2.4.5. Site Response Analysis¶
s3hark allows users to determine the event at the base of the building by performing an effective free-field site response analysis of a soil column. In this panel, the user specifies a ground motion at the bottom of the soil column. After the soil layers have been properly defined, the motion at the ground surface is given at the end of the analysis and that motion can be used in the simulation of the building response.
The full user graphic interface looks like what is shown in Fig. 2.4.5.1

Fig. 2.4.5.1 Full Graphic Interface¶
Clicking the arrow between the Soil Column Graphic and the FE Mesh Graphic will hide the FE Mesh Graphic, which makes the UI look like what is shown in Fig. 2.4.5.2.

Fig. 2.4.5.2 Collapse Graphic Interface¶
The UI of s3hark consists of the following components:
2.4.5.1. Soil Column Graphic¶
The first graphic on the left of the panel shows a visualization of the soil column created. Each layer has a different randomly generated color. When the user adds or deletes a soil layer, this graphic will refresh.
2.4.5.2. FE Mesh Graphic¶
The second graphic on the left shows the finite element mesh and profile plots.
Upon the finish of the analysis, select any of the tabs on the right inside this graphic (i.e., PGA,
2.4.5.3. Operations Area¶
The right side of this area shows some information on the created soil column, such as the total height and number of soil layers. The user also finds the Ground Water Table (GWT) input field, plus and minus buttons in this area. If the user presses the plus button, a layer will be added below a currently selected layer. If the minus button is pressed the currently selected layer will be removed. The GWT input field allows the user to specify the level of the groundwater table.
Note
Variables are assumed to have m, kPa, and kN units in s3hark.
2.4.5.4. Soil Layer Table¶
This table is where the user provides the characteristics of soil layers, such as layer thickness, density, Vs30, material type, and element size in the finite element mesh. Single click at a cell will make a soil layer, which will highlight the layer using green color in the table. Also the layer will be highlighted by a red box in the Soil Column Graphic. Meanwhile the Layer Properties Tab will be activated. Double-click a cell to edit it in the table. If you change the Material
cell of a layer, the Layer Properties Tab will change correspondingly.
2.4.5.5. Tabbed Area¶
This area contains the three tabbed widgets described below.
Configure Tab¶
This tab allows the user to specify the paths to the OpenSees executable and a ground motion file that represent the ground shaking at the
bedrock. The rock motion file must follow the SimCenter event format.
Examples of SimCenter event files are available in the motion demos
.
s3hark will determine whether to use a 2D column or 3D column based on the ground motion file provided.
When a ground motion file is selected from the local computer or the path of the ground motion file is typed in,
s3hark will figure out if it’s a 1D or 2D shaking file. If it’s 1D shaking, all elements will be 2D. If it’s 2D shaking,
all elements will be 3D.
The definitions of 2D and 3D slope are different. See Fig. 2.4.5.8.2 and Fig. 2.4.5.8.4.
More details about this tab can be found in Configure.
Layer Properties Tab¶
This tab allows the user to enter additional material properties for the selected soil layer Fig. 2.4.5.5.1.

Fig. 2.4.5.5.1 Layer properties¶
Response Tab¶
Once the site response analysis has been performed, this tab provides information about element and nodal time varying response quantities. See Fig. 2.4.5.5.2.

Fig. 2.4.5.5.2 Response¶
2.4.5.6. Analyze Button¶
This Analyze button is located at the top-right corner of the UI and shall be used to run the simulation locally on your computer. A progress bar will show up at the bottom of the application indicating the status of the analysis. Upon the finish of the simulation, a message will be displayed (Fig. 2.4.5.6.1).

Fig. 2.4.5.6.1 Analysis is done¶
2.4.5.7. View Results¶
Click the button to dismiss the message window, the response tab will be activated. The user can click on any element in the mesh graphic, the selected element will be highlighted in red and the selected nodes will be pointed out by blue arrows. The time history of the selected element/node will be shown in the Response Tab. This allows the user to review the ground motion predicted at selected nodes Fig. 2.4.5.7.1.

Fig. 2.4.5.7.1 Response at a selected node¶
Note
If the Analyze button is not pressed, no simulation will be performed, therefore no simulation is performed and there will be no ground motions provided to the building if you are using s3hark inside other SimCenter applications.
2.4.5.8. Configure¶

Fig. 2.4.5.8.1 Configuration with a 1D shaking motion¶
In the configure tab, two paths need to be specified. You can either type them or click the ‘+’ button to select them from your computer. If you don’t have OpenSees installed, the instruction can be found here. If you don’t have a ground motion file, demos can be downloaded here
.
Note
Variables are assumed to have m, kPa, and kN units in s3hark.
The first demo is SRT-GM-Input-Style3.json, which contains the shaking motion in one direction (1D shaking).
If you select this file as the input motion, your tab will look like the one shown in Fig. 2.4.5.8.1.
You can edit the slope degree

Fig. 2.4.5.8.2 Slope definition for 2D Column¶
The second demo is SRT-GM-Input-Style3-2D.json, which contains the shaking motion in two directions (2D shaking). If you select this file as the input motion, your tab will look like the one shown in Fig. 2.4.5.8.3.

Fig. 2.4.5.8.3 Configuration with a bi-directional shaking motion¶
You can see s3hark detected the file you provided is a 2D shaking, s3hark automatically treats the problem as a 3D problem. 3D elements will be used. The slope diagram is plotted in Fig. 2.4.5.8.4:

Fig. 2.4.5.8.4 Slope definition for 3D Column¶
For flat ground
2.4.5.9. Modeling Spatial Variability Uncertainty of Soil¶
The most recent version of s3hark allows the user to include spatial variability in the definition of soil profile. This functionality is achieved using several newly added SimCenter backend python scripts.
Generating Gaussian Random field¶
Physical properties of soils vary from place to place within a soil deposit due to varying geologic formation and loading histories such as sedimentation, erosion, transportation, and weathering processes. This spatial variability in the soil properties cannot be simply described by a mean and variance since the estimation of the two statistic values does not account for the spatial variation of the soil property data in the soil profile. Spatial variability is often modeled using two separated components: a known deterministic trend and a residual variability about the trend. These components are illustrated in Fig. 2.4.5.9.1.
This simplified spatial variability proposed by [PK99] can be expressed as,
where
Gaussian stochastic random fields are generated for the liquefiable soil layer by randomizing the assigned soil strength parameter over the soil layers with a certain spatial probability density. [Shi07] introduced a procedure for generating stochastic random field based on the method outlined in [YS88] considering uncertainties in soil properties. As explained earlier, the stochastic random field for a soil property consists of a trend (or mean) field and a residual field,
The trend field (
A summary of the random field preparation procedure for the site response event analysis is summarized here: Enumerated lists:
Generate mean field using mean target soil property, e.g., relative density or shear wave velocity
Generate Gaussian random field for target soil property using Gauss1D.py with mean = 0.0 and
= 1.0Interpolate Gaussian field to FEM mesh
Combine the mean field and Gaussian field to obtain a stochastic field using the following equation:
Note
A reasonable mesh resolution is recommended. The selection of element size should consider several factors, including but not limited to, layer shear wave velocity (for frequency resolution), correlation length (for random field resolution), and computation efficiency.
Calibration of Constitutive Model¶
Since soil properties, instead of material input parameters, are randomized, it is imperative to choose representative input parameters for constitutive models based on the random variable chosen by the user.
An independent calibration process of the constitutive model should be carried out carefully. Currently, a couple of pre-calibrated correlations are included in s3hark, including PM4Sand and PDMY03 based on relative
density (
Currently, three constitutive models are supported in s3hark to have random fields, namely, Elastic Isotropic (Elastic_Random), PM4Sand (PM4Sand_Random), and PDMY03 (PDMY03_Random). When these models are selected, the analysis will be carried out using SimCenter workflow. As a result, profile and response plots are not updated inside s3hark.
Note
Currently only 2D plain-strain materials (including PDMY03 and ElasticIsotropic) are supported when using random field. Therefore, 1-component motion is required.
Elastic Isotropic¶
Shear wave velocity (Vs) can be selected to be randomized for this material. Subsequently, Young’s modulus is calculated based the stochastic shear velocity profile at the center of each element. No special calibration is required.
Note
Vs is bounded between 50 and 1500 m/s in calibration.py
PM4Sand¶
The calibration of the PM4Sand model is based on a parametric study using quoFEM [CA20]. The calibration procedure for PM4Sand is straightforward for general sand-like soil behaviors as intended by the model developers.
When detailed laboratory test results are available, the apparent relative density
On the other hand, when comprehensive laboratory tests are not available for specific sites, model calibration needs to be based on in-situ test data such as SPT blow count, CPT penetration resistance, or shear wave velocity (Vs).
For example,
where
where
Alternatively, a simpler expression can be used when combined with a range of typical densities as,
Subsequently,
Using this tool,
The results were processed through linear regression analysis using Matlab to find the correlation between the input,
with
Then this equation can be rearranged to isolate
where
Note
is bounded between 0.2 and 0.95 in calibration.py
PressureDenpendentMultiYield03¶
PressureDenpendentMultiYield03 is updated from PressureDenpendentMultiYield02, which was developed for liquefaction and cyclic mobility, to comply with the established guidelines on the dependence of liquefaction triggering to the number of loading cycles,
effective overburden stress (
Note
is bounded between 0.33 and 0.87 in calibration.py