3.2. Shear Building: HAZUS Assessment

This study explores a simple uncertainty propagation problem in the following three story shear building and employs the HAZUS methodology for assessing damage and loss:

A diagram depicting a three storyone bay structure with three horizontally aligned rigid beams. The first and second floors have a mass labeled "w". At the top floor, the mass is labeled "w/2". The columns at the based end by a symbol indicating a fixed support.

Fig. 3.2.1 Three Story Shear Building Model (P10.2.9, “Dynamics of Structures”, A.K.Chopra)

This example uses the PBE application to automatically prepare an column model that represents the three-story structure, subject it to a suite of ground motion time histories, and evaluate the seismic performance of the building using the Hazus Earthquake methodology.

Each step of the workflow for this problem is explained below by sequentially walking through the input panels and highlighting their role in the simulation. The file input.json contains all of the settings for this exercise. It can be opened (using File/Open) to automatically populate the fields in the user interface.

3.2.1. Step 1: UQ

This panel provides an interface to various forward propagation procedures which are used to sample the random variables defined in later panels and propagate each realization through the workflow. This process can be used to characterize the uncertainty in the workflow outputs. For this example, a latin hypercube sampling procedure (LHS) is used with 40 samples and a seed of 775. Fixing the seed ensures the same random sample every time the calculation is run.

Screenshot of a graphical user interface for a software program with a sidebar and a main content area. The sidebar includes the acronyms UQ, GI, SIM, EVT, FEM, RV, DL, and RES in white text against a dark background, which are likely navigation menu items or module names. The main content area displays settings related to the "UQ Engine" with "Dakota" selected from a dropdown menu. There is a section titled "Dakota Method Category" with "Forward Propagation" selected, followed by options to choose a method ("LHS" currently selected), set the number of samples ("40"), and input a seed value ("867"). Lastly, checkboxes for "Parallel Execution" and "Save Working dirs" are visible with "Parallel Execution" checked. The layout suggests that this is a configuration panel for running uncertainty quantification (UQ) simulations or analyses.

3.2.2. Step 2: GI

Next, the GI panel may be used to define metadata and other general information about the model. Some of the values are automatically updated by later panels while others are only providing information about the model and not used for the simulation.

It is important to review and specify the desired Units for the calculation here. It is important to provide all inputs assuming these units when no other instructions are given by the following panels. The length unit is used to define velocity and acceleration units as well.

Screenshot of a user interface showing "Building Information" with fields for name, properties (including year built, number of stories, structural type, height, width, depth, and plan area), location (latitude and longitude), and units (force in kips, length in inches, and temperature in Celsius). The building name is entered as "Test", the year built is "1990", and it has "3" stories with a "RM1" structural type. No image of the actual building is present, just the data entry interface.

3.2.3. Step 3: SIM

The SIM panel can be used to define the simulation model. In this example we leverage the convenient MDOF tool which provides a high-level interface for defining simple parameterized structural analysis models. Either variable names, or literal values can be entered in the fields of this panel, as shown in the following figure.

This model could have random properties that we could sample and propagate the corresponding uncertainty through the workflow. If a variable name is entered, PBE automatically identifies it as a random variable, and creates a corresponding entry in the RV panel. Several examples in the documentation of the EE-UQ application demonstrate this feature on models of various complexity. In this example, we use a deterministic structural model for the sake of simplicity.

Screenshot of a Building Model Generator software interface displaying various input fields and parameters for engineering simulations. The left panel shows a selection menu with options like UQ, GI, SIM, EVT, among others highlighted, with SIM currently selected. The central panel titled "Building Information" includes data input fields for properties such as Number of Stories, Floor Weights, Story Stiffness in X and Y directions, Yield Strength, Damping Ratio, and others, with numerical values entered. To the right is a simple representation of a multi-degree of freedom (MDOF) system with three horizontal blue squares, symbolizing floor masses, connected by vertical lines, indicating the building model's response to simulations.

3.2.4. Step 4: EVT

The EVT panel provides various Load Generator options that can either import ground motion loads from external files or connect to the PEER NGA database and obtain loads that represent a target spectrum or generate loads during the simulation using a stochastic process. We will use the latter solution in this example by selecting the Stochastic Ground Motion option.

The Vlachos et al. (2018) model generates ground motion time histories based on three parameters: magnitude, distance, and shear-wave velocity in the top 30 meters of the soil. We specify a magnitude 7 earthquake 40 kms from the site of interest. As for the shear-wave velocity, we introduce a random variable by providing vs as input. This is recognized by PBE and the corresponding variable is automatically added to the RV panel.

Screenshot of a software interface titled "Load Generator" for a Stochastic Ground Motion simulation. The interface shows a selected stochastic loading model referencing Vlachos et al. (2018), along with input fields for Moment Magnitude (set to 7), Closest-to-Site Rupture Distance in kilometers (set to 40), and Average shear-wave velocity for the top 30 meters in meters per second (labeled 'vs'), with a radio button for providing a seed value (set to 500). There is a navigation sidebar on the left with various options like UQ, GI, SIM, EVT (selected), FEM, RV, DL, and RES.

3.2.5. Step 5: FEM

We now proceed to the FEM panel where we can adjust settings for running the dynamic analysis. The default settings are typically appropriate for analyses that use the MDOF tool.

Screenshot of a user interface for a finite element application named OpenSees. The panel is showing various input fields classified under headings like Analysis, Integration, Algorithm, ConvergenceTest, Solver, Damping Model, and Selected Tangent Stiffness. Each category has predetermined choices or numerical inputs, with a 'Choose' button at the bottom right. On the left sidebar, 'FEM' is highlighted, indicating the current section the user is in, with other sections like UQ, GI, SIM, EVT, RV, DL, and RES listed above and below.

3.2.6. Step 6: RV

Now in the RV panel we will enter the distributions and values for our random variables. Because of the steps we have followed and entries we have made, when this tab is opened it already contains the vs random variable. We choose to model the uncertainty in the shear wave velocity using a normal distribution with a mean of 400 m/s and a standard deviation of 100 m/s.

Screenshot of a software interface for inputting random variables. On the left side is a vertical menu with options including UQ, GI, SIM, EVT, FEM, RV (highlighted in blue), DL, and RES. The main panel is titled "Input Random Variables" with fields for Variable Name (populated with 'vs'), Distribution (set to 'Normal'), Mean (set to '400'), and Standard Deviation (set to '100'). There are buttons for 'Add', 'Clear All', 'Correlation Matrix', 'Show PDF', 'Export', and 'Import'. The background and menu are dark gray, while the main panel has a white background with blue highlights.

Warning

Do not leave any of the distributions for these values as constant when using the Dakota UQ engine.

3.2.7. Step 7: DL

The last step in the setup is the DL panel. We use the four tabs in this panel to specify the performance model following the Hazus Earthquake methodology.

First, in the Asset tab, we choose the Hazus Earthquake component vulnerability database that is bundled with the PBE application. This loads all of the building archetypes handled by Hazus in the Available in DB list. We assign the STR.S1M.MC steel frame archetype as the structural component. NSD and NSA.MC components are added to represent drift and acceleration-sensitive non-structural components.

Because Hazus components are assigned at the building level, there is only one performance group created for each. The acceleration-sensitive component is assigned to the roof of the building (to obtain roof acceleration from there) while the drift-sensitive components are assigned to the first floor. This latter assignment is used with roof drift EDPs in buildings regardless of the number of floors they have.

Screenshot of a damage and loss assessment software interface with various sections for inputting information about a building's characteristics and components. The General Information section includes fields for 'Number of Stories' and 'Plan Area'. A section for Component Assignment is shown with buttons for 'Load', 'Save', 'Add', 'Add All', 'Remove', 'Remove All', and lists 'Available in DB' and 'Assigned' components. There is a portion labeled 'Databases' with a dropdown menu for 'Component Vulnerability' currently set to 'Hazus Earthquake' and a button to 'Export DB'. The interface also includes vertical navigation tabs on the left side with labels such as UQ, GI, SIM, EVT, FEM, RV, DL, and RES, with the DL tab highlighted.

Under the Demands tab, we specify that the demand data is provided by the Workflow automatically; we assume that demands follow a multivariate lognormal distribution. After fitting such a distribution to the data, we sample 500 demand realizations for damage and loss assessment.

Screenshot of a user interface for a 'Damage and Loss Assessment' application named Pelicun. The interface includes tabs for inputs categorized under Asset, Demands, Damage, and Losses. Current visible settings include 'Data Source' with 'Demand Data: from Workflow,' 'Stochastic Model' with 'Distribution: fit lognormal,' checkboxes for 'Add Uncertainty' and 'Remove collapses,' 'Sample' with 'Sample Size' of 500 and a checkbox for 'Directly use raw demand data,' and 'Residual Drifts' with a setting 'do not infer.' On the left side, there's a vertical menu with the options UQ, GI, SIM, EVT, FEM, RV, DL (highlighted), and RES.

The Damage tab setup is simple when the Hazus earthquake methodology is used because this method includes collapse in the structure component damage states and does not consider irreparable damage. The Damage Process employed by this method is included in PBE and selected for this example.

Screenshot of a user interface for a damage and loss assessment application named Pelicun with a menu on the left side showing acronyms UQ, GI, SIM, EVT, FEM, RV, DL, RES with 'DL' highlighted, indicating the current section. The main panel has tabs labeled 'Asset,' 'Demands,' 'Damage,' 'Losses' and sections titled 'Global Vulnerabilities' with checkboxes for 'Irreparable Damage' and 'Collapse,' and 'Damage Process' with a dropdown menu set to 'Hazus Earthquake.' The interface has a clean, professional layout with a grey and teal color scheme.

Losses are calculated using the included Hazus Earthquake consequence functions for repair costs and an Automatic mapping between damaged components and consequence models. This mapping uses the occupancy type and component types specified in the Asset tab earlier and selects the corresponding consequence functions following the Hazus methodology.

Screenshot of a Damage and Loss Assessment software interface titled "Pelicun" displaying various tabs and options for analysis, including a selected tab labeled 'DL' on the left sidebar, and categories such as Asset, Demands, Damage, and Losses with subcategories like Repairs, Global Consequences, Database, and Mapping on the main panel. An option to export the database is visible, and the dropdown menu shows "Hazus Earthquake" as the selected consequence data.

3.2.8. Analysis & Results

Once a full workflow has been defined click on the Run button. When the analysis is complete the RES tab will be activated and the results will be displayed. When a HAZUS assessment has been conducted, the results panel will resemble the following figures which show the Summary and Data tabs, respectively.

A screenshot of a computer interface displaying a summary table with decision variables related to repair scenarios. The variables include "repair cost," "repair time - parallel," "repair time - sequential," "collapsed?" and "irreparable?" with corresponding statistical values for probability, mean, standard deviation, and log standard deviation. Some fields are filled with numerical data, while others are marked with dashes or "N/A" to indicate unavailable information.
A screenshot showing a software interface with a bar chart and a data table. The bar chart is labeled "Frequency %" on the y-axis and "repair cost" on the x-axis, with bars representing different frequencies at varying repair cost intervals. The data table beneath the chart lists numerical values across columns with headers such as "repair cost," "pair time - paral," "air time - sequer," "collapsed?" and "irreparable?" The interface also includes a sidebar with various menu options like UQ, GI, SIM, EVT, FEM, RV, DL, and RES highlighted in turquoise.

In the Data tab of the RES panel, we are presented with both a graphical plot and a tabular listing of the data. By left- and right-clicking on the individual columns the plot axis changes (left mouse click controls vertical axis, right mouse click the horizontal axis). If a singular column of the tabular data is selected with both right and left mouse buttons, a frequency and CDF plot will be displayed.