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A short-term model for extrapolating unconfined creep deformation data for woven geotextiles
Geotextiles and Geomembranes xxx (xxxx) xxxx
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A short-term model for extrapolating unconfined creep deformation data for woven geotextiles José Luiz Ernandes Dias Filho∗, Paulo Cesar de Almeida Maia, Gustavo de Castro Xavier Civil Engineering Laboratory, Darcy Ribeiro State University of Northern Rio de Janeiro, 28013-602, Campos dos Goytacazes, RJ, Brazil
A R T I C LE I N FO
A B S T R A C T
Keywords: Geosynthetics Geotextiles Creep Durability
This study reports results for creep deformation with data acquired in 72 h of testing. A system capable of performing 8 simultaneous tests was used to test four woven geotextiles of different weights, following all of the recommendations outlined in the standards related to equipment setup. A mathematical model was used to generate time-dependent creep curves for four different load levels up to 40% for each sample and using a database which presented stage II creep conditions (i.e. without rupture) through the end of the tests, up to 10,000 h. The coefficients of variation for the conventional creep tests were below 10%. The compatibility between the experimental data and the model indicates that short-term (72 h) loading tests may be used to extrapolate long-term creep deformation in woven geotextiles.
1. Introduction Creep is the deformation that occurs in a material that is subjected to constant loading over time. Creep testing is important for the characterization of the durability of a geosynthetic, because the results serve as an estimate of the useful life of the material. Since projects that involve the use of geosynthetics require long-term performance, it is reasonable to characterize the material according to this property. Consequently, geosynthetics are generally characterized with standardized creep tests (NBR 15.226, 2005, ASTM D 5262, 2007; ISO 13431, 2016), performed under controlled conditions of temperature and relative humidity. However, this technique involves the use of costly long-term tests to obtain a significant creep deformation response, which can take up to 10,080 h. The three stages of creep behavior can be identified in the curve which measures strain as a function of time for a geosynthetic under constant load over an extended period. Primary creep, also known as the transient phase, is characterized by a strain rate that decreases with time. In secondary creep the linearity of the curve prevails. Whereas tertiary creep is characterized by an increase in the creep strain rate that causes the material to rupture in a short period of time. It is important to note that this behavior pattern may vary according to the type of polymer (Yeo and Hsuan, 2010; Guimarães et al., 2016), the loading level of the test specimen (Simonini and Gottardi, 2003; Balakrishnan and Viswanadham, 2017) and the rate of application of the load (Shinoda and Bathurst, 2004; Bathurst et al., 2012). Depending
∗
on these variables, creep curves may obtain a predominant stage characteristic. The curve format can be described with mathematical models (Costanzi et al., 2003; Guo et al., 2005; Bueno et al., 2005; Kongkitkul et al., 2014) enabling extrapolation of data obtained in the laboratory in order to identify patterns of interest, such as the rate of creep deformation relative to variations in temperature or load level, as well as rupture. This test method is intended for use in determining the unconfined tension creep and creep rupture behavior of geosynthetics at constant temperature when subjected to a sustained tensile loading and is applicable to all geosynthetics. According to NBR 15226 (2005), there are two variants of creep testing: the determination of creep deformation behavior and the determination of the creep rupture load. In the present study, for the determination of creep deformation behavior, four tests were performed at different load levels ranging from 5% to 60% and employing a testing time of up to 1008 h. However, creep rupture tests conducted to analyze rupture loads would apply higher levels between 50% and 90% of tensile strength. The evaluation of alternatives for obtaining creep deformation results in a fast, precise and representative way, is the focus of numerous recent studies. Such studies examine the factors that affect geosynthetic deformation behavior when submitted to constant loading. The principal approaches include: the Stepped Isothermal Method (SIM) and Time-Temperature Superposition (TTS), which accelerate creep strain with increasing temperature (Zornberg et al., 2004; Yeo and Hsuan, 2009, 2010; Leshchinsky et al., 2010; França and Bueno, 2011;
Corresponding author. E-mail addresses: [email protected] (J.L.E. Dias Filho), [email protected] (P.C.d.A. Maia), [email protected] (G.d.C. Xavier).
https://doi.org/10.1016/j.geotexmem.2019.103492 Received 20 June 2019; Received in revised form 4 August 2019; Accepted 4 August 2019 0266-1144/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: José Luiz Ernandes Dias Filho, Paulo Cesar de Almeida Maia and Gustavo de Castro Xavier, Geotextiles and Geomembranes, https://doi.org/10.1016/j.geotexmem.2019.103492
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Table 1 Reference values of the nominal characteristics of the woven geotextiles. Property
PET340
PP500
PET740
PP925
Ultimate tensile strength (kN/m) Elongation at rupture (%) Mass per unit area (g/m2) Thickness (mm)
52.5 ± 1.6 16.5 ± 1,8 340 ± 8 0.51 ± 0.02
106.2 ± 2.0 20.1 ± 1.3 500 ± 9 1.53 ± 0.04
150.7 ± 5.2 34.8 ± 1.8 740 ± 23 1.17 ± 0.01
155 ± 1.6 28.5 ± 2.1 925 ± 25 2.62 ± 0.06
Fig. 1. Broad view of the 8 machines for execution of creep tests.
Fig. 2. Typical curves obtained from the creep tests.
This study seeks to contribute to the understanding of creep deformation behavior in woven geotextiles by evaluating an alternative to conventional creep testing using short-term unconfined tension creep test data for extrapolating deformation behavior.
Achereiner et al., 2013); procedures for examining degradation due to exposure (Guimarães et al., 2016; Pinho-Lopes et al., 2018); as well as analyses of the influence of soil confinement on the behavior of geosynthetics, (Sabir and Brachman, 2012; Zhang et al., 2014; Becker and Nunes, 2015; Holtz, 2017; Plácido et al., 2018; Nuntapanich et al., 2018). Studies that evaluated deformations in structures dimensioned with geosynthetics reported strain limit data under 10% (Perkins, 2000; Hinchberger and Rowe, 2003; Cantré and Saathoff, 2011; Van Eekelen et al., 2012; Yapage et al., 2014; Liu et al., 2017; Zhao et al., 2019), which in engineering practice indicates low deformation in soil-geosynthetic interaction, increasing project stability.
2. Materials and methods 2.1. Study material For this study, four woven geotextiles of different weights were chosen for the testing program. Two tests were carried out on monofilament polypropylene (PP) and two on multifilament polyester (PET) 2
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Fig. 3. Comparison between the experimental data and the extrapolation model for the creep deformation tests at four loading levels for each polymer tested.
Table 2 Creep curve parameters calculated from experimental data collection over time for each geotextile tested. Time
minutes
hours
days
PET340
4 8 15 30 1 2 4 8 1 3 7 14 21 42
PP500
PET740
PP925
c
d
e
c
d
e
c
d
e
c
d
e
0.411 0.348 0.222 0.180 0.184 0.168 0.172 0.168 0.150 0.143 0.139 0.136 0.135 0.136
-0.265 -0.149 0.045 0.119 0.118 0.153 0.137 0.147 0.191 0.210 0.221 0.226 0.233 0.203
0.361 0.369 0.374 0.374 0.377 0.376 0.374 0.374 0.375 0.375 0.375 0.375 0.375 0.376
0.082 0.091 0.085 0.088 0.099 0.094 0.093 0.089 0.089 0.089 0.088 0.089 0.089 0.087
0.253 0.250 0.249 0.251 0.247 0.247 0.245 0.243 0.240 0.240 0.240 0.240 0.240 0.240
0.520 0.483 0.496 0.491 0.448 0.465 0.460 0.463 0.456 0.465 0.454 0.452 0.452 0.461
0.055 0.035 0.021 0.015 0.011 0.009 0.008 0.007 0.007 0.006 0.006 0.006 0.006 0.006
0.489 0.589 0.722 0.803 0.864 0.909 0.947 0.973 0.974 0.988 0.987 0.996 0.991 0.991
0.406 0.399 0.398 0.395 0.393 0.392 0.392 0.390 0.389 0.389 0.389 0.389 0.389 0.390
0.010 0.007 0.007 0.011 0.014 0.018 0.021 0.025 0.025 0.024 0.022 0.024 0.024 0.0243
0.889 0.986 0.995 0.883 0.838 0.788 0.758 0.718 0.724 0.736 0.757 0.740 0.741 0.7361
0.275 0.275 0.276 0.277 0.280 0.282 0.285 0.286 0.287 0.288 0.288 0.288 0.288 0.2878
c, d = multiplication coefficient c (%/Td) and the dimensionless power d of the power behavior of “a” in Eq. (1). e = slope coefficient (%/kN/m) and the linear behavior of “b” from Eq. (1).
coefficients of variation falling below 10%. The samples were cut in the machine direction, and the tensile strength of the virgin sample was determined by wide-width strip method test according to the NBR 15865 (2010) and ASTM D 5035-11 (2015).
as shown in Table 1. The physical index tests were conducted according to the norms for determining mass per unit area (ISO 9864, 2013, ISO 9864, 2005, ASTM D5261, 2010) and nominal thickness (NBR ISO 9863–1, 2013, ISO 9863-1, 2016, ASTM D5199, 2012), with 3
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Table 3 Coefficient statistics for the creep curve parameters. Time
PET340 c
minutes
hours
days
4 8 15 30 1 2 4 8 1 3 7 14 21 42
PP500
d
e
c
PET740
d
e
c
PP925
d
e
c
d
e
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
0.192 0.175 0.161 0.155 0.153 0.149 0.147 0.144 0.140 0.138 0.136 0.135 0.135 0.136
42 32 16 12 11 10 9 8 4 2 1 0 0 0
0.113 0.143 0.167 0.178 0.184 0.191 0.196 0.204 0.214 0.219 0.221 0.221 0.218 0.203
125 69 33 24 21 18 17 13 7 5 5 6 7 0
0.374 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.376
1 0 0 0 0 0 0 0 0 0 0 0 0 0
0.089 0.090 0.090 0.090 0.090 0.090 0.089 0.088 0.088 0.088 0.088 0.088 0.088 0.087
4 4 4 4 4 2 2 1 1 1 1 1 1 0
0.245 0.244 0.244 0.243 0.242 0.242 0.241 0.240 0.240 0.240 0.240 0.240 0.240 0.240
2 2 2 1 1 1 1 0 2 2 2 2 2 0
0.469 0.465 0.464 0.461 0.458 0.459 0.458 0.458 0.457 0.457 0.455 0.455 0.457 0.461
4 3 3 2 1 1 1 1 0 0 0 0 0 0
0.014 0.011 0.009 0.008 0.007 0.007 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006
98 74 49 34 22 14 8 4 3 2 2 3 2 0
0.873 0.903 0.929 0.947 0.962 0.973 0.981 0.986 0.988 0.991 0.991 0.993 0.991 0.991
18 14 9 6 4 3 2 1 1 0 0 0 0 0
0.393 0.392 0.391 0.391 0.390 0.390 0.390 0.389 0.389 0.389 0.389 0.389 0.390 0.390
1 1 1 1 0 0 0 0 0 0 0 0 0 0
0.018 0.019 0.020 0.021 0.022 0.023 0.024 0.024 0.024 0.024 0.024 0.024 0.024 0.024
37 35 30 22 16 10 6 3 3 3 3 1 1 0
0.806 0.800 0.784 0.765 0.754 0.744 0.739 0.736 0.739 0.742 0.743 0.739 0.738 0.736
11 12 10 6 4 3 2 2 1 1 1 0 0 0
0.283 0.284 0.284 0.285 0.286 0.286 0.287 0.287 0.288 0.288 0.288 0.288 0.288 0.288
2 2 2 1 1 1 0 0 0 0 0 0 0 0
M = mean; CV = coefficient of variation in %; c, d = multiplication coefficient c (%/Td) and the dimensionless power d of the power behavior of “a” in Eq. (1); e = slope coefficient (%/kN/m) and the linear behavior of “b” from Eq. (1).
laboratory could be realistically estimated from a short-term response. Tests were conducted in the laboratory with internal temperature controlled at 20 ± 2 °C and relative humidity of 65 ± 5% for a period of up to 10,080 h. Creep deformation behavior for the four woven geotextile samples was determined for loads of 10%, 20%, 30% and 40% of the ultimate tensile strength according to the testing standards (NBR 15.226, 2005; ASTM D 5262, 2007; ISO 13431, 2016). Isochronous curves, representing both short-term and long-term straintime relationships, were obtained from the laboratory test results for all samples and load levels. Measurements of the displacements in the test samples were taken at predetermined times of 1, 2, 4, 8, 15, 30 and 60 min, then at 2, 4, 8 and 24 h, and finally at 3, 7, 14, 21 and 42 days. While, all four materials studied were tested over a period of 1008 h, the test was continued for the full 420-day, or 10,080-hour, measurements only for some load levels, due to the limited availability of the testing equipment. The final resulting creep strain data from conventional tests enables the analysis of the behavior of the geosynthetic over the long term, that is, its durability. Therefore, in order to analyze creep strain in this study, experimental data was collected for up to 420 days or 10,080 h for samples PET340 10%, PP500 10%, PET740 10%, PET740 20%, PP925 10% and PP925 20%. However, the study was able to show that similar durability results could be achieved by extrapolating the data from only 3 days, or 72 h, of testing, yielding a significant reduction in the time for data acquisition and analysis. The width of the test specimens was 50 ± 5 mm and, gripped in the clamps with a gauge length of 25 mm, according to tensile strength strip
Table 4 Evaluation of the correlation coefficients between the database measured tensile strain at end of test and the tensile strain extrapolated with Eq. (2). Sample
Load level (%T)
Time (hours)
Measured tensile strain (%)
Tensile strain extrapolated (%)
R2 (dimensionless)
PET340
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40
10080 2520 2520 2520 10080 2520 2520 2520 10080 10080 5040 5040 10080 10080 5040 5040
3.8 5.1 7.1 9.0 4.5 6.9 9.6 12.4 6.6 13.2 19.0 25.8 5.0 10.0 15.2 19.6
3.2 5.0 7.1 9.1 4.1 6.7 9.6 12.4 6.4 12.8 19.0 25.3 5.3 10.2 14.8 19.6
0.998 0.999 0.999 0.998 0.999 0.999 0.998 0.999 0.99 0.999 0.997 0.995 0.997 0.998 0.999 0.999
PP500
PET740
PP925
R2 = correlation coefficient.
2.2. Methodology The test program consisted of characterization of creep deformation for the four geotextiles selected. The main objective was to determine whether the long-term response of the materials studied in the
Table 5 Evaluation of the correlation coefficients between the database from key research studies and estimates obtained in the present study. Reference
Geosynthetic type
Polymer
Load level analysed (T%)
Total time (h)
Method
c
d
e
R2
Andrawes et al. (1984) Bueno et al. (2005)
GTXw GTXnw
conventional conventional
GGR GGR
1700 6
conventional SIM
Becker and Nunes (2015)
GGR
1000
Guimarães et al. (2016)
GTXw
PP
10, 20, 10, 20, 10, 20, 20, 30, 20, 30, 10, 20, 25, 40, 25, 40, 5, 10
1000 1000
Guo et al. (2005) Yeo and Hsuan (2010)
PP PP PET HDPE PET HDPE HDPE
conventional confined field test
0.005 0.059 0.044 0.001 0.044 0.044 0.130 0.001 0.070
0.626 0.456 0.611 0.583 0.611 0.611 0.618 2.044 0.585
0.600 1.047 0.980 0.185 0.072 0.119 0.982 0.101 0.316
0.986 0.950 0.950 0.986 0.937 0.930 0.976 0.932 0.930
30 40, 60 40, 60 40, 50, 55 40 30 55 55
2160
GTXw = = woven geotextile; GTXnw = nonwoven geotextile; GGR = geogrid; PP = polypropylene; PET = polyester; HPDE = High density polyethylene; SIM = Stepped Isothermal Method; c, d = multiplication coefficient c (%/Td) and the dimensionless power d of the power behavior of “a” in Eq. (1); e = slope coefficient (%/kN/m) and the linear behavior of “b” of Eq. (1); R2 = correlation coefficient. 4
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statistical calculations excluded data recorded at 4 and 8 min). Table 3 shows that, from the first day of testing, the data showed good representativeness, with coefficients of variation below 10% for all the geotextiles tested. Therefore, based on the coefficient data from the first 72 h (3 days) of testing, curves derived from Equation (2) were generated for each of the 4 datasets, and are illustrated by the red lines in Fig. 3. The graphs illustrate the low variation between the trends for each load level in the modeled data derived from the coefficients (the red line) and the experimental data represented by the black markers. This is confirmed by the correlation coefficient values greater than 0.990. The vertical line separating the primary and secondary creep stages was defined according the parameter a of Eq. (1), that is, the moment at which the tangent of the creep curve became constant. Table 4 shows a direct comparison, for the four types of geosynthetics, between the measured tensile strain at 10,080 h and the tensile strain extrapolated with Eq. (2) using the parameters derived from the measured data at three days. The results indicate that model can accurately extrapolate the tensile strain. This methodology has been applied, with other materials and test conditions, in a number of published studies to evaluate the potential for extrapolating experimental data. These studies also evaluated creep curve coefficients to perform the extrapolations. Table 5 presents these values, as well as the correlation between the database from the cited articles and the estimates obtained in the present study. This comparison shows satisfactory correlations, with R2 values greater than 0.95 for conventional tests and close to 0.93 for other test methods (SIM, confined tests and field tests). These behaviors may not be observed with test setup conditions different from those in the presented methodology.
tests (; NBR 15865, 2010), which obtained a lateral contraction of less than 10% (NBR 15226, 2005). It is important to note that the apparatus basically consists of a device (clamps) for securing the specimen without slipping and in such a way as to not to cause any damage, a system for determining the variation in the length of the measurement over time and a loading system with load application within 1 min, according to the standards (NBR 15226, 2005). Eight simultaneous creep tests (Fig. 1) were performed on suitable tension creep clamping systems, and in order to model the curve of the experimental data, a time-unit-dependent equation was used, as represented by Equation (1): y = aln(x) + b
(1)
Whereby, strain y can be obtained over time x. In the first part of the equation, the multiplier a corresponds to the creep index, which represents the slope of the curve formed by the deformation with application of the constant load. In the second part of the equation, b corresponds to the initial strain values obtained during one hour of creep test. When 0 < x < 1, the data range is not excluded, since parameter b corrects the data according to the applied load.
3. Results Based on the data, in order to demonstrate the short-term model, the creep index and initial strain values were found to follow a behavior trend as a function of the loading levels T at each stage of the creep test, according to Equation (2) and Fig. 2a: ε = cTdln (t) + eT
(2)
The behavior of the strain ε (%), over time t (hours), observed both in this study and in the literature, (for example Andrawes et al., 1984, Bueno et al., 2005, Guo et al., 2005; Yeo and Hsuan, 2010; Becker and Nunes, 2015; Guimarães et al., 2016), allowed the first portion of the curve to be considered similar to a potential function with the multiplication coefficient c and power d (Fig. 2b). Parameter c is a coefficient which correlates the deformation with the load level T raised to the power d (%/Td) and the load level T (kN/m) increases with the dimensionless attribute d, but does so at a slower rate than that of proportionality. This is aligned with the fact that in the creep tests the inclination of the curves gradually change with the increase in the load applied to the test sample. In the second part of the equation, the initial deformation behaves incrementally and linearly, according to the slope coefficient e, which correlates the deformation with the load level (%/kN/m) and is proportional to the magnitude of the imposed load, forming parallel curves according to the loading levels T in the tensile strength tests (Fig. 2c). It is important to highlight that Eq. (2) does not accurately predict the tensile strain of the geosynthetic in the condition where the tensile load is not constant. Fig. 3 represents a comparison between the experimental data and the results of the mathematical model, for the creep tests conducted at four loading levels for each material tested. The shape of the graphs shows linearity in the deformation behavior over time, indicating secondary stage creep. The formation of parallel curves for each of the loading levels was confirmed and the validity of the creep deformation equation model was determined for periods up to 10,080 h of constant load. The parameters of the creep curves, derived from Equation (2), were calculated from the first three measurements collected, that is, at 1, 2 and 4 min. Then, as each new data point was collected at the predetermined times in the testing program, the parameters were recalculated. Table 2 presents the values obtained for each geotextile, where the calculations were obtained with variable t in days. The parameters were evaluated statistically and Table 3 presents the mean and coefficient of variation for each parameter over time. In order to minimize possible differences in the manual loading mechanism, the statistical calculations excluded prior data readings, using only the measurement for a given time and subsequent data (e.g. at 15 min, the
4. Conclusions The present study developed a logarithmic model to determine the creep deformation behavior of woven geotextiles based on creep deformation tests in unconfined conditions. Eight creep-testing machines were used to evaluate four woven geotextiles of different weights, subjected to four different loading levels, with data collection over at least 1008 h of testing. Time-dependent creep deformation curves were generated in order to better interpret the behavior of the studied materials. A mathematical model was created to generate the creep curves and the results for each geotextile were analysed statistically. Coefficients of variation below 10% and confirmed compatibility and representativity. The results were also compared to a database from other published studies that have applied this extrapolation methodology. The evaluation of the data from only 72 h (3 days) of testing yielded reliable results for achieving fast and efficient creep deformation estimates. Findings show that short-term data measurements can be safely extrapolated to obtain long-term durability estimates for the material, in accordance with deformation limits defined by a project. Acknowledgements This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) Finance Code 001. The authors are also thankful to UENF and Huesker Brazil for additional financial support. References ABNT NBR 15226, 2005. Geossintéticos - Determinação do comportamento em deformação e na ruptura, por fluência sob tração não confinada. ABNT, Rio de Janeiro, RJ, Brazil. ABNT NBR 15865, 2010. Geomembranas e produtos correlatos — Determinação das propriedades de tração. ABNT, Rio de Janeiro, RJ, Brazil. ABNT NBR ISO 9863-1, 2013. Geossintéticos - Determinação da espessura a pressões
5
Geotextiles and Geomembranes xxx (xxxx) xxxx
J.L.E. Dias Filho, et al.
ISO 9863-1, 2016. Geosynthetics – Determination of Thickness at Specified Pressures – Part 1: Single Layers. ISO, Geneva, Switzerland. ISO 9864, 2005. Geosynthetics – Test Method for the Determination of Mass Per Unit Area of Geotextiles and Geotextile-Related Products. ISO, Geneva, Switzerland. Kongkitkul, W., Chantachot, T., Tatsuoka, F., 2014. Simulation of geosynthetic load–strain–time behaviour by the non-linear three-component model. Geosynth. Int. 21 (4), 244–255. Leshchinsky, D., Imamoglu, B., Meehan, C.L., 2010. Exhumed geogrid-reinforced retaining wall. J. Geotech. Geoenviron. Eng. 136 (10), 1311–1323. Liu, K.W., Rowe, R.K., Su, Q., Liu, B., Yang, Z., 2017. Long-term reinforcement strains for column supported embankments with viscous reinforcement by FEM. Geotext. Geomembranes 45 (4), 307–319. Nuntapanich, N., Kongkitkul, W., Tatsuoka, F., Jongpradist, P., 2018. Prediction of creep behaviour from load relaxation behaviour of polymer geogrids. Geosynth. Int. 1–16. Perkins, S.W., 2000. Constitutive modeling of geosynthetics. Geotext. Geomembranes 18 (5), 273–292. Pinho-Lopes, M., Paula, A.M., Lopes, M.L., 2018. Long-term response and design of two geosynthetics: effect of field installation damage. Geosynth. Int. 25 (1), 98–117. Plácido, R., Portelinha, F.H.M., Futai, M.M., 2018. Field and laboratory time-dependent behaviors of geotextiles in reinforced soil walls. Geosynth. Int. 25 (2), 215–229. Sabir, A., Brachman, R.W.I., 2012. Time and temperature effects on geomembrane strain from a gravel particle subjected to sustained vertical force. Can. Geotech. J. 49 (3), 249–263. Shinoda, M., Bathurst, R.J., 2004. Strain measurement of geogrids using a video-extensometer technique. Geotech. Test J. 27 (5), 456–463. Simonini, P., Gottardi, G., 2003. The viscoplastic behaviour of a geogrid-reinforced model wall. Geosynth. Int. 10 (1), 34–46. Van Eekelen, S.J., Bezuijen, A., Lodder, H.J., Van Tol, E.A., 2012. Model experiments on piled embankments. Part I. Geotext. Geomembranes 32, 69–81. Yapage, N.N.S., Liyanapathirana, D.S., Kelly, R.B., Poulos, H.G., Leo, C.J., 2014. Numerical modeling of an embankment over soft ground improved with deep cement mixed columns: case history. J. Geotech. Geoenviron. Eng. 140 (11), 04014062. Yeo, S.S., Hsuan, Y.G., 2009. Effects of temperature and stress on the short-and long-term compressive behavior of expanded polystyrene. Geosynth. Int. 16 (5), 374–383. Yeo, S.S., Hsuan, Y.G., 2010. Evaluation of creep behavior of high density polyethylene and polyethylene-terephthalate geogrids. Geotext. Geomembranes 28 (5), 409–421. Zhang, C.C., Zhu, H.H., Xu, Q., Shi, B., Mei, G.X., 2014. Time-dependent pullout behavior of glass fiber reinforced polymer (GFRP) soil nail in sand. Can. Geotech. J. 52 (6), 671–681. Zhao, L.S., Zhou, W.H., Geng, X., Yuen, K.V., Fatahi, B., 2019. A closed-form solution for column-supported embankments with geosynthetic reinforcement. Geotext. Geomembranes (in press). Zornberg, J.G., Byler, B.R., Knudsen, J.W., 2004. Creep of geotextiles using time–temperature superposition methods. J. Geotech. Geoenviron. Eng. 130 (11), 1158–1168.
especificadas. ABNT, Rio de Janeiro, RJ. ABNT NBR ISO 9864, 2013. Geossintéticos - Método de ensaio para determinação da massa por unidade de área de geotêxteis e produtos correlatos. ABNT, Rio de Janeiro, RJ. Achereiner, F., Engelsing, K., Bastian, M., Heidemeyer, P., 2013. Accelerated creep testing of polymers using the stepped isothermal method. Polym. Test. 32 (3), 447–454. Andrawes, K.Z., McGown, A., Kabir, M.H., 1984. Uniaxial strength testing of woven and nonwoven geotextiles. Geotext. Geomembranes 1 (1), 41–56. ASTM D 5035-11, 2015. Standard Test Method for Breaking Force and Elongation of Textile Fabrics (Strip Method). ASTM, West Conshohocken, PA, USA. ASTM D5199, 2012. Standard Test Method for Measuring the Nominal Thickness of Geosynthetics. ASTM, West Conshohocken, PA, USA. ASTM D5261, 2010. Standard Test Method for Measuring Mass Per Unit Area of Geotextiles. ASTM, West Conshohocken, PA, USA. ASTM D5262, 2007. Standard Test Method for Evaluating the Unconfined Tension Creep and Creep Rupture Behavior of Geosynthetics. ASTM, West Conshohocken, PA, USA. Balakrishnan, S., Viswanadham, B.V.S., 2017. Evaluation of tensile load-strain characteristics of geogrids through in-soil tensile tests. Geotext. Geomembranes 45 (1), 35–44. Bathurst, R.J., Huang, B., Allen, T.M., 2012. Interpretation of laboratory creep testing for reliability-based analysis and load and resistance factor design (LRFD) calibration. Geosynth. Int. 19 (1), 39–53. Becker, L.D.B., Nunes, A.L.L.S., 2015. Influence of soil confinement on the creep behavior of geotextiles. Geotext. Geomembranes 43 (4), 351–358. Bueno, B.S., Costanzi, M.A., Zornberg, J.G., 2005. Conventional and accelerated creep tests on nonwoven needle-punched geotextiles. Geosynth. Int. 12 (6), 276–287. Cantré, S., Saathoff, F., 2011. Design method for geotextile tubes considering strain formulation and verification by laboratory tests using photogrammetry. Geotext. Geomembranes 29 (3), 201–210. Costanzi, M.A., Bueno, B.S., Baras, L.C.S., Zornberg, J.G., 2003. Avaliação da Fluência de Geotêxteis não Tecidos com Ensaios Acelerados. Solos Rochas 26 (3), 217–228. França, F.A.N., Bueno, B.S., 2011. Creep behavior of geosynthetics using confined-accelerated tests. Geosynth. Int. 18 (5), 242–254. Guimarães, M.G.A., de Mattos Vidal, D., de Carvalho Urashima, D., Castro, C.A.C., 2016. Degradation of polypropylene woven geotextile: tensile creep and weathering. Geosynth. Int. 24 (2), 213–223. Guo, Y.C., Xin, C.L., Song, M.S., He, Y.D., 2005. Study on short-and long-term creep behavior of plastics geogrid. Polym. Test. 24 (6), 793–798. Hinchberger, S.D., Rowe, R.K., 2003. Geosynthetic reinforced embankments on soft clay foundations: predicting reinforcement strains at failure. Geotext. Geomembranes 21 (3), 151–175. Holtz, R.D., 2017. 46th Terzaghi lecture: geosynthetic reinforced soil: from the experimental to the familiar. J. Geotech. Geoenviron. Eng. 143 (9), 3117001. ISO 13431, 2016. Geotextiles and Geotextile-Related Products - Determination of Tensile Creep and Creep Rupture Behaviour. ISO, Geneva, Switzerland.
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Geotextiles and Geomembranes journal homepage: www.elsevier.com/locate/geotexmem
A short-term model for extrapolating unconfined creep deformation data for woven geotextiles José Luiz Ernandes Dias Filho∗, Paulo Cesar de Almeida Maia, Gustavo de Castro Xavier Civil Engineering Laboratory, Darcy Ribeiro State University of Northern Rio de Janeiro, 28013-602, Campos dos Goytacazes, RJ, Brazil
A R T I C LE I N FO
A B S T R A C T
Keywords: Geosynthetics Geotextiles Creep Durability
This study reports results for creep deformation with data acquired in 72 h of testing. A system capable of performing 8 simultaneous tests was used to test four woven geotextiles of different weights, following all of the recommendations outlined in the standards related to equipment setup. A mathematical model was used to generate time-dependent creep curves for four different load levels up to 40% for each sample and using a database which presented stage II creep conditions (i.e. without rupture) through the end of the tests, up to 10,000 h. The coefficients of variation for the conventional creep tests were below 10%. The compatibility between the experimental data and the model indicates that short-term (72 h) loading tests may be used to extrapolate long-term creep deformation in woven geotextiles.
1. Introduction Creep is the deformation that occurs in a material that is subjected to constant loading over time. Creep testing is important for the characterization of the durability of a geosynthetic, because the results serve as an estimate of the useful life of the material. Since projects that involve the use of geosynthetics require long-term performance, it is reasonable to characterize the material according to this property. Consequently, geosynthetics are generally characterized with standardized creep tests (NBR 15.226, 2005, ASTM D 5262, 2007; ISO 13431, 2016), performed under controlled conditions of temperature and relative humidity. However, this technique involves the use of costly long-term tests to obtain a significant creep deformation response, which can take up to 10,080 h. The three stages of creep behavior can be identified in the curve which measures strain as a function of time for a geosynthetic under constant load over an extended period. Primary creep, also known as the transient phase, is characterized by a strain rate that decreases with time. In secondary creep the linearity of the curve prevails. Whereas tertiary creep is characterized by an increase in the creep strain rate that causes the material to rupture in a short period of time. It is important to note that this behavior pattern may vary according to the type of polymer (Yeo and Hsuan, 2010; Guimarães et al., 2016), the loading level of the test specimen (Simonini and Gottardi, 2003; Balakrishnan and Viswanadham, 2017) and the rate of application of the load (Shinoda and Bathurst, 2004; Bathurst et al., 2012). Depending
∗
on these variables, creep curves may obtain a predominant stage characteristic. The curve format can be described with mathematical models (Costanzi et al., 2003; Guo et al., 2005; Bueno et al., 2005; Kongkitkul et al., 2014) enabling extrapolation of data obtained in the laboratory in order to identify patterns of interest, such as the rate of creep deformation relative to variations in temperature or load level, as well as rupture. This test method is intended for use in determining the unconfined tension creep and creep rupture behavior of geosynthetics at constant temperature when subjected to a sustained tensile loading and is applicable to all geosynthetics. According to NBR 15226 (2005), there are two variants of creep testing: the determination of creep deformation behavior and the determination of the creep rupture load. In the present study, for the determination of creep deformation behavior, four tests were performed at different load levels ranging from 5% to 60% and employing a testing time of up to 1008 h. However, creep rupture tests conducted to analyze rupture loads would apply higher levels between 50% and 90% of tensile strength. The evaluation of alternatives for obtaining creep deformation results in a fast, precise and representative way, is the focus of numerous recent studies. Such studies examine the factors that affect geosynthetic deformation behavior when submitted to constant loading. The principal approaches include: the Stepped Isothermal Method (SIM) and Time-Temperature Superposition (TTS), which accelerate creep strain with increasing temperature (Zornberg et al., 2004; Yeo and Hsuan, 2009, 2010; Leshchinsky et al., 2010; França and Bueno, 2011;
Corresponding author. E-mail addresses: [email protected] (J.L.E. Dias Filho), [email protected] (P.C.d.A. Maia), [email protected] (G.d.C. Xavier).
https://doi.org/10.1016/j.geotexmem.2019.103492 Received 20 June 2019; Received in revised form 4 August 2019; Accepted 4 August 2019 0266-1144/ © 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: José Luiz Ernandes Dias Filho, Paulo Cesar de Almeida Maia and Gustavo de Castro Xavier, Geotextiles and Geomembranes, https://doi.org/10.1016/j.geotexmem.2019.103492
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Table 1 Reference values of the nominal characteristics of the woven geotextiles. Property
PET340
PP500
PET740
PP925
Ultimate tensile strength (kN/m) Elongation at rupture (%) Mass per unit area (g/m2) Thickness (mm)
52.5 ± 1.6 16.5 ± 1,8 340 ± 8 0.51 ± 0.02
106.2 ± 2.0 20.1 ± 1.3 500 ± 9 1.53 ± 0.04
150.7 ± 5.2 34.8 ± 1.8 740 ± 23 1.17 ± 0.01
155 ± 1.6 28.5 ± 2.1 925 ± 25 2.62 ± 0.06
Fig. 1. Broad view of the 8 machines for execution of creep tests.
Fig. 2. Typical curves obtained from the creep tests.
This study seeks to contribute to the understanding of creep deformation behavior in woven geotextiles by evaluating an alternative to conventional creep testing using short-term unconfined tension creep test data for extrapolating deformation behavior.
Achereiner et al., 2013); procedures for examining degradation due to exposure (Guimarães et al., 2016; Pinho-Lopes et al., 2018); as well as analyses of the influence of soil confinement on the behavior of geosynthetics, (Sabir and Brachman, 2012; Zhang et al., 2014; Becker and Nunes, 2015; Holtz, 2017; Plácido et al., 2018; Nuntapanich et al., 2018). Studies that evaluated deformations in structures dimensioned with geosynthetics reported strain limit data under 10% (Perkins, 2000; Hinchberger and Rowe, 2003; Cantré and Saathoff, 2011; Van Eekelen et al., 2012; Yapage et al., 2014; Liu et al., 2017; Zhao et al., 2019), which in engineering practice indicates low deformation in soil-geosynthetic interaction, increasing project stability.
2. Materials and methods 2.1. Study material For this study, four woven geotextiles of different weights were chosen for the testing program. Two tests were carried out on monofilament polypropylene (PP) and two on multifilament polyester (PET) 2
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Fig. 3. Comparison between the experimental data and the extrapolation model for the creep deformation tests at four loading levels for each polymer tested.
Table 2 Creep curve parameters calculated from experimental data collection over time for each geotextile tested. Time
minutes
hours
days
PET340
4 8 15 30 1 2 4 8 1 3 7 14 21 42
PP500
PET740
PP925
c
d
e
c
d
e
c
d
e
c
d
e
0.411 0.348 0.222 0.180 0.184 0.168 0.172 0.168 0.150 0.143 0.139 0.136 0.135 0.136
-0.265 -0.149 0.045 0.119 0.118 0.153 0.137 0.147 0.191 0.210 0.221 0.226 0.233 0.203
0.361 0.369 0.374 0.374 0.377 0.376 0.374 0.374 0.375 0.375 0.375 0.375 0.375 0.376
0.082 0.091 0.085 0.088 0.099 0.094 0.093 0.089 0.089 0.089 0.088 0.089 0.089 0.087
0.253 0.250 0.249 0.251 0.247 0.247 0.245 0.243 0.240 0.240 0.240 0.240 0.240 0.240
0.520 0.483 0.496 0.491 0.448 0.465 0.460 0.463 0.456 0.465 0.454 0.452 0.452 0.461
0.055 0.035 0.021 0.015 0.011 0.009 0.008 0.007 0.007 0.006 0.006 0.006 0.006 0.006
0.489 0.589 0.722 0.803 0.864 0.909 0.947 0.973 0.974 0.988 0.987 0.996 0.991 0.991
0.406 0.399 0.398 0.395 0.393 0.392 0.392 0.390 0.389 0.389 0.389 0.389 0.389 0.390
0.010 0.007 0.007 0.011 0.014 0.018 0.021 0.025 0.025 0.024 0.022 0.024 0.024 0.0243
0.889 0.986 0.995 0.883 0.838 0.788 0.758 0.718 0.724 0.736 0.757 0.740 0.741 0.7361
0.275 0.275 0.276 0.277 0.280 0.282 0.285 0.286 0.287 0.288 0.288 0.288 0.288 0.2878
c, d = multiplication coefficient c (%/Td) and the dimensionless power d of the power behavior of “a” in Eq. (1). e = slope coefficient (%/kN/m) and the linear behavior of “b” from Eq. (1).
coefficients of variation falling below 10%. The samples were cut in the machine direction, and the tensile strength of the virgin sample was determined by wide-width strip method test according to the NBR 15865 (2010) and ASTM D 5035-11 (2015).
as shown in Table 1. The physical index tests were conducted according to the norms for determining mass per unit area (ISO 9864, 2013, ISO 9864, 2005, ASTM D5261, 2010) and nominal thickness (NBR ISO 9863–1, 2013, ISO 9863-1, 2016, ASTM D5199, 2012), with 3
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Table 3 Coefficient statistics for the creep curve parameters. Time
PET340 c
minutes
hours
days
4 8 15 30 1 2 4 8 1 3 7 14 21 42
PP500
d
e
c
PET740
d
e
c
PP925
d
e
c
d
e
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
M
CV
0.192 0.175 0.161 0.155 0.153 0.149 0.147 0.144 0.140 0.138 0.136 0.135 0.135 0.136
42 32 16 12 11 10 9 8 4 2 1 0 0 0
0.113 0.143 0.167 0.178 0.184 0.191 0.196 0.204 0.214 0.219 0.221 0.221 0.218 0.203
125 69 33 24 21 18 17 13 7 5 5 6 7 0
0.374 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.376
1 0 0 0 0 0 0 0 0 0 0 0 0 0
0.089 0.090 0.090 0.090 0.090 0.090 0.089 0.088 0.088 0.088 0.088 0.088 0.088 0.087
4 4 4 4 4 2 2 1 1 1 1 1 1 0
0.245 0.244 0.244 0.243 0.242 0.242 0.241 0.240 0.240 0.240 0.240 0.240 0.240 0.240
2 2 2 1 1 1 1 0 2 2 2 2 2 0
0.469 0.465 0.464 0.461 0.458 0.459 0.458 0.458 0.457 0.457 0.455 0.455 0.457 0.461
4 3 3 2 1 1 1 1 0 0 0 0 0 0
0.014 0.011 0.009 0.008 0.007 0.007 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006
98 74 49 34 22 14 8 4 3 2 2 3 2 0
0.873 0.903 0.929 0.947 0.962 0.973 0.981 0.986 0.988 0.991 0.991 0.993 0.991 0.991
18 14 9 6 4 3 2 1 1 0 0 0 0 0
0.393 0.392 0.391 0.391 0.390 0.390 0.390 0.389 0.389 0.389 0.389 0.389 0.390 0.390
1 1 1 1 0 0 0 0 0 0 0 0 0 0
0.018 0.019 0.020 0.021 0.022 0.023 0.024 0.024 0.024 0.024 0.024 0.024 0.024 0.024
37 35 30 22 16 10 6 3 3 3 3 1 1 0
0.806 0.800 0.784 0.765 0.754 0.744 0.739 0.736 0.739 0.742 0.743 0.739 0.738 0.736
11 12 10 6 4 3 2 2 1 1 1 0 0 0
0.283 0.284 0.284 0.285 0.286 0.286 0.287 0.287 0.288 0.288 0.288 0.288 0.288 0.288
2 2 2 1 1 1 0 0 0 0 0 0 0 0
M = mean; CV = coefficient of variation in %; c, d = multiplication coefficient c (%/Td) and the dimensionless power d of the power behavior of “a” in Eq. (1); e = slope coefficient (%/kN/m) and the linear behavior of “b” from Eq. (1).
laboratory could be realistically estimated from a short-term response. Tests were conducted in the laboratory with internal temperature controlled at 20 ± 2 °C and relative humidity of 65 ± 5% for a period of up to 10,080 h. Creep deformation behavior for the four woven geotextile samples was determined for loads of 10%, 20%, 30% and 40% of the ultimate tensile strength according to the testing standards (NBR 15.226, 2005; ASTM D 5262, 2007; ISO 13431, 2016). Isochronous curves, representing both short-term and long-term straintime relationships, were obtained from the laboratory test results for all samples and load levels. Measurements of the displacements in the test samples were taken at predetermined times of 1, 2, 4, 8, 15, 30 and 60 min, then at 2, 4, 8 and 24 h, and finally at 3, 7, 14, 21 and 42 days. While, all four materials studied were tested over a period of 1008 h, the test was continued for the full 420-day, or 10,080-hour, measurements only for some load levels, due to the limited availability of the testing equipment. The final resulting creep strain data from conventional tests enables the analysis of the behavior of the geosynthetic over the long term, that is, its durability. Therefore, in order to analyze creep strain in this study, experimental data was collected for up to 420 days or 10,080 h for samples PET340 10%, PP500 10%, PET740 10%, PET740 20%, PP925 10% and PP925 20%. However, the study was able to show that similar durability results could be achieved by extrapolating the data from only 3 days, or 72 h, of testing, yielding a significant reduction in the time for data acquisition and analysis. The width of the test specimens was 50 ± 5 mm and, gripped in the clamps with a gauge length of 25 mm, according to tensile strength strip
Table 4 Evaluation of the correlation coefficients between the database measured tensile strain at end of test and the tensile strain extrapolated with Eq. (2). Sample
Load level (%T)
Time (hours)
Measured tensile strain (%)
Tensile strain extrapolated (%)
R2 (dimensionless)
PET340
10 20 30 40 10 20 30 40 10 20 30 40 10 20 30 40
10080 2520 2520 2520 10080 2520 2520 2520 10080 10080 5040 5040 10080 10080 5040 5040
3.8 5.1 7.1 9.0 4.5 6.9 9.6 12.4 6.6 13.2 19.0 25.8 5.0 10.0 15.2 19.6
3.2 5.0 7.1 9.1 4.1 6.7 9.6 12.4 6.4 12.8 19.0 25.3 5.3 10.2 14.8 19.6
0.998 0.999 0.999 0.998 0.999 0.999 0.998 0.999 0.99 0.999 0.997 0.995 0.997 0.998 0.999 0.999
PP500
PET740
PP925
R2 = correlation coefficient.
2.2. Methodology The test program consisted of characterization of creep deformation for the four geotextiles selected. The main objective was to determine whether the long-term response of the materials studied in the
Table 5 Evaluation of the correlation coefficients between the database from key research studies and estimates obtained in the present study. Reference
Geosynthetic type
Polymer
Load level analysed (T%)
Total time (h)
Method
c
d
e
R2
Andrawes et al. (1984) Bueno et al. (2005)
GTXw GTXnw
conventional conventional
GGR GGR
1700 6
conventional SIM
Becker and Nunes (2015)
GGR
1000
Guimarães et al. (2016)
GTXw
PP
10, 20, 10, 20, 10, 20, 20, 30, 20, 30, 10, 20, 25, 40, 25, 40, 5, 10
1000 1000
Guo et al. (2005) Yeo and Hsuan (2010)
PP PP PET HDPE PET HDPE HDPE
conventional confined field test
0.005 0.059 0.044 0.001 0.044 0.044 0.130 0.001 0.070
0.626 0.456 0.611 0.583 0.611 0.611 0.618 2.044 0.585
0.600 1.047 0.980 0.185 0.072 0.119 0.982 0.101 0.316
0.986 0.950 0.950 0.986 0.937 0.930 0.976 0.932 0.930
30 40, 60 40, 60 40, 50, 55 40 30 55 55
2160
GTXw = = woven geotextile; GTXnw = nonwoven geotextile; GGR = geogrid; PP = polypropylene; PET = polyester; HPDE = High density polyethylene; SIM = Stepped Isothermal Method; c, d = multiplication coefficient c (%/Td) and the dimensionless power d of the power behavior of “a” in Eq. (1); e = slope coefficient (%/kN/m) and the linear behavior of “b” of Eq. (1); R2 = correlation coefficient. 4
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statistical calculations excluded data recorded at 4 and 8 min). Table 3 shows that, from the first day of testing, the data showed good representativeness, with coefficients of variation below 10% for all the geotextiles tested. Therefore, based on the coefficient data from the first 72 h (3 days) of testing, curves derived from Equation (2) were generated for each of the 4 datasets, and are illustrated by the red lines in Fig. 3. The graphs illustrate the low variation between the trends for each load level in the modeled data derived from the coefficients (the red line) and the experimental data represented by the black markers. This is confirmed by the correlation coefficient values greater than 0.990. The vertical line separating the primary and secondary creep stages was defined according the parameter a of Eq. (1), that is, the moment at which the tangent of the creep curve became constant. Table 4 shows a direct comparison, for the four types of geosynthetics, between the measured tensile strain at 10,080 h and the tensile strain extrapolated with Eq. (2) using the parameters derived from the measured data at three days. The results indicate that model can accurately extrapolate the tensile strain. This methodology has been applied, with other materials and test conditions, in a number of published studies to evaluate the potential for extrapolating experimental data. These studies also evaluated creep curve coefficients to perform the extrapolations. Table 5 presents these values, as well as the correlation between the database from the cited articles and the estimates obtained in the present study. This comparison shows satisfactory correlations, with R2 values greater than 0.95 for conventional tests and close to 0.93 for other test methods (SIM, confined tests and field tests). These behaviors may not be observed with test setup conditions different from those in the presented methodology.
tests (; NBR 15865, 2010), which obtained a lateral contraction of less than 10% (NBR 15226, 2005). It is important to note that the apparatus basically consists of a device (clamps) for securing the specimen without slipping and in such a way as to not to cause any damage, a system for determining the variation in the length of the measurement over time and a loading system with load application within 1 min, according to the standards (NBR 15226, 2005). Eight simultaneous creep tests (Fig. 1) were performed on suitable tension creep clamping systems, and in order to model the curve of the experimental data, a time-unit-dependent equation was used, as represented by Equation (1): y = aln(x) + b
(1)
Whereby, strain y can be obtained over time x. In the first part of the equation, the multiplier a corresponds to the creep index, which represents the slope of the curve formed by the deformation with application of the constant load. In the second part of the equation, b corresponds to the initial strain values obtained during one hour of creep test. When 0 < x < 1, the data range is not excluded, since parameter b corrects the data according to the applied load.
3. Results Based on the data, in order to demonstrate the short-term model, the creep index and initial strain values were found to follow a behavior trend as a function of the loading levels T at each stage of the creep test, according to Equation (2) and Fig. 2a: ε = cTdln (t) + eT
(2)
The behavior of the strain ε (%), over time t (hours), observed both in this study and in the literature, (for example Andrawes et al., 1984, Bueno et al., 2005, Guo et al., 2005; Yeo and Hsuan, 2010; Becker and Nunes, 2015; Guimarães et al., 2016), allowed the first portion of the curve to be considered similar to a potential function with the multiplication coefficient c and power d (Fig. 2b). Parameter c is a coefficient which correlates the deformation with the load level T raised to the power d (%/Td) and the load level T (kN/m) increases with the dimensionless attribute d, but does so at a slower rate than that of proportionality. This is aligned with the fact that in the creep tests the inclination of the curves gradually change with the increase in the load applied to the test sample. In the second part of the equation, the initial deformation behaves incrementally and linearly, according to the slope coefficient e, which correlates the deformation with the load level (%/kN/m) and is proportional to the magnitude of the imposed load, forming parallel curves according to the loading levels T in the tensile strength tests (Fig. 2c). It is important to highlight that Eq. (2) does not accurately predict the tensile strain of the geosynthetic in the condition where the tensile load is not constant. Fig. 3 represents a comparison between the experimental data and the results of the mathematical model, for the creep tests conducted at four loading levels for each material tested. The shape of the graphs shows linearity in the deformation behavior over time, indicating secondary stage creep. The formation of parallel curves for each of the loading levels was confirmed and the validity of the creep deformation equation model was determined for periods up to 10,080 h of constant load. The parameters of the creep curves, derived from Equation (2), were calculated from the first three measurements collected, that is, at 1, 2 and 4 min. Then, as each new data point was collected at the predetermined times in the testing program, the parameters were recalculated. Table 2 presents the values obtained for each geotextile, where the calculations were obtained with variable t in days. The parameters were evaluated statistically and Table 3 presents the mean and coefficient of variation for each parameter over time. In order to minimize possible differences in the manual loading mechanism, the statistical calculations excluded prior data readings, using only the measurement for a given time and subsequent data (e.g. at 15 min, the
4. Conclusions The present study developed a logarithmic model to determine the creep deformation behavior of woven geotextiles based on creep deformation tests in unconfined conditions. Eight creep-testing machines were used to evaluate four woven geotextiles of different weights, subjected to four different loading levels, with data collection over at least 1008 h of testing. Time-dependent creep deformation curves were generated in order to better interpret the behavior of the studied materials. A mathematical model was created to generate the creep curves and the results for each geotextile were analysed statistically. Coefficients of variation below 10% and confirmed compatibility and representativity. The results were also compared to a database from other published studies that have applied this extrapolation methodology. The evaluation of the data from only 72 h (3 days) of testing yielded reliable results for achieving fast and efficient creep deformation estimates. Findings show that short-term data measurements can be safely extrapolated to obtain long-term durability estimates for the material, in accordance with deformation limits defined by a project. Acknowledgements This study was financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) Finance Code 001. The authors are also thankful to UENF and Huesker Brazil for additional financial support. References ABNT NBR 15226, 2005. Geossintéticos - Determinação do comportamento em deformação e na ruptura, por fluência sob tração não confinada. ABNT, Rio de Janeiro, RJ, Brazil. ABNT NBR 15865, 2010. Geomembranas e produtos correlatos — Determinação das propriedades de tração. ABNT, Rio de Janeiro, RJ, Brazil. ABNT NBR ISO 9863-1, 2013. Geossintéticos - Determinação da espessura a pressões
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ISO 9863-1, 2016. Geosynthetics – Determination of Thickness at Specified Pressures – Part 1: Single Layers. ISO, Geneva, Switzerland. ISO 9864, 2005. Geosynthetics – Test Method for the Determination of Mass Per Unit Area of Geotextiles and Geotextile-Related Products. ISO, Geneva, Switzerland. Kongkitkul, W., Chantachot, T., Tatsuoka, F., 2014. Simulation of geosynthetic load–strain–time behaviour by the non-linear three-component model. Geosynth. Int. 21 (4), 244–255. Leshchinsky, D., Imamoglu, B., Meehan, C.L., 2010. Exhumed geogrid-reinforced retaining wall. J. Geotech. Geoenviron. Eng. 136 (10), 1311–1323. Liu, K.W., Rowe, R.K., Su, Q., Liu, B., Yang, Z., 2017. Long-term reinforcement strains for column supported embankments with viscous reinforcement by FEM. Geotext. Geomembranes 45 (4), 307–319. Nuntapanich, N., Kongkitkul, W., Tatsuoka, F., Jongpradist, P., 2018. Prediction of creep behaviour from load relaxation behaviour of polymer geogrids. Geosynth. Int. 1–16. Perkins, S.W., 2000. Constitutive modeling of geosynthetics. Geotext. Geomembranes 18 (5), 273–292. Pinho-Lopes, M., Paula, A.M., Lopes, M.L., 2018. Long-term response and design of two geosynthetics: effect of field installation damage. Geosynth. Int. 25 (1), 98–117. Plácido, R., Portelinha, F.H.M., Futai, M.M., 2018. Field and laboratory time-dependent behaviors of geotextiles in reinforced soil walls. Geosynth. Int. 25 (2), 215–229. Sabir, A., Brachman, R.W.I., 2012. Time and temperature effects on geomembrane strain from a gravel particle subjected to sustained vertical force. Can. Geotech. J. 49 (3), 249–263. Shinoda, M., Bathurst, R.J., 2004. Strain measurement of geogrids using a video-extensometer technique. Geotech. Test J. 27 (5), 456–463. Simonini, P., Gottardi, G., 2003. The viscoplastic behaviour of a geogrid-reinforced model wall. Geosynth. Int. 10 (1), 34–46. Van Eekelen, S.J., Bezuijen, A., Lodder, H.J., Van Tol, E.A., 2012. Model experiments on piled embankments. Part I. Geotext. Geomembranes 32, 69–81. Yapage, N.N.S., Liyanapathirana, D.S., Kelly, R.B., Poulos, H.G., Leo, C.J., 2014. Numerical modeling of an embankment over soft ground improved with deep cement mixed columns: case history. J. Geotech. Geoenviron. Eng. 140 (11), 04014062. Yeo, S.S., Hsuan, Y.G., 2009. Effects of temperature and stress on the short-and long-term compressive behavior of expanded polystyrene. Geosynth. Int. 16 (5), 374–383. Yeo, S.S., Hsuan, Y.G., 2010. Evaluation of creep behavior of high density polyethylene and polyethylene-terephthalate geogrids. Geotext. Geomembranes 28 (5), 409–421. Zhang, C.C., Zhu, H.H., Xu, Q., Shi, B., Mei, G.X., 2014. Time-dependent pullout behavior of glass fiber reinforced polymer (GFRP) soil nail in sand. Can. Geotech. J. 52 (6), 671–681. Zhao, L.S., Zhou, W.H., Geng, X., Yuen, K.V., Fatahi, B., 2019. A closed-form solution for column-supported embankments with geosynthetic reinforcement. Geotext. Geomembranes (in press). Zornberg, J.G., Byler, B.R., Knudsen, J.W., 2004. Creep of geotextiles using time–temperature superposition methods. J. Geotech. Geoenviron. Eng. 130 (11), 1158–1168.
especificadas. ABNT, Rio de Janeiro, RJ. ABNT NBR ISO 9864, 2013. Geossintéticos - Método de ensaio para determinação da massa por unidade de área de geotêxteis e produtos correlatos. ABNT, Rio de Janeiro, RJ. Achereiner, F., Engelsing, K., Bastian, M., Heidemeyer, P., 2013. Accelerated creep testing of polymers using the stepped isothermal method. Polym. Test. 32 (3), 447–454. Andrawes, K.Z., McGown, A., Kabir, M.H., 1984. Uniaxial strength testing of woven and nonwoven geotextiles. Geotext. Geomembranes 1 (1), 41–56. ASTM D 5035-11, 2015. Standard Test Method for Breaking Force and Elongation of Textile Fabrics (Strip Method). ASTM, West Conshohocken, PA, USA. ASTM D5199, 2012. Standard Test Method for Measuring the Nominal Thickness of Geosynthetics. ASTM, West Conshohocken, PA, USA. ASTM D5261, 2010. Standard Test Method for Measuring Mass Per Unit Area of Geotextiles. ASTM, West Conshohocken, PA, USA. ASTM D5262, 2007. Standard Test Method for Evaluating the Unconfined Tension Creep and Creep Rupture Behavior of Geosynthetics. ASTM, West Conshohocken, PA, USA. Balakrishnan, S., Viswanadham, B.V.S., 2017. Evaluation of tensile load-strain characteristics of geogrids through in-soil tensile tests. Geotext. Geomembranes 45 (1), 35–44. Bathurst, R.J., Huang, B., Allen, T.M., 2012. Interpretation of laboratory creep testing for reliability-based analysis and load and resistance factor design (LRFD) calibration. Geosynth. Int. 19 (1), 39–53. Becker, L.D.B., Nunes, A.L.L.S., 2015. Influence of soil confinement on the creep behavior of geotextiles. Geotext. Geomembranes 43 (4), 351–358. Bueno, B.S., Costanzi, M.A., Zornberg, J.G., 2005. Conventional and accelerated creep tests on nonwoven needle-punched geotextiles. Geosynth. Int. 12 (6), 276–287. Cantré, S., Saathoff, F., 2011. Design method for geotextile tubes considering strain formulation and verification by laboratory tests using photogrammetry. Geotext. Geomembranes 29 (3), 201–210. Costanzi, M.A., Bueno, B.S., Baras, L.C.S., Zornberg, J.G., 2003. Avaliação da Fluência de Geotêxteis não Tecidos com Ensaios Acelerados. Solos Rochas 26 (3), 217–228. França, F.A.N., Bueno, B.S., 2011. Creep behavior of geosynthetics using confined-accelerated tests. Geosynth. Int. 18 (5), 242–254. Guimarães, M.G.A., de Mattos Vidal, D., de Carvalho Urashima, D., Castro, C.A.C., 2016. Degradation of polypropylene woven geotextile: tensile creep and weathering. Geosynth. Int. 24 (2), 213–223. Guo, Y.C., Xin, C.L., Song, M.S., He, Y.D., 2005. Study on short-and long-term creep behavior of plastics geogrid. Polym. Test. 24 (6), 793–798. Hinchberger, S.D., Rowe, R.K., 2003. Geosynthetic reinforced embankments on soft clay foundations: predicting reinforcement strains at failure. Geotext. Geomembranes 21 (3), 151–175. Holtz, R.D., 2017. 46th Terzaghi lecture: geosynthetic reinforced soil: from the experimental to the familiar. J. Geotech. Geoenviron. Eng. 143 (9), 3117001. ISO 13431, 2016. Geotextiles and Geotextile-Related Products - Determination of Tensile Creep and Creep Rupture Behaviour. ISO, Geneva, Switzerland.
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