7 – Linear analysis with FEM engine

1.0 Introduction

This tutorial introduces the basic site response analysis flow using the finite element engine in RSSeismic by re-running the linear analysis examples from Tutorial 1 using the finite element engine. Because finite element analysis is conducted in the time domain, we will only be recreating the time domain examples from tutorial 1.

The overall steps involved in building and analyzing a model with the finite element engine are very similar to those for the lumped mass engine. The main differences are the additional constitutive model parameters required in the properties tab as well as additional options in the compute and project setup tabs. For these linear analyses, the results are identical to those from tutorial 1. 

Topics Covered in this Tutorial:

• Undamped linear analysis with rigid bedrock
• Undamped linear analysis with elastic bedrock
• Damped linear analysis with elastic bedrock

Finished Product:

The finished products of this tutorial can be found in the Tutorial 7 folder. All tutorial files installed with RSSeismic can be accessed by selecting File > Recent files/folders > Tutorials Folder from the RSSeismic main menu.

2.0 Example 1 – Undamped linear analysis with rigid bedrock

2.1 Project Setup

1. Begin by opening RSSeismic and selecting New Project . A new project will open, and you will be taken to the Project Setup tab.
2. In the Project Setup tab, set the Unit System to Metric, stress as kPa.
3. For the Profile Generation, we will be leaving the default: Create Profiles Manually . Since we are only defining one soil profile, Create Multiple Profiles will remain turned off. See the Profiles topic for details on creating multiple profiles.
4. For the Solution Type select Time Domain.
5. For the Solver Type select Finite Elements
6. For the Input Motion Configuration select Uni-directional shaking
7. For Analysis Method select Linear.

2.2 Profile

1. Select the Profile tab.
2. In the table on the right, select Layer 1 and enter a Thickness of 20 m.
3. Tick the checkbox for Water table at top of layer. Layer 1 will be selected as it is the only layer.

2.3 Properties

1. Select the Properties tab.
2. For Layer 1, under Basic Properties enter:
   1. Unit Weight (kN/m³) = 20
   2. Shear Wave Velocity (m/s) = 500
   3. Effective Vertical Stress (kPa) = 101.9
   4. K₀ = 0.5

   5. Poisson’s ratio (ν) = 0.33

      

3. Select the Soil Model Properties tab.
   1. For Dmin (%) we will leave the default value of 0 for undamped soil.
4. Select the Pressure dependence properties tab.
   1. We will leave the default values recommended by Numanoglu et al., 2023.
5. Select the Volumetric response properties tab.
   1. We will leave the default values for this tab as well.
6. Select the Bedrock layer.

   1. We will leave the Halfspace option set to Rigid halfspace

      

7. Select the Profile Plots tab to review your data.

You are encouraged to carefully examine these graphs to confirm that the input of selected profile characteristics are as intended. This includes shear wave velocity, the maximum frequency that can be propagated through the soil profile and implied strength properties.

2.4 Motions

1. Select the Motions tab.
2. Under Resources\Input Motions, select ChiChi.

2.5 Damping Formulation

1. Select the Damping Formulation  tab.
2. For Damping Matrix Type we will use the default selection of Frequency Independent.
3. For Damping matrix update, use the default Do not update matrix.

2.6 Compute

1. Select the Compute Options tab.
2. For the Time Domain (Finite elements) analysis use the default value:
   1. Timestep reduction factor = 0.9
3. For Output settings ensure Layers = Surface only is selected.
4. Click Compute.

2.7 Results

1. Go to the Results tab.
2. The Time History Plots and Spectral Plots should look as follows.

3.0 Example 2 – Undamped linear analysis with elastic bedrock

3.1 Project setup

1. Return to the Project Setup tab.
2. Select File > Save Project As and save this project as Tutorial 7 Example 2.rsseismicfile.

3.2 Properties

1. Go to the Properties tab and select Layer Properties.
2. Select the Bedrock layer by either clicking on the soil profile on the left or using the drop down list.
3. Change the Halfspace option to Elastic Halfspace.
4. Enter the following:
   1. Shear wave velocity (m/s) = 760
   2. Unit weight (kN/m³) = 25
   3. Damping Ratio (%) = 2

3.3 Compute

1. Go to the Compute Options tab.
2. Use the same compute options from Example 1. Click Compute.

3.4 Results

1. Go to the Results tab.
2. The Time History Plots and Spectral Plots should look as follows

4.0 Example 3 – Damped linear analysis with elastic bedrock

4.1 Project Setup

1. Return to the Project Setup tab.
2. Select File > Save Project As and save this project as Tutorial 7 Example 3.rsseismicfile

4.2 Properties

1. Go to the Properties tab.
2. Ensure Layer 1 is selected.
3. Select the Soil model properties tab.
4. Enter Dmin (%) = 5

4.3 Compute

1. Go to the Compute Options tab.
2. Use the same compute options from Example 1. Click Compute.

4.4 Results

1. Go to the Results tab.
2. The Time History Plots and Spectral Plots should look as follows