displacement on the surface. -.. warning:: - Plotting FFT's will slow down the animation speed significantly, especially as the length of the time histories increase. +.. figure:: ./images/case4_dd.png + :scale: 60 % + :align: center + :figclass: align-center -.. bibliography:: references.bib + Figure 9. 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