9 – Nonlinear Finite Element Analysis with Pore Water Pressure

1.0 Introduction

In this tutorial, we will carry out a nonlinear finite element analysis with pore water pressure generation and dissipation. Unlike a lumped-mass analysis, where pore pressures are generated and soil stiffness is degraded using empirical pore-pressure models, a finite element analysis employs a fully coupled formulation in which pore-pressure generation is governed by the response of the constitutive model.

Topics Covered in this Tutorial:

• Nonlinear time domain analysis with FEM engine
• Pore water pressure generation and dissipation with FEM engine

Finished Product:

The finished product of this tutorial can be found in the Tutorial 9 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 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 Imperial, stress as psf.
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. 
4. For Solution type select Time Domain.
5. For Solver type select Finite elements.
6. For Input motion configuration select Uni-directional shaking.
7. For Analysis Method select Nonlinear. 
   1. Notice that the Pore Pressure Options are no longer greyed out. Tick the checkbox for Generate excess pore water pressure.
   2. Select Enable Dissipation. Leave the permeability option at the top of the profile boundary selected.
8. For Default Soil Model, ensure I-soil model (Numanoglu et al., 2023) is selected.

9. For Default hysteretic re/unloading formulation ensure the default Non-masing re/unloading (recommended) is selected.

   When conducting an effective stress Nonlinear analysis, users have the option of obtaining the site response results using frequency domain effective stress analysis and time domain total stress lumped mass analysis automatically. This can be done by using the Complementary analyses option. We will not be using this option for the tutorial.
10. For Complementary analyses, turn OFF both Equivalent Linear – Frequency Domain and Nonlinear Total Stress - Time Domain.

3.0 Profile

1. Go the Profile tab.

For this tutorial, we will be creating a soil profile with a total of 5 soil layers.

2. Add 4 more layers to the soil profile. This can be done by clicking Add Layer Below 4 times, or by clicking Append Rows and entering 4. You should now have 5 layers total.
3. Change the Thickness of each layer as indicated in the table below:

4. Tick the Water table at top of layer checkbox to add a water table above Layer 1. This implies that the ground water table is at the ground surface.

4.0 Properties

1. Go to the Properties tab.
2. Select the Advanced Table View.
3. Copy and paste the basic soil profile values from the table below:

We will use the same curve fitting procedure we used in the previous tutorials.

4. Return to the Layer Properties tab.
5. Under Reference Curve > Sand select the Darendeli, 2001 reference curve.
6. Enter Ko = 0.5. Leave all others values as the defaults shown below:
   1. OCR = 1
   2. Ko = 0.5
   3. N = 10
   4. Frequency = 1
   5. PI = 0
7. Under Curve Fitting, enter Fitting Procedure = MRDF with UIUC Reduction Factor.
8. Click Fit.
9. The Fitting Limits dialog will appear. Leave the default values (Max strain = 0.05% and Min Strength = 95%) selected and click OK.

10. The Soil Model properties and Reduction factor formulation will be calculated. Click Use Fit to apply the fitted curve to Layer 1.

    

11. Select the Pressure dependence properties tab.

    1. We will leave the default values recommended by Numanoglu et al., 2023

    

12. Select the Volumetric response properties tab.

    1. We will leave the default values for this tab as well.

    

13. Repeat steps 4-11 above for layers 2-5.

14. Return to Layer 1 and select the PWP Properties tab.

    1. Enter Permeability = 3e-4 ft/s and Porosity = 1

    

15. Enter the same pore water pressure properties for Layers 2-5. (This can be done more quickly by copy and pasting the values into the Advanced Table View tab. A CSV of the Advanced Table View values has been included in your tutorial folder to make this easier.)

16. After completing the curve fitting for all the soil layers, return to the Layer Properties tab and select the Bedrock layer. Enter:

    1. Halfspace option = Elastic Halfspace
    2. Shear wave velocity (ft/s) = 5000
    3. Unit Weight (lbf/ft³) = 160
    4. Damping ratio (%) = 2
    5. For Halfspace porewater pressure, Use Cv of last layer should be selected by default.

    

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

5.0 Motions 

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

The time-histories (Acceleration, Velocity, Displacement, Arias and Housner Intensity), FAS, and 5% damped spectral acceleration for Kocaeli motion can be viewed below.

6.0 Damping Formulation

1. Select the Damping Formulation tab.
2. For Damping Matrix Type we will use the default selection of Frequency Independent.

7.0 Compute Options

1. Go to the Compute Options tab.
2. For Time domain (Finite elements) analysis use the default values:
   1. Timestep reduction factor = 0.9
3. For Output settings ensure Layers = All Layers, since we will be comparing the results of the different layers.
4. Click Compute.
5. After the compute is completed, save the file

8.0 Results

1. Go to the Results tab.
2. In the Time history plots tab, tick the checkboxes for Layer 1 and Layer 3 to compare the results.
3. To better view the layers, use the Color Mode drop down in the bottom right of the screen and select Blend motion and layer color.

The Acceleration, Velocity, Displacement, and Arias Intensity time histories are displayed.

4. Select the Profile Plots tab. The results are shown below.

   

5. Select the Stress-strain plots tab. Maximum strain of approximately 0.04% in site profile occurs in Layer 3 due to development of significant level of pore water pressure

   

6. Select the Spectral Plots tab. 5% damped spectral acceleration, Fourier Amplitude Spectrum and Ratio for Layer 1 and Layer 3 are presented.