### Free software for earthquake engineering and structural dynamic

This page provides links to softwares, which can be free downloaded and may be used at own risk. The softwares were initially developped for MATLAB. They were however slightly adapted to be compatible with the free software OCTAVE. Nevertheless, they run with both MATLAB and OCTAVE.

The extension of OCTAVE files is “.m”; they are text files and they can be edited by any text editor.

To run OCTAVE files, you should download the files on your PC (if necessary, use the command “save as”) OCTAVE download .

#### These software may be free downloaded and used at own risk

### SimSeisme

SimSeisme is an OCTAVE code for the generation of synthetic earthquakes with stationary simulation corresponding to the well-known program SIMQKE.

SimSeisme generates synthetic earthquakes compatible to a prescribed target spectrum (SpectreCible). The fonction used to match iteratively the target spectrum provides generally faster convergence than the one of SIMQKE. By contrast to SIMQKE, two uniform frequency repartitions are available (logarithmic and linear). Since the peak acceleration is not the main parameter for structural response, SimSeisme does not include a matching of a prescribed peak ground acceleration.

#### To run SimSeisme.m:

- Define the target spectrum and the corresponding tolerable divergence in SpectreCible.m
- Set the parameters (NbPt, EFz, S, RepFrequ, EnvelUsed, Nseisme, MaxIter, Z) in SimSeisme.m
- Run Octave
- Type SimSeisme and Return

#### Informations and recommendations

- SimSeisme is based on the work of Gasparini and Vanmarcke. More informations may be found in their publication:Gasparini D. A., Vanmarcke E. H.: Simulated Earthquake Motions Compatible with Prescribed Response Spectra.

MIT Civil Engineering. Research Report R76-4. Massachussets Institute of Technology, Cambridge, Mass., 1976.

- Since SimSeisme is based on a stationary simulation, i. e. on a superposition of sinus waves, the generated earthquakes provide a poor simulation of recorded earthquakes. The dynamic response calculated with stationary synthetic earthquakes may considerably diverge from those calculating with recorded earthquakes, more specifically by non-linear structural behaviour. Synthetic earthquakes generated with a non-stationary simulation such as the one of Sabetta and Pugliese provide a much better simulation of recorded earthquakes.

- The following parameters defining the target spectrum are specified in SpectreCible.m:SaCible: target spectrum, generally a design spectrum

LimSup and LimInf: upper and lower limites of the tolerable divergence to target spectrum

PlatoSup and PlatoInf: upper and lower frequencies defining the plateau of target spectrum (used by SimSeisme for accelerogram adaptation)

- The following parameters are specified in SimSeisme.m:NbPt: number of points, should be a power of 2 with a linear frequency repartition for using FFT

EFz: discretisation frequency, EFz=1/(time interval)

S: strong motion duration (depends on the envelope used)

RepFrequ: uniform frequency repartition for the generation, linear or logarithmic.

EnvelUsed: envelope used for the multiplication of the gross acceleration, compound (comp), exponential (expn) or without (sans)

Nseisme: desired number of earthquakes to be generated

MaxIter: maximum number of iterations for matching target spectrum (if reached, restart with a new phase angle content)

Z: damping ratio, usually Z=5%

- The following parameters define the envelopes in SimSeisme.m:Trise: rise time in envelope compound

Ipow: parameter of rising curve in envelope compound

Tlevel: level time in envelope compound

alpha: parameter of decreasing curve in envelope compoundalpha: parameter of positive exponential part in envelope exponential

beta: parameter of negative exponential part in envelope exponential

- Due to the use of FFT, linear frequency repartition leads to much faster calculations than logarithmic frequency repartition. However, calculating time depends on the specified tolerable divergence to the target spectrum. Too small tolerable divergences may lead to unpracticable calculating time. Moreover, the Fourier amplitude content of the earthquake is altered at each iteration for matching target spectrum. For this reason, it is recommended to keep the maximum iteration number (MaxIter) as small as possible.

- Since in the model the phase angle content is randomly distributed, it is recommended to change the seed value of the random generator

before each start: rand(“seed”,sum(069*clock)), i. e. change the actual value of 069 by any other value.

### Sabetta

Sabetta is an OCTAVE code for the generation of synthetic earthquakes with a non-stationary simulation according to the model of Sabetta and Pugliese.

By contrast to the stationary simulation of SimSeisme, Sabetta does not lead to synthetic earthquakes compatible to a design spectrum. However the simulation is much closer to recorded earthquakes and provides more reliable seismic structural response, more specifically by non-linear structural behaviour. The three input parameters (magnitude, epicentral distance and soil conditions) may be adjusted to approach a design spectrum for the mean values of several generated synthetic earthquakes.

#### To run Sabetta.m:

- Run Octave
- Type Sabetta and Return
- Answer the questions concerning magnitude, epicentral distance and soil conditions

#### Informations and recommendations

- Sabetta is based on the work of Sabetta and Pugliese. More informations may be found in their publication:Sabetta F., Pugliese A.: Estimation of Response Spectra and Simulation of Nonstationary Earthquake Ground Motions.

Bulletin of the Seismological Society of America, Vol. 86, No. 2, pp. 337-352, April 1996.

- Patience, the generation of an accelerogram takes several minutes! The calculating time may be shortened by the modification (300 or less instead of 400) of the considered frequencies in the generation (near the end of Sabetta.m):for N=1:400,

f=N/(T4/3.0); …

- Since in the model the phase angle content is randomly distributed, it is recommended to change the seed value of the random generator

before each start: rand(“seed”,sum(871*clock)), i. e. change the actual value of 871 by any other value.

### Takeda

Takeda is an OCTAVE code for the calculation of the seismic response of a non-linear SDOF defined by the well-known Takeda hysteretic model.

#### To run Takeda.m:

- Run Octave
- Type Takeda and Return
- Answer the questions to define the non-linear SDOF

#### Informations and recommendations

- The hysteretic model was first proposed by Takeda et al. and afterwards extended by different authors. More informations may be found in the following publications:Takeda T., Sozen M. A., Nielsen N. N.: Reinforced Concrete Response to Simulated Earthquakes.

ASCE, Journal of the Structural Division, Vol. 96, No. ST12, December 1970.Allahabadi R., Powel G.: Drain-2DX User Guide. Report No. UCB/EERC-88/06.

College of Engineering, University of California, Berkeley 1988.

- The following parameters are used in Takeda.m:Fileacc: name of the file containing the ground accelerations

Scale: percentage of the earthquake to be used for the calculation

f: initial natural frequency of the SDOF

hard: post yield stiffness in % of the initial stiffness

z: damping ratio in %

Frict: friction ratio in o/oo

Ulin: elastic displacement (elastic behaviour of the SDOF), if unknown set a large value for its determination

R: strength reduction factor, the yield displacement corresponds to Ulin/R

Alpha: parameter defining the degradation of unloading stiffness (actual stiff.=initial stiff.*(peak displ./yield displ.)^-alpha)

Beta: parameter defining the reloading curve (beta=1 target peak displacement and beta=0 target yield displacement)

Mfz: discretisation frequency, Mfz=1/(time interval)

nb: number of points to be considered

- Check always the calculated relative displacement reaction force relationships carefully because, in some special cases, the implemented rules of the hysteretic model may lead to unrealistic structural seismic response.

- Since Takeda runs with the Central Difference Algorithmus, the numerical stability is ensured only for initial natural frequencies below Mfz/pi.

### Qmodel

Qmodel is an OCTAVE code for the calculation of the seismic response of a non-linear SDOF defined by the well-known Q hysteretic model.

The Q-model is a simplified (set symmetric) Takeda model in which the absolute value of peak displacement is considered for both directions in order to define the degradation of unloading stiffness and the reloading curves.

#### To run Qmodel.m:

- Run Octave
- Type Qmodel and Return
- Answer the questions to define the non-linear SDOF

#### Informations and recommendations

- The hysteretic model was proposed by Saiidi and Sozen. More informations may be found in their publication:Saiidi M., Sozen M. A.: Simple Nonlinear Seismic Analysis of R/C Structures.

ASCE, Journal of the Structural Division, Vol. 107, No. ST5, May 1981.

- The following parameters are used in Qmodel.m:Fileacc: name of the file containing the ground accelerations

Scale: percentage of the earthquake to be used for the calculation

f: initial natural frequency of the SDOF

hard: post yield stiffness in % of the initial stiffness

z: damping ratio in %

Frict: friction ratio in o/oo

Ulin: elastic displacement (elastic behaviour of the SDOF), if unknown set a large value for its determination

R: strength reduction factor, the yield displacement corresponds to Ulin/R

Alpha: parameter defining the degradation of unloading stiffness (actual stiff.=initial stiff.*(peak displ./yield displ.)^-alpha)

Mfz: discretisation frequency, Mfz=1/(time interval)

nb: number of points to be considered

- Check always the calculated relative displacement reaction force relationships carefully because, in some special cases, the implemented rules of the hysteretic model may lead to unrealistic structural seismic response.

- Since Qmodel runs with the Central Difference Algorithmus, the numerical stability is ensured only for initial natural frequencies below Mfz/pi.

### GamaModel

GamaModel is an OCTAVE code for the calculation of the seismic response of a non-linear SDOF defined by the gamma-model and the elasto-plastic model.

The gamma-model is an improved elasto-plastic model in which the reloading curves of large yield excursion cross the elastic portion of the envelope at a relative height of 1-gamma. Otherwise the reloading curves take for target the point corresponding to the actual peak displacement. Even if the gamma-model does not consider the degradation of the unloading stiffness, the model provides a good simulation of reinforced concrete structures. The name of the model derives from the shape of the created force displacement relationships for the first cycles which look like the greek symbol gamma. GamaModel also includes the too simple elasto-plastic model.

GamaModel.m

#### To run GamaModel.m:

- Run Octave
- Type GamaModel and Return
- Answer the questions to define the non-linear SDOF

#### Informations and recommendations

- The hysteretic model was proposed in my PhD thesis.

- The following parameters are used in GamaModel.m:Fileacc: name of the file containing the ground accelerations

Scale: percentage of the earthquake to be used for the calculation

f: initial natural frequency of the SDOF

hard: post yield stiffness in % of the initial stiffness

z: damping ratio in %

Frict: friction ratio in o/oo

ulin: elastic displacement (elastic behaviour of the SDOF), if unknown set a large value for its determination

R: strength reduction factor, the yield displacement corresponds to Ulin/R

soft: parameter defining the model used (soft=0 for elasto-plastic and soft=1 for gamma-model)

Gama: parameter defining the cross point between reloading curve and the elastic portion of the envelope for large yield excursion

Mfz: discretisation frequency, Mfz=1/(time interval)

nb: number of points to be considered

- By using Gama=0 with the gamma-model, the whole reloading curves take the point corresponding to yield displacement for target.

- Check always the calculated relative displacement reaction force relationships carefully because, in some special cases, the implemented rules of the hysteretic model may lead to unrealistic structural seismic response.

- Since GamaModel runs with the Central Difference Algorithmus, the numerical stability is ensured only for initial natural frequencies below Mfz/pi.

### RespSpectra

RespSpectra is an OCTAVE code, which enables the calculation of the response spectrum of earthquake acceleration time-histories.

#### To run RespSpectra.m:

- Run Octave
- Type RespSpectra and Return
- Answer the questions

#### Informations and recommendations

- Since RespSpectra runs with the Central Difference Algorithmus, the upper frequency corresponds to 1/(time interval * pi).
- RespSpectra calculates the spectral values for 200 frequencies with an uniform logarithmic distribution. The number of frequencies may be changed by changing the variable nf.