Edt Fem Models

Quick Start Guide to EDT
These guidelines aim to familiarize new users with the ElastoDynamics Toolbox (EDT) for MATLAB as
quickly as possible. First, the installation of EDT is addressed. Next, three examples are discussed where
EDT is used to model site amplification, to compute surface waves in a layered medium, and to calculate
the response of a layered medium due to a harmonic point load.The examples only cover a fraction of the
possibilities of the toolbox. For a more profound discussion of the functionality and background of EDT,
please refer to the user’s manual.

Obtaining and installing EDT
EDT can be downloaded from the internet at http://www.kuleuven.be/bwm/edt.
It is
distributed as a ZIP archive, which should be extracted to a directory on the hard disk, e.g.C:\Program Files\MATLAB\R2010a\toolbox\edt. After extraction of the ZIP archive, this directory
should contain a number of P-files, M-files, and MEX-files.
The EDT directory must be added to the MATLAB path to make the toolbox functions available in MATLAB:
- In MATLAB, click on ‘File’, ‘Set Path...’
- Click on ‘Add Folder’ and select the EDT directory.
- Save the path and close the dialog window.A license file license.dat is required to use the toolbox. This file must reside in the EDT directory or one
of its parent directories.
You can either buy a permanent license, or request a free trial license for one month. Type edtlicense at
the MATLAB command prompt for instructions on how to obtain a permanent or trial license.

Amplification problems
Site amplification is an important issuein the assessment of the seismic hazard at sites where the top soil
layers are particularly soft. In such cases, the seismic motion at the surface can be much higher than the
outcrop motion due to resonance of the soft layers.
In the following, the amplification of an incident P-wave in a layered soil is computed with EDT. The soil
consists of five homogeneous layers with a thickness of 2 m on ahomogeneous halfspace. The shear wave
velocity Cs increases linearly with depth, from 140 m/s in the first layer to 460 m/s in the fifth layer. The
shear wave velocity Cs of the halfspace is 500 m/s. The Poisson’s ratio ν is equal to 1/3 in all layers and
in the halfspace, which implies that the dilatational wave velocity Cp is twice the shear wave velocity Cs .
The damping ratio Ds = Dp forboth shear waves and dilatational waves decreases linearly with depth, from
0.045 in the first layer to 0.005 in the fifth layer. Zero damping is assumed in the halfspace. The density of
the soil is ρ = 1800 kg/m3.
The amplification of an incident P-wave is computed with the EDT function amp_p. Three angles of incidence
θ are considered: 90◦ , 60◦ , and 30◦ . The amplification factor is computed inthe frequency range from 0 Hz
to 50 Hz.
% SOIL PROPERTIES
h
= [2 2 2 2 2 inf];
Cs = [140 220 300 380 460 500];
Cp = [280 440 600 760 920 1000];
Ds = [0.045 0.035 0.025 0.015 0.005 0];
Dp = [0.045 0.035 0.025 0.015 0.005 0];
rho = 1800;

%
%
%
%
%
%

Element thickness [m]
S-wave velocity [m/s]
P-wave velocity [m/s]
S-wave damping ratio [-]
P-wave damping ratio [-]
Density[kg/m^3]

% INCIDENT WAVE PROPERTIES
f = [0:0.1:50];
% Frequency [Hz]
omega = 2*pi*f;
% Frequency [rad/s]
phi = [90 60 30]/180*pi; % Angle of incidence [rad]

1

% RECEIVER DEPTH
z = 0; % Receiver depth [m]
% AMPLIFICATION FACTOR
[Ux,Uz] = amp_p(h,Cs,Cp,Ds,Dp,rho,phi,z,omega);
% PLOT HORIZONTAL RESPONSE
figure;
plot(f,squeeze(abs(Ux)));
xlabel(³Frequency [Uz]³);
ylabel(³Verticalamplification [-]³);
% PLOT VERTICAL RESPONSE
figure;
plot(f,squeeze(abs(Uz)));
xlabel(³Frequency [Uz]³);
ylabel(³Amplification factor [-]³);
6
Amplification factor [ − ]

Amplification factor [ − ]

6
5
4
3
2
1
0

0

10

(a)

20
30
Frequency [Hz]

40

5
4
3
2
1
0

50

(b)

0

10

20
30
Frequency [Hz]

40

50

Figure 1: Amplification factor for...