Integrated Solver Optimized for the next generation 64-bit platform

Finite Element Solutions for Geotechnical Engineering

MIDASoft Inc.

Angel Francisco Martinez

Civil Engineer

Email : a.martinez@midasuser.com

Dynamic-Slope Coupled Analysis

GTS NX

2

Strength Reduction Method (SRM)

Slope stability analysis using the finite element method is a numerical analysis method that

analyzes the minimum safety factor and failure behavior using various shapes, loads and

boundary conditions. In particular, the strength reduction method can be used to simulate the

failure process without any previous assumptions(Griffith et. al. 1999; Matsui, 1990).

The strength reduction method gradually decreases the shear strength and friction

angle until the calculation does not converge, and that point is considered to be the failure

point of the slope.

The maximum strength reduction ratio at that

point is used to calculate the minimum safety

factor of the slope.

SRM

GTS NX

3

Strength Reduction Theory

To simulate slope failure using the strength reduction method, the safety factor is

computed at an arbitrary point where the Mohr circle is in contact with the failure

envelope, as shown in the figure below. The stress state at this point can be

determined as the failure state and when this failure point increases, overall slope

collapse occurs. The finite element analysis at this limit state diverges, and the

safety factor at this point is defined as the minimum safety factor.

SRM

GTS NX

4

Staged Excavation with SRM at every stage

SRM

GTS NX

5

Seepage Pore Pressure

Shear Force total Shear Force Iso surface

Seepage + SRM Coupled

GTS NX

6

Dynamic Coupled

GTS NX

7

GTS NX supports nonlinear time history analysis that includes geometric, material

nonlinearity and it is based on implicit time integration.

The dynamic equilibrium equation in nonlinear time history analysis uses the

method as implicit time integration, just like for linear time history analysis, and uses the

following modified equilibrium equation.

Nonlinear time history analysis calculates the

convergence solution for each time step using

the nonlinear finite element solution; a method

of converging the accumulated incremental

solution from iterative calculations to the

correct solution. In the figure, and

each represent the external forces at time

and time , and the solution and incremental

solution between time and time can be

expressed as the following relationship:

Nonlinear Dynamic Response

Accumulated incremental solution and nonlinear finite element

convergence:Incremental solution occurring at time increment t

GTS NX

8

GTS NX considers two types of damping: mass-proportional damping and

stiffness-proportional damping. There is also mode damping, which is only

applied for mode superposition. The damping effects in linear time history

analysis are applied to the damping matrix in the following form:

: Mass proportional damping coefficient for j th element

: Stiffness proportional damping coefficient for j th element

: Mass matrix of jth element

: Stiffness matrix due to material nonlinearity

: Damping matrix due to damping element (damper)

Damping effect

GTS NX

9

Dynamic-Slope Coupled

Slope stability analysis using the general SRM cannot be used as a factor of safety for the

dynamic state since slopes are more vulnerable to dynamic loads such as earthquakes. In a

dynamic equilibrium state, the ground receives stress from not only its self-weight, but also

from the inertial force due to vibrations.

GTS NX can conduct such slope stability analysis for the dynamic equilibrium state. The slope

stability analysis is based on the SRM and can be applied to 2D, axis symmetric and 3D

problems.

The input time during nonlinear time history

Analysis can use the stress state of the

Ground at that point as the initial values

to calculate the slope stability.

→ Check F.S. of slope using Pseudo-

dynamic analysis

→ Check F.S. of slope directly through

Nonlinear + SRM coupled analysis

GTS NX

10

Geometry Import

Import Materials

Mesh generation

Boundary Conditions

Dynamic Load Conditions

Eigenvalue Analysis

STEP 01

STEP 02

STEP 03

STEP 04

STEP 05

STEP 06

TH + SRM Analysis CaseSTEP 07

STEP 08 Perform analysis and check result

Overview

GTS NX

Procedure

11

01 2D Slope

• 2D nonlinear time history analysis

coupled with slope stability

•Plane strain elements are used tomodel ground condition.

•Free Field boundary conditions usedfor time history analysis.

•Ground Acceleration used as dynamic load.

For performing slope stability analysis using the finite element method (FEM), use higher order

elements and triangle shaped elements.

GTS NX

1-12

02 Material for Soil

Name Ground

Material Isotropic

Model Type Mohr-Coulomb

General

Elastic Modulus (E) (kN/m^2) 50,000

Poisson’s Ratio(v) 0.4

Unit Weight(r) (kN/m^3) 19

K0 1

Porous

Unit Weight(Saturated) (kN/m^3) 19

Non-Linear

Friction Angle 5

Cohesion (kN/m^2) 30

GTS NX

1-13

03 Property for Soil

Name Ground

Property 2D

Model TypePlain

Strain

Material Ground

GTS NX

Procedure

14

01 Create New Project

11

Main Menu > New

Analysis Setting > Model

Type > 2D

Set units to kN / m / sec

2

2

GTS NX

Procedure

15

02

1

1

Main Menu > Open

Select NTH with SRM > DXF>

Open

Select OK

2

2

3

3

Geometry works (Create or Import from AutoCAD)

GTS NX

Procedure

16

03 Define Material / Property for Soil & Structures

1 Mesh > Prop. > Property

• Import Materials and Properties

from finished file (Refer to Project

Overview > Material / Property).

Import All

1

1

GTS NX

Procedure

17

04 Generate Mesh (2D Element)

1 Mesh > Generate > 2D > Auto -

Area

Select Edge(s) > Select 6 edges

highlighted in figure.

Input element Size : 1

(1m between two nodes)

Select Property : Ground

Input Mesh Set Name : Ground

Click on the ‘>>’ icon to open

the Advanced Option Window

Select Triangle as Element Type

Activate Higher Order Elements

Click OK > OK

2

2

2

3

4

5

3

4

5

6

6

1

7

8

9

8

1

9

7

GTS NX

Procedure

18

05 Define Free Field Boundary

1 Mesh > Element > Free Field

Line: Select the left and right

vertical edges of the mode’s

boundary as shown in the

image.

Create Free Field Property >

Free field type: Line

Width Factor : 10

Press Ok>OK

1

2

2

3

3

4

4

GTS NX

Procedure

19

06 Define Boundary Condition (Ground)

1 Static / Slope Analysis >

Boundary > Constraint >

Advanced

Select all the bottom nodes

and the bottom free field as

shown in the images.

Restrict DOF Tx and Ty

Press OK

1

2

3

2

3

4

4

GTS NX

Procedure

20

07 Load Condition (Self Weight)

1

1 Static / Slope Analysis >

Load > Self Weight

Load Set Name : Self weight2

2

GTS NX

Procedure

21

08 Dynamic Load > Gravity

Create Dynamic Load Case for

gravity to be considered in dynamic

analysis

Dynamic Analysis > Load > Time

Varying Static

Select load set and click ADD

Dynamic Load Set : gravity

Press OK

1

2

1

3

4

2

3

4

GTS NX

Procedure

22

08 Dynamic Load > Ground Acceleration

Create Time History Load Funcition

for dynamic analysis

Dynamic Analysis > Load > Ground

Acceleration

Activate X direction, Scale Factor: -1

and click in the icon to define the

function

Click ADD Time Function

Click EARTHQUAKE to select

function from out data base

Select 1940 El Centro, 270 degree

Press OK, > OK > CLOSE > OK

1

2

1

3

4

2

3

4

1

2

5

6

3

4

5

6

6

6

6

GTS NX

Procedure

23

09 Analysis Case

1

Create EigenValue Analysis Cases

1. Analysis > Analysisi Case >

General > Eigenvalue

2. Activate All Sets

3. Analysis Control > 30 Modes

4. Press OK > OK

2

3 1

2

3

3

4

4

4

GTS NX

Procedure

24

10 Perform Analysis and Check Results

1 Analysis > Analysis > Perform

Select OK

1

2

2

GTS NX

Procedure

25

11 Post Processing (Results)

* After analysis, model view

will be converted to Post-

Mode automatically, can

back to Pre-Mode to change

model information.

1 1

Results can be Viewed in table

format.

Find the 2 highest mass

participation modes and write

down their corresponding periods.

MODE 1: 2.122940 sec

MODE 3: 1.256590 sec

3

2

GTS NX

Procedure

26

12 Analysis Case (Nonlinear Time History + SRM )

1

Create Nonlinear Time History &

SRM analysis Cases

1. Analysis > General > Nonlinear

Time History & SRM

2. Activate all sets

3. Define Time Step

Name: time

Time Duration: 4 sec

Time Increment:: 0.02 sec

Intermediate Output:: 10

Press Add > OK > CLOSE

4. Analysis Control > Dynamic >

Damping Method

-Select > Calculate from Modal

Damping > Period

-Type in the 2 periods from

Eigenvalue results

-Damping Ratio : 0.05

-Press OK

5. Analysis Control > SRM

-Time: 2.14 sec

Press Add > OK

Press OK

2

3

1

2

3

3

4

4

4

4

5

5

6

6

GTS NX

Procedure

27

13 Perform Analysis and Check Results

1 Analysis > Analysis > Perform

Select Nonlinear Time History

with SRM

Select OK

1

3

2

3

2

GTS NX

Procedure

28

1 Inspect the FOS or the SRM

analysis case.

FOS: 1.1

SRM>Plane Strain Strains>E-

Equivalent

Inspect the Maximum Total

Relative Displacements for the

non linear time history.

Nonlinear Time History > Max >

Total Relative Displacement

Max value: 1.349 m

2

14 Post Processing (Post mode)

1

2

GTS NX

29

Thank you

Angel Francisco Martineza.martinez@midasuser.com