A Constitutive Model for Describing the Tensile Response of Woven Polyethylene Terephthalate Geogrids after Damage
Abstract
:1. Introduction
- T: tensile load per unit width;
- J: tangent stiffness;
- ε: tensile strain;
- a, b, and c: model parameters;
- εmax: strain at maximum load.
- RT, RJ and Rε: scaling factors;
- X: undamaged sample;
- Y: damaged sample.
- Apply a constitutive model to describe the short-term tensile response of undamaged and damaged specimens of two woven Polyethylene Terephthalate (PET) geogrids; estimate the model parameters; assess the goodness of the fits; statistically compare experimental and fitted data.
- Determine the scaling factors by relating the tensile properties of undamaged and damaged samples of the geogrids.
- For each geogrid, obtain the tensile load–strain curve of damaged samples by applying scaling factors to the plot of the undamaged sample; assess the goodness of the fits; statistically compare predicted and fitted data.
2. Materials
3. Methods
3.1. Numerical Regressions (Curve Fittings)
3.2. Mathematical Relations between the Model Parameters and the Tensile Properties
- Ji: initial tangent stiffness;
- Tmax: tensile strength;
- εi: strain for which the hyperbolic and exponential components intersect (Figure 1).
3.3. Damaged Curves Described Using Undamaged Data and Scaling Factors
4. Results and Discussions
5. Conclusions
- The model was able to qualitatively describe the tensile load–strain response of undamaged and damaged specimens of both geogrids (high R2 values).
- If compared to experimental values, the model proved capable of fitting the tensile strength of most samples of the geogrids (for most samples, there was no significant mean difference between the experimental and fitted tensile strength).
- The model allowed us to describe the tensile load–strain curve of a geogrid (before and after damage) only from its tensile properties: , and .
- Regardless of the type of damage, the model was able to describe tensile load–strain curves of damaged samples using data from undamaged samples and scaling factors.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Geosynthetic | GWP55 | GWP60 | ||
---|---|---|---|---|
Type | Geogrid | Geogrid | ||
Structure | Woven | Woven | ||
Constituent polymer | PET | PET | ||
Nominal tensile strength (kN/m) | 55 | 60 | ||
Nominal tensile strain (%) | 10.5 | 14.0 | ||
Grid spacing (mm × mm) | 25 × 25 | 20 × 20 |
Term | Symbol | Definition |
---|---|---|
Model parameters | Parameters of the constitutive model (Equation (1)) | |
Parameter estimates | – | Model parameters estimated via numerical regressions of experimental data |
Mean parameter estimates | – | Mean estimates of the model parameter of a sample |
Median parameter estimates | – | Median estimates of the model parameter of a sample |
Tensile properties | Tensile properties of a certain geogrid | |
Mean undamaged tensile properties | – | Mean experimental tensile properties of an undamaged sample |
Mean damaged tensile properties | – | Mean experimental tensile properties of a damaged sample |
Predicted damaged parameters | Model parameters for the response after damage predicted from undamaged data using scaling factors (Equations (3)–(5)) | |
Representative curve: | – | Load–strain curve that best represents the trends in the data of a sample |
| – | Load–strain curve plotted using mean parameter estimates |
| – | Load–strain curve plotted using median parameter estimates |
| – | Experimental load–strain curve that visually is in an intermediate position relative to the other curves of a sample |
Mean Experimental Tensile Properties | Mean Fitted Tensile Properties (Equation (1)) | |||
---|---|---|---|---|
Sample | εmax | Tmax | Tmax | Ji |
% | kN/m | kN/m | kN/m | |
GWP55 UND | 8.5 | 46.72 | 44.66 | 957.03 |
GWP55 MEC | 7.8 | 39.80 | 37.88 | 938.93 |
GWP60 UND | 14.0 | 66.84 | 62.70 * | 734.53 |
GWP60 MEC | 13.8 | 50.11 | 48.16 | 744.54 |
GWP60 DDI S90 | 14.7 | 63.01 | 59.19 | 708.04 |
GWP60 DDI S98 | 14.2 | 59.23 | 55.99 | 786.16 |
Sample | Mean Parameter Estimates | Tensile Properties | Scaling Factors | ||||||
---|---|---|---|---|---|---|---|---|---|
Sample | Size | Equation (1) (SPSS®) | Mean Curve | Equation (3) | Equation (4) | Equation (5) | |||
N | a | b | c | Tmax | Ji | ||||
– | m/kN | m/kN | – | kN/m | kN/m | – | – | – | |
GWP55 UND | 20 | 0.1085 | 0.0198 | 0.1763 | 44.28 | 921.50 | – | – | – |
GWP55 MEC | 15 | 0.0936 | 0.0240 | 0.1957 | 37.55 | 1068.35 | 0.848 | 1.159 | 0.917 |
GWP60 UND | 5 | 0.1364 | 0.0139 | 0.0703 | 62.69 | 733.18 | – | – | – |
GWP60 MEC | 5 | 0.1220 | 0.0190 | 0.0598 | 47.57 | 819.48 | 0.759 | 1.118 | 0.985 |
GWP60 DDI90 | 5 | 0.1418 | 0.0149 | 0.0675 | 59.03 | 705.14 | 0.942 | 0.962 | 1.050 |
GWP60 DDI98 | 5 | 0.1278 | 0.0159 | 0.0701 | 55.82 | 782.26 | 1.013 | 0.890 | 1.067 |
Predicted Parameters | Mean Parameter Estimates | |||||
---|---|---|---|---|---|---|
Sample | Equation (9) | Equation (10) | Equation (11) | Equation (1) (SPSS®) | ||
m/kN | m/kN | – | m/kN | m/kN | – | |
GWP55 MEC | 0.0936 | 0.0240 | 0.1957 | 0.0936 | 0.0240 | 0.1957 |
GWP60 UND | 0.1220 | 0.0190 | 0.0598 | 0.1220 | 0.0190 | 0.0598 |
GWP60 DDI90 | 0.1418 | 0.0149 | 0.0675 | 0.1418 | 0.0149 | 0.0675 |
GWP60 DDI98 | 0.1278 | 0.0159 | 0.0701 | 0.1278 | 0.0159 | 0.0701 |
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Lombardi, G.; Pinho-Lopes, M.; Paula, A.M.; Pereira, A.B. A Constitutive Model for Describing the Tensile Response of Woven Polyethylene Terephthalate Geogrids after Damage. Materials 2023, 16, 5384. https://doi.org/10.3390/ma16155384
Lombardi G, Pinho-Lopes M, Paula AM, Pereira AB. A Constitutive Model for Describing the Tensile Response of Woven Polyethylene Terephthalate Geogrids after Damage. Materials. 2023; 16(15):5384. https://doi.org/10.3390/ma16155384
Chicago/Turabian StyleLombardi, Giovani, Margarida Pinho-Lopes, António Miguel Paula, and António Bastos Pereira. 2023. "A Constitutive Model for Describing the Tensile Response of Woven Polyethylene Terephthalate Geogrids after Damage" Materials 16, no. 15: 5384. https://doi.org/10.3390/ma16155384