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The fracture characteristics of any type of concrete can be determined using a suitable analytical model combined with inverse analysis. The inverse analysis procedure generally consists of iterative modus operandi, which fit experimental flexural test data to obtain the parameters that define the tensile stress-crack opening (σ-w) curves. The problem with this procedure is that it could yield ambiguous results, i.e., the procedure could yield more than one solution. To resolve this, a sophisticated optimization programme known as the probabilistic global optimization Lausanne (PGSL) has been used, along with the analytical model. In addition, the invention includes the closed-form solution for the tetralinear model, which is most suited for fibre reinforced concrete. The advantage of this invention is that the user can indirectly determine the fracture properties without performing a tedious tensile test. The obtained tensile constitutive relation can be used in finite element analysis to predict the behavior of concrete structures subjected to different types of loading conditions.
sigw-Concrete©: Software for obtaining the tensile constitutive model of
plain and fibre reinforced concrete using inverse analysis of experimental
data from three-point bending tests of notched beams
User Guide
is a software developed to provide a set of parameters that characterize
the tensile behavior of plain and fiber reinforced concrete using an inverse analysis
approach (Refer Stephen et al., 20192 for details on the analysis). This document describes
the procedure to obtain the tensile constitutive model using sigw-Concrete.
First, copy the sigw-Concrete folder (all files) to your computer. The sigw-Concrete folder
consists of set of .dat and .exe files, which can be used to run the inverse analysis procedure
to obtain the parameters required for constructing the tensile stress-crack opening (σ-w)
curve. Note that the .dat files can be edited using Notepad software. The steps involved are
as follows (default values are already specified):
Step 1:
Open experiment.dat file and import the three-point bending experimental test data as two
columns, load (kN) in the first column and CMOD (mm) in the second column. The
experiment.dat file has typical three-point bending test data of fibre reinforced concrete,
which can be used to get familiarized with the software.
Open Output_sigw-Concrete.xls from the sigw-Concrete directory. If the Microsoft office
does not allow to edit the excel sheet, select the edit anyway options in the protection view
settings. Copy and paste the data in the experiment.dat file to the experiment excel sheet.
Note down the Youngs modulus of concrete, E. Make sure the P/CMOD is calculated
within the initial elastic region.
Step 3:
Open problem.dat. Input the range in the file stating the minimum value, maximum value
and accuracy of the variable, separated by commas. For example, for ft, the range should be
specified as var1= 2,6,0.1. In the case of Youngs modulus, use the value obtained in the
previous step, both the minimum and maximum value will be the same. The optimization
algorithm finds a solution for each variable of the model within the specified range, which
can be chosen based on Stephen et al. (2019). Enter the range in the following order:
var1= (ft)min, (ft)max, accuracy (in MPa)
var2= (E)min, (E)max, accuracy (in MPa)
sigw-Concrete© is supposed to be used only for research purposes. Comments are
welcome, although the developers are not responsible for maintenance or consequences
from misuse. Refer Stephen et al., 20192 for nomenclature.
2Stephen S. J., Raphael B., Gettu R., and Jose S., “Determination of the tensile constitutive relations of fibre
reinforced concrete using inverse analysis”, Construction and Building Materials, 195, 405-414 (2019)
var3= (σ1/ft)min, (σ1/ft)max, accuracy (in MPa/MPa)
var4= (σ2/ft)min, (σ2/ft)max, accuracy (in MPa/MPa)
var5= (σ3/ft)min, (σ3/ft)max, accuracy (in MPa/MPa)
var6= (w1)min, (w1)max, accuracy (in mm)
var7= (w2)min, (w2)max, accuracy (in mm)
var8= (w3)min, (w3)max, accuracy (in mm).
The range for different variables has to be specified in order to minimize the optimization
Step 4:
Open rilemb5.dat. Input the dimensions of the notched beam in the following order:
Span (in mm)
Depth (in mm)
Width (in mm)
Notch length (in mm)
Thickness of knife edge (in mm)
Normal force in beam (in kN)
Fibre length (in mm)
Step 5:
Once all the .dat files are ready, open sigw-Concrete(Open#1).exe
and then sigw-Concrete(Open#2 and Click Start Optimisation).exe application.
It is important to note the order of opening application, as the software does not respond
properly, if the order is changed.
Step 6:
Click START OPTIMISATION to initiate the inverse analysis procedure. The error
between the experimental and predicted values will be displayed on the optimization client
toolbar. As the optimization progresses, the error value decreases. Stop the optimization,
once there is no further decrease in the error value. Close the two toolbars.
Step 7:
Open compare.dat, to obtain the final fit between the experimental and predicted curve. For
obtaining the parameters of the σ-w curve, export the values from bestrun.dat. Select all the
data in the compare.dat and bestrun.dat file, copy and paste it in the designated area in the
sheet named sigw-Concrete, in the Output_sigw-Concrete.xls excel file. The tensile
stress-crack opening (σ-w) curve can be obtained from the same worksheet.
For the next set of experimental data, close all toolbars and repeat the whole procedure.
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