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Creep testing and data extrapolation of reinforced GCLs
Geotextiles and Geomembranes 19 (2001) 413–425
Creep testing and data extrapolation of reinforced GCLs Robert M. Koernera,*, Te-Yang Soongb, George R. Koernerc, Alex Gontara a
Department of Civil Engineering, Drexel University, Philadelphia, PA 19104, USA b Earth Tech Consultants, Inc., Livonia, MI 48150, USA c Geosynthetic Institute, Folsom, PA 19033, USA
Received 23 December 2000; received in revised form 11 June 2001; accepted 4 July 2001
Abstract Presented herein are the results of creep tests on three internally reinforced geosynthetic clay liners (GCLs) conducted for 1000 h at each increment of loading. Two of the GCLs were reinforced by needle punched and one was by stitch bonding. All three GCLs sustained loads up to 60% of their short-term strengths without any evidence of fiber pullout or breakage. The recorded deformations were nil at 20% loadings and were small, but measurable, at the higher loadings. Having the experimental data, the Kelvin–Chain model was used for extrapolation out to 1.0 106 h (114 years) from which isochronous time curves were plotted. The 100-year predicted deformation data at a 30% stress level is approximately 5 and 10 mm for the two needle punched GCLs, and approximately 10 mm for the stitch bonded GCL. It is concluded that such deformations are reasonable and can be accommodated by the reinforced GCLs currently being produced. There is a need, however, for additional investigation and to formalize a GCL specification to ensure that the proper polymer formulation is used in these materials. r 2001 Published by Elsevier Science Ltd. Keywords: Geosynthetic clay liners; Creep testing; Lifetime prediction
1. Introduction Of the commercially available geosynthetic clay liners (GCLs), the internally reinforced types are generally used on slopes greater than approximately 7–101. This *Corresponding author. Tel.: +1-610-522-8440; fax: +1-610-522-8441. E-mail address: [email protected] (R.M. Koerner). 0266-1144/01/$ - see front matter r 2001 Published by Elsevier Science Ltd. PII: S 0 2 6 6 - 1 1 4 4 ( 0 1 ) 0 0 0 1 5 - 2
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limiting value coincides with the shear strength of hydrated bentonite which is the hydraulic barrier material within a GCL. When slopes are steeper than the above values, as they often are, the GCLs must (i) have a resisting force placed against them (e.g., a passive wedge of soil or solid waste), (ii) remain dry (for example, by encapsulation between two geomembranes), or (iii) have some type of internal reinforcement. Such internal reinforcement can be provided by needle punching fibers from a nonwoven geotextile layer through the bentonite and the opposing geotextile layer. Thus, a fiber structure is created from top-to-bottom of the GCL which can be further augmented by thermally bonding or gluing the fibers to the penetrated geotextile, see Fig. 1a. Alternatively, the two opposing geotextiles with a bentonite layer between them can be reinforced by sewing the entire composite together with parallel rows of stitch bonded yarns, see Fig. 1b. Currently, there are two major types of needle punched products (Bentofixs and Bentomats) and two major types of stitch bonded products (Claymaxs and Nabentos). All four manufacturers have variations within their product lines which are important to recognize if one is attempting to utilize a specific set of data and/or to compare results from different studies. At this point in time, all geotextile carrier layers, and their reinforcing fibers and yarns are polypropylene formulations, i.e., polypropylene resins containing proprietary additive packages. When GCLs are placed on slopes, the fiber reinforcement structure is challenged by the gravitational weight of the overlying materials, typically soil and/or solid waste. Applied shear stresses imposed on the upper geotextile must be transferred to the lower geotextile via the fibers or yarns penetrating through the bentonite layer. Thus, the importance of the fiber reinforcement structure is readily apparent. The fibers are forced into tension by the imposed shear stresses and this tension must be sustained for the time required by the site specific conditions. This could be very
Fig. 1. Two different types of internally reinforced GCLs: (a) needle punched GCL (from Naue Fasertechnik, GmbH), (b) stitch bonded GCL (from Huesker, GmbH).
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short if a passive wedge is placed against the slope, or very long if the slope is left nonsupported. The assessment of the internal strength of reinforced GCLs is generally accomplished by direct shear testing according to ASTM D6243. The shearing aspect of these tests, however, rarely lasts more than a few hours. Thus, the typical GCL test can be considered as a short-term test. The issue of long-term testing and performance of the above mentioned fiber structure of GCLs has been raised. For example, the focus of the fourteen full scale field test plots in Cincinnati, Ohio was directly targeted at this issue, see Daniel et al. (1998). When considering long-term performance of reinforced GCLs, two aspects must be addressed. One is long-term polymer degradation of the fibers. This issue is addressed by Hsuan (2000). The other issue is long-term polymer creep under the imposed shear stresses. It is the issue addressed in this paper. A laboratory test program was initiated to address the above issue which consists of creep shear tests on the internal structure of three different reinforced GCLs. By stressing the upper and lower geotextiles with opposing forces, the entire fiber structure of the GCL test specimen is challenged. The upper and lower geotextiles are sheared against the bentonite layer between them and, most importantly, the fiber structure connecting the geotextiles to one another goes into tension. The state of tension is greatly complicated due to the presence of the surrounding bentonite, thus the GCL must be tested as a composite material. This is the procedure taken in this set of tests. The test setup and subsequent results form the data base of the paper. Having this data, the Kelvin–Chain model (Soong and Koerner, 1998) is used to extrapolate the data well beyond the laboratory testing time. This data is then used to generate isochronous time curves out to 100-year lifetime. A discussion and conclusion section based on the findings of this experimental/analytic extrapolation study concludes the paper.
2. Laboratory test setup The direct shear testing system utilized was essentially in accordance with the ASTM D6243 test method except now modified for sustained loads, i.e., for creep loadings. The upper shear box section was 300 300 mm2 square while the lower section was extended 100 mm making it 300 mm in width 400 mm in length. Thus, during shear there was always a 300 300 mm2 surface being tested. The upper geotextile of the GCL was mechanically fixed to the upper platen and the lower geotextile of the GCL was mechanically fixed to the lower platen, see Fig. 2. The mechanical fixing was done using serrated files with holes so as to grip the geotextiles yet allow drainage during hydration and subsequent shear testing. After fixing the upper and lower geotextiles to their respective halves of the shear box, a gap of approximately 7.0 mm was set to assure that shear stresses were resisted by the internal structure of the different GCL test specimens. The GCL test specimens were hydrated with tap water for 10 days during which they were consolidated under a normal stress of 17 kPa. This value was selected
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Fig. 2. General configuration and photograph of internal shear test setup of a GCL.
because it coincides with the cover soil simulation tests of the Cincinnati test plots mentioned earlier. Conventional direct shear tests were performed to establish the short-term shear strength of the different test specimens. They were conducted at a shearing rate of 1.0 mm/min. This value was selected because it is the usual default shearing rate used in practice and felt to replicate short-term conditions. Having these short-term values, replicate GCL test specimens were prepared, hydrated in the same manner, and tested under an initial creep load (i.e., a ‘‘dead’’ load) of 20% of the short-term value. Load was applied by dead weight using a pulley system as shown in the photograph of Fig. 2. Loads were maintained for 1000 h during which time deformation readings were taken. After 1000 h elapsed, the dead load was increased to 30%, and the process repeated. This process was repeated in 10% increments until sufficient data was accumulated to provide for the analytic extrapolations. There were three GCLs tested in the above described manner. Two were needle punched and one was stitch bonded. Details of the products tested will be given later.
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3. Analytic extrapolation method It has been shown that the creep behavior of a wide range of materials can be described by a Kelvin–Chain model which consists of a finite number of Kelvin units in series, Roscoe (1950). As a subtle variation, a spring can be added to the original Kelvin–Chain model. This provides to the model the capability of simulating an initial instantaneous (elastic) strain which is typically seen in creep measurements. Fig. 3 shows the modified Kelvin–Chain model used in this study. A Kelvin unit consists of a spring and a dashpot in parallel. In the Kelvin–Chain model, each Kelvin unit is identified by the letter ‘‘i’’ and characterized by a retardation time, ti ; where ti ¼ Zi =Ei : Experience shows that in an ideal Kelvin– Chain model, the spring modulus in each Kelvin unit is generally inversely proportional to its corresponding dashpot viscosity. In other words, Kelvin units consisting of high-modulus springs possess dashpots with low viscosities. The relative degrees vary. When such a model is subjected to an external stress, s; as illustrated in Fig. 3, an instantaneous deformation is created by the single spring. Note that this deformation stays constant regardless of time as long as the applied stress remains. Subsequently, the Kelvin units with higher spring moduli and lower dashpot viscosities deform. Note that such deformations will be retarded more rapidly. Succeedingly, the units with lower spring moduli will respond to the external stress owing to the higher resistance from the dashpots. However, continuous deformations will be observed in these units over a longer period of time, until their corresponding retardation times are reached. Fig. 4 illustrates how the above concept functions on a hypothetical set of 100 h creep data. It plots a set of creep data along with the calculated curve corresponding to a Kelvin–Chain model consisting of four Kelvin units and a single spring. It is seen that the calculated uppermost curve (a superposition of the five lower individual curves) accurately models the experimental data. The individual behavior of each
Fig. 3. The Kelvin–Chain model.
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Fig. 4. Creep data simulated by a Kelvin–Chain Model consisting of four Kelvin units and one single spring.
component in the model is also shown in the figure where the concept of ‘‘retardation time’’ is clearly demonstrated. To utilize a Kelvin–Chain model, the creep behavior is viewed as a so-called strain function eðtÞ ¼ e0 þ
n X
1=Ei ð1 et=ti Þ;
ð1Þ
i¼1
where e0 ¼ 1=E0 is the elastic strain (i.e., strain induced immediately after the stress is applied) caused by a unit stress (i.e., s ¼ 1). Note that the end of the elastic deformation portion of the experimental data, i.e., e0 ; is defined herein as the point of which the second derivative first changes its sign, generally from negative to positive. In Eq. (1), the retardation times, ti ’s, are values which can be arbitrarily chosen providing some restrictions are satisfied, (Bazant, 1988; Bazant and Prasannan, 1989). However, any two adjacent Kelvin units having a relationship of Dðlog ti Þ ¼ 1 generally gives sufficiently smooth creep curves; (Bazant and Xi, 1995). That is to say, if the smallest retardation time is chosen as 103 h, the subsequent retardation times will generally be selected as102, 101, 100, 101 h, etc.
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Furthermore, a ‘‘N’’-unit Kelvin–Chain model can generally simulate creep data of ‘‘N’’ orders of magnitude on the time scale. Note, however, if extrapolation of the experimental data is desirable, more Kelvin units are necessary. For example, if an extrapolation out to 104 h is desirable using a 1000 h creep data (i.e., one-order extrapolation), one additional Kelvin unit with retardation time of 104 h is necessary. As to the selection of Ei ’s, they are determined by optimum fitting of the creep data under the constraints of the preselected retardation times. It is clear that a regression analysis (optimum fitting) for determining six or more unknowns (number of Ei ’s, in this case) can be extremely time consuming. A procedure which reduces the number of independent variables to only two, regardless of the actual number of Ei ’s, is recommended herein. The following expression is proposed to serve the aforementioned purpose (see Bazant and Xi (1995) for detailed mathematical derivations): 1 2n2 ð3ti Þ2n3 ðn 1 ð3ti Þn Þ ¼ 1:151ðaÞð3ti Þ3 Ei ð1 þ ð3ti Þn Þ3 nðn 2Þð3ti Þn3 ðn 1ð3t1 Þn Þ n2 ð3ti Þ2n3 þ : ð2Þ ð1 þ ð3ti Þn Þ2 In Eq. (2), ‘‘a’’ and ‘‘n’’ are the new targeted unknowns (instead of Ei ’s) associated with the modeled creep data. Note that the new curve fitting process involves only two variables and is much simpler. By varying the two independent variables ‘‘a’’ and ‘‘n’’ in Eq. (2), different combinations of Ei ’s with respect to the pre-selected retardation times, ti ’s, can be obtained. This allows a comparison of each calculated result of Eq. (1) to the actual experimental data. The calculated result is then optimized using the least-squares approximation (weighing by ‘‘time’’ is recommended) and iteration of this process will eventually converge on the actual experimental data. The resulting optimum model can then be used to predict experimental creep behavior beyond the actual measured data. This will be illustrated using the experimental creep data for the GCLs that are evaluated in this study.
4. Experimental data, curve fitting, and extrapolation Three reinforced GCLs were selected for testing and evaluation using the procedures described previously. They were selected since they were sampled directly from the products used in the Cincinnati field study mentioned earlier. GCL-1 was a needle punched product with nonwoven needle punched geotextiles on both upper and lower surfaces. The short-term data produced an internal friction angle of 301 with 9.8 kPa shear strength at 17 kPa normal stress. GCL-2 was a needle punched product with a nonwoven needle punched geotextile on one surface and a slit film woven geotextile on the other. The short-term data produced an internal friction angle of 251 with 7.9 kPa shear strength at 17 kPa normal stress. GCL-3 was a stitch bonded product (with stitching rows at 25 mm spacing) with a combined woven slit
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film and monofilament geotextile on both upper and lower surfaces. The short-term data produced an internal friction angle of 451 with 17.0 kPa shear strength at 17 kPa normal stress. Note that the products are not specifically identified since each of them have changed significantly since the field testing program was initiated in 1994. Needle punched GCL-1 was evaluated at 20%, 30%, 40% and 50% of its shortterm strength with each load held for 1000 h, see Fig. 5a. Using the Kelvin–Chain model, the 20%, 30% and 40% data was extrapolated to beyond 1 106 h (114 years) in Fig. 5b. Note that the 50% data was not used due to the anomalous step in the data at the end of the 40% test. From these graphs isochronous time curves were plotted in Fig. 5c for 1000 h (the actual data) and then for 1, 10 and 100 years. Needle punched GCL-2 was evaluated at 20%, 30%, 40%, 50% and 60% of its short-term strength with each load held for 1000 h, see Fig. 6a. Using the Kelvin– Chain model, the data was extrapolated to beyond 1 106 h (114 years) in Fig. 6b. Note that the 60% data required considered judgment in this regard. From these graphs isochronous time curves were plotted in Fig. 6c for 1000 h (the actual data) and then for 1, 10 and 100 years. Stitch bonded GCL-3 was evaluated at 20%, 30%, 40% and 50% of its short-term strength with each load held for 1000 h, see Fig. 7a. Using the Kelvin–Chain model, the data was extrapolated to beyond 1 106 h (114 years) in Fig. 7b. From these graphs isochronous time curves were plotted in Fig. 7c for 1000 h (the actual data) and then for 1, 10 and 100 years. A concern was expressed among the group regarding the reproducibility of the experimental data considering the long testing times that were involved. Thus, the needle punched GCL-2 product was retested for both the 20% and 30% loads. It was seen that the two sets of response curves were essentially identical to one another.
5. Discussion Concern by designers, owners and regulators has rightfully been expressed as to the long-term strength of the fiber or yarn components of reinforced GCLs. Thus, this effort has been undertaken to attempt to address the situation. The mechanical creep behavior of three reinforced GCLs under long-term laboratory creep testing has been investigated. In general, there were no ongoing creep deformations up to 30% of the short-term strength. Note that the initial deformations shown in Figs. 5a, 6a and 7a are elastic and of a short time period. At 40%, there was evidence of a slight amount of ongoing creep deformation and at 50% the deformation was more pronounced. At no time, however, was secondary creep (much less tertiary creep) evidenced in any of the test specimens. This gave impetus to extrapolation of the data to longer time periods. Using the Kelvin–Chain model, the data was extrapolated out to 1 106 h (114 years). The obvious target was 100 years which is a time period considered in some GCL applications. Having this data in Figs. 5b, 6b and 7b allowed for the plotting of isochronous time curves. They were presented in Fig. 5c, 6c and 7c for the three
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Fig. 5. (a) Creep strain date for needle punched GCL-1. (b) Kelvin–Chain extrapolated creep strain data for GCL-1. (c) Isochronous creep strain curves for GCL-1.
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Fig. 6. (a) Creep strain data for needle punched GCL-2. (b) Kelvin–Chain extrapolated creep strain data for GCL-2. (c) Isochronous creep strain curves for GCL-2.
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Fig. 7. (a) Creep strain data for needle punched GCL-3. (b) Kelvin–Chain extrapolated creep strain data for GCL-3. (c) Isochronous creep strain curves for GCL-3.
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products evaluated. All products appear to result in tolerable deformations up to loads equal to 30% of their short-term strengths, i.e., deformations of 10, 5 and 10 mm, respectively, for the three reinforced GCLs that were evaluated. It is suggested by these observations that the internal shear strength of both needle punched fibers and stitch bonded yarns used to reinforce the evaluated GCLs is adequate.
6. Conclusions and recommendations The creep deformation behavior of the fibers of needle punched reinforced GCLs and the yarns of stitch bonded GCLs was measured and furthermore extrapolated out to 100-year lifetimes. There was no evidence of fiber or yarn pullout or breakage in any of the tests. The extrapolation from 1000 h tests to 100-year lifetime is a three order of magnitude increase, which is indeed ‘‘bold’’. However, to do creep tests on hydrated GCLs for 10,000 h, or longer, is not without its own difficulties. Such operational problems such as rusting of equipment, biological algae growth, evaporation of water, and physical or vibrational disturbance of the test setup were all experienced within the 1000 h tests. They would probably be more difficult at considerably longer times. Possible changes in the bentonite component over time would also be a consideration, e.g., ion exchange as described by Daniel (2000). On a practical basis, the time and cost of such extremely long tests almost forces them to be put into a research classification. It should also be noted that fiber structure of both the needle punched and stitch bonded types of GCLs is very complex. It is indeed a textile engineering challenge complicated greatly by the encapsulating hydrated bentonite. The type of ‘‘yielding’’ confinement that the bentonite provides is clearly a topic for further research. The basic conclusion reached from these tests, however, is that the fiber structure maintained its integrity in all three of these GCL products over all loads that were evaluated. Even further, the deformations measured were very small and even with the extrapolation of the data out to 100-year lifetime the deformations are still within reasonable limits. Thus the polymers used (resin type, antioxidants, additives, etc.) appear to be appropriate. It seems necessary to develop specifications and testing guidelines to assure that the polymer formulation is consistent in light of this type of long-term testing. In the authors opinion, a generic specification should be developed.
Acknowledgements The financial assistant of the member organizations of the Geosynthetic Institute and its related institutes for research, information, education, accreditation and certification is sincerely appreciated. Their identification and contact number information is available on the institute’s web site at ‘‘geosyntheticinstitute.org’’.
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References ASTM D6243, Determining the Internal and Interface Shear Resistance of Geosynthetic Clay Liners by the Direct Shear Method. Bazant, Z.P. (Ed.), 1988. Mathematical Modeling of Creep and Shrinkage of Concrete. Wiley, NY, USA. Bazant, Z.P., Prasannan, S., 1989. Solidification theory of concrete creep II: verification and application. J. Eng. Mech., ASCE 115 (5), 1691–1703. Bazant, Z.P., Xi, Y., 1995. Continuous retardation spectrum for solidification theory of concrete creep. J. Eng. Mech., ASCE 121 (2), 281–288. Daniel, D.E., 2000. Hydraulic durability of geosynthetic clay liners. Proceedings of the GRI-14 Conference, Hot Topics in Geosynthetics I. GII Publ., Folsom, PA, pp. 116–135. Daniel, D.E., Koerner, R.M., Bonaparte, R., Landreth, R.E., Carson, D.A., Scranton, H.B., 1998. Slope stability of geosynthetic clay liner test plots. J. Geotech.Geoenviron. Eng. 124 (7), 628–637. Hsuan, Y.G., 2000. The Durability of Reinforced Fibers and Yarns in Geosynthetic Clay Liners. Proceedings of the GRI-14 Conference, Hot Topics in Geosynthetics I. GII Publ., Folsom, PA, pp. 211–226. Roscoe, R., 1950. Mechanical models for the representation of viscoelastic properties. Br. J.Appl. Phys. 1, 171–172. Soong, T.-Y., Koerner, R.M., 1998. Modeling and Extrapolation of Creep Behavior of Geosynthetics. Proceedings of the 6th International Conference on Geosynthetics, Atlanta. IFAI Publ., Roseville, MN, pp. 707–710.
Creep testing and data extrapolation of reinforced GCLs Robert M. Koernera,*, Te-Yang Soongb, George R. Koernerc, Alex Gontara a
Department of Civil Engineering, Drexel University, Philadelphia, PA 19104, USA b Earth Tech Consultants, Inc., Livonia, MI 48150, USA c Geosynthetic Institute, Folsom, PA 19033, USA
Received 23 December 2000; received in revised form 11 June 2001; accepted 4 July 2001
Abstract Presented herein are the results of creep tests on three internally reinforced geosynthetic clay liners (GCLs) conducted for 1000 h at each increment of loading. Two of the GCLs were reinforced by needle punched and one was by stitch bonding. All three GCLs sustained loads up to 60% of their short-term strengths without any evidence of fiber pullout or breakage. The recorded deformations were nil at 20% loadings and were small, but measurable, at the higher loadings. Having the experimental data, the Kelvin–Chain model was used for extrapolation out to 1.0 106 h (114 years) from which isochronous time curves were plotted. The 100-year predicted deformation data at a 30% stress level is approximately 5 and 10 mm for the two needle punched GCLs, and approximately 10 mm for the stitch bonded GCL. It is concluded that such deformations are reasonable and can be accommodated by the reinforced GCLs currently being produced. There is a need, however, for additional investigation and to formalize a GCL specification to ensure that the proper polymer formulation is used in these materials. r 2001 Published by Elsevier Science Ltd. Keywords: Geosynthetic clay liners; Creep testing; Lifetime prediction
1. Introduction Of the commercially available geosynthetic clay liners (GCLs), the internally reinforced types are generally used on slopes greater than approximately 7–101. This *Corresponding author. Tel.: +1-610-522-8440; fax: +1-610-522-8441. E-mail address: [email protected] (R.M. Koerner). 0266-1144/01/$ - see front matter r 2001 Published by Elsevier Science Ltd. PII: S 0 2 6 6 - 1 1 4 4 ( 0 1 ) 0 0 0 1 5 - 2
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limiting value coincides with the shear strength of hydrated bentonite which is the hydraulic barrier material within a GCL. When slopes are steeper than the above values, as they often are, the GCLs must (i) have a resisting force placed against them (e.g., a passive wedge of soil or solid waste), (ii) remain dry (for example, by encapsulation between two geomembranes), or (iii) have some type of internal reinforcement. Such internal reinforcement can be provided by needle punching fibers from a nonwoven geotextile layer through the bentonite and the opposing geotextile layer. Thus, a fiber structure is created from top-to-bottom of the GCL which can be further augmented by thermally bonding or gluing the fibers to the penetrated geotextile, see Fig. 1a. Alternatively, the two opposing geotextiles with a bentonite layer between them can be reinforced by sewing the entire composite together with parallel rows of stitch bonded yarns, see Fig. 1b. Currently, there are two major types of needle punched products (Bentofixs and Bentomats) and two major types of stitch bonded products (Claymaxs and Nabentos). All four manufacturers have variations within their product lines which are important to recognize if one is attempting to utilize a specific set of data and/or to compare results from different studies. At this point in time, all geotextile carrier layers, and their reinforcing fibers and yarns are polypropylene formulations, i.e., polypropylene resins containing proprietary additive packages. When GCLs are placed on slopes, the fiber reinforcement structure is challenged by the gravitational weight of the overlying materials, typically soil and/or solid waste. Applied shear stresses imposed on the upper geotextile must be transferred to the lower geotextile via the fibers or yarns penetrating through the bentonite layer. Thus, the importance of the fiber reinforcement structure is readily apparent. The fibers are forced into tension by the imposed shear stresses and this tension must be sustained for the time required by the site specific conditions. This could be very
Fig. 1. Two different types of internally reinforced GCLs: (a) needle punched GCL (from Naue Fasertechnik, GmbH), (b) stitch bonded GCL (from Huesker, GmbH).
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short if a passive wedge is placed against the slope, or very long if the slope is left nonsupported. The assessment of the internal strength of reinforced GCLs is generally accomplished by direct shear testing according to ASTM D6243. The shearing aspect of these tests, however, rarely lasts more than a few hours. Thus, the typical GCL test can be considered as a short-term test. The issue of long-term testing and performance of the above mentioned fiber structure of GCLs has been raised. For example, the focus of the fourteen full scale field test plots in Cincinnati, Ohio was directly targeted at this issue, see Daniel et al. (1998). When considering long-term performance of reinforced GCLs, two aspects must be addressed. One is long-term polymer degradation of the fibers. This issue is addressed by Hsuan (2000). The other issue is long-term polymer creep under the imposed shear stresses. It is the issue addressed in this paper. A laboratory test program was initiated to address the above issue which consists of creep shear tests on the internal structure of three different reinforced GCLs. By stressing the upper and lower geotextiles with opposing forces, the entire fiber structure of the GCL test specimen is challenged. The upper and lower geotextiles are sheared against the bentonite layer between them and, most importantly, the fiber structure connecting the geotextiles to one another goes into tension. The state of tension is greatly complicated due to the presence of the surrounding bentonite, thus the GCL must be tested as a composite material. This is the procedure taken in this set of tests. The test setup and subsequent results form the data base of the paper. Having this data, the Kelvin–Chain model (Soong and Koerner, 1998) is used to extrapolate the data well beyond the laboratory testing time. This data is then used to generate isochronous time curves out to 100-year lifetime. A discussion and conclusion section based on the findings of this experimental/analytic extrapolation study concludes the paper.
2. Laboratory test setup The direct shear testing system utilized was essentially in accordance with the ASTM D6243 test method except now modified for sustained loads, i.e., for creep loadings. The upper shear box section was 300 300 mm2 square while the lower section was extended 100 mm making it 300 mm in width 400 mm in length. Thus, during shear there was always a 300 300 mm2 surface being tested. The upper geotextile of the GCL was mechanically fixed to the upper platen and the lower geotextile of the GCL was mechanically fixed to the lower platen, see Fig. 2. The mechanical fixing was done using serrated files with holes so as to grip the geotextiles yet allow drainage during hydration and subsequent shear testing. After fixing the upper and lower geotextiles to their respective halves of the shear box, a gap of approximately 7.0 mm was set to assure that shear stresses were resisted by the internal structure of the different GCL test specimens. The GCL test specimens were hydrated with tap water for 10 days during which they were consolidated under a normal stress of 17 kPa. This value was selected
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Fig. 2. General configuration and photograph of internal shear test setup of a GCL.
because it coincides with the cover soil simulation tests of the Cincinnati test plots mentioned earlier. Conventional direct shear tests were performed to establish the short-term shear strength of the different test specimens. They were conducted at a shearing rate of 1.0 mm/min. This value was selected because it is the usual default shearing rate used in practice and felt to replicate short-term conditions. Having these short-term values, replicate GCL test specimens were prepared, hydrated in the same manner, and tested under an initial creep load (i.e., a ‘‘dead’’ load) of 20% of the short-term value. Load was applied by dead weight using a pulley system as shown in the photograph of Fig. 2. Loads were maintained for 1000 h during which time deformation readings were taken. After 1000 h elapsed, the dead load was increased to 30%, and the process repeated. This process was repeated in 10% increments until sufficient data was accumulated to provide for the analytic extrapolations. There were three GCLs tested in the above described manner. Two were needle punched and one was stitch bonded. Details of the products tested will be given later.
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3. Analytic extrapolation method It has been shown that the creep behavior of a wide range of materials can be described by a Kelvin–Chain model which consists of a finite number of Kelvin units in series, Roscoe (1950). As a subtle variation, a spring can be added to the original Kelvin–Chain model. This provides to the model the capability of simulating an initial instantaneous (elastic) strain which is typically seen in creep measurements. Fig. 3 shows the modified Kelvin–Chain model used in this study. A Kelvin unit consists of a spring and a dashpot in parallel. In the Kelvin–Chain model, each Kelvin unit is identified by the letter ‘‘i’’ and characterized by a retardation time, ti ; where ti ¼ Zi =Ei : Experience shows that in an ideal Kelvin– Chain model, the spring modulus in each Kelvin unit is generally inversely proportional to its corresponding dashpot viscosity. In other words, Kelvin units consisting of high-modulus springs possess dashpots with low viscosities. The relative degrees vary. When such a model is subjected to an external stress, s; as illustrated in Fig. 3, an instantaneous deformation is created by the single spring. Note that this deformation stays constant regardless of time as long as the applied stress remains. Subsequently, the Kelvin units with higher spring moduli and lower dashpot viscosities deform. Note that such deformations will be retarded more rapidly. Succeedingly, the units with lower spring moduli will respond to the external stress owing to the higher resistance from the dashpots. However, continuous deformations will be observed in these units over a longer period of time, until their corresponding retardation times are reached. Fig. 4 illustrates how the above concept functions on a hypothetical set of 100 h creep data. It plots a set of creep data along with the calculated curve corresponding to a Kelvin–Chain model consisting of four Kelvin units and a single spring. It is seen that the calculated uppermost curve (a superposition of the five lower individual curves) accurately models the experimental data. The individual behavior of each
Fig. 3. The Kelvin–Chain model.
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Fig. 4. Creep data simulated by a Kelvin–Chain Model consisting of four Kelvin units and one single spring.
component in the model is also shown in the figure where the concept of ‘‘retardation time’’ is clearly demonstrated. To utilize a Kelvin–Chain model, the creep behavior is viewed as a so-called strain function eðtÞ ¼ e0 þ
n X
1=Ei ð1 et=ti Þ;
ð1Þ
i¼1
where e0 ¼ 1=E0 is the elastic strain (i.e., strain induced immediately after the stress is applied) caused by a unit stress (i.e., s ¼ 1). Note that the end of the elastic deformation portion of the experimental data, i.e., e0 ; is defined herein as the point of which the second derivative first changes its sign, generally from negative to positive. In Eq. (1), the retardation times, ti ’s, are values which can be arbitrarily chosen providing some restrictions are satisfied, (Bazant, 1988; Bazant and Prasannan, 1989). However, any two adjacent Kelvin units having a relationship of Dðlog ti Þ ¼ 1 generally gives sufficiently smooth creep curves; (Bazant and Xi, 1995). That is to say, if the smallest retardation time is chosen as 103 h, the subsequent retardation times will generally be selected as102, 101, 100, 101 h, etc.
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Furthermore, a ‘‘N’’-unit Kelvin–Chain model can generally simulate creep data of ‘‘N’’ orders of magnitude on the time scale. Note, however, if extrapolation of the experimental data is desirable, more Kelvin units are necessary. For example, if an extrapolation out to 104 h is desirable using a 1000 h creep data (i.e., one-order extrapolation), one additional Kelvin unit with retardation time of 104 h is necessary. As to the selection of Ei ’s, they are determined by optimum fitting of the creep data under the constraints of the preselected retardation times. It is clear that a regression analysis (optimum fitting) for determining six or more unknowns (number of Ei ’s, in this case) can be extremely time consuming. A procedure which reduces the number of independent variables to only two, regardless of the actual number of Ei ’s, is recommended herein. The following expression is proposed to serve the aforementioned purpose (see Bazant and Xi (1995) for detailed mathematical derivations): 1 2n2 ð3ti Þ2n3 ðn 1 ð3ti Þn Þ ¼ 1:151ðaÞð3ti Þ3 Ei ð1 þ ð3ti Þn Þ3 nðn 2Þð3ti Þn3 ðn 1ð3t1 Þn Þ n2 ð3ti Þ2n3 þ : ð2Þ ð1 þ ð3ti Þn Þ2 In Eq. (2), ‘‘a’’ and ‘‘n’’ are the new targeted unknowns (instead of Ei ’s) associated with the modeled creep data. Note that the new curve fitting process involves only two variables and is much simpler. By varying the two independent variables ‘‘a’’ and ‘‘n’’ in Eq. (2), different combinations of Ei ’s with respect to the pre-selected retardation times, ti ’s, can be obtained. This allows a comparison of each calculated result of Eq. (1) to the actual experimental data. The calculated result is then optimized using the least-squares approximation (weighing by ‘‘time’’ is recommended) and iteration of this process will eventually converge on the actual experimental data. The resulting optimum model can then be used to predict experimental creep behavior beyond the actual measured data. This will be illustrated using the experimental creep data for the GCLs that are evaluated in this study.
4. Experimental data, curve fitting, and extrapolation Three reinforced GCLs were selected for testing and evaluation using the procedures described previously. They were selected since they were sampled directly from the products used in the Cincinnati field study mentioned earlier. GCL-1 was a needle punched product with nonwoven needle punched geotextiles on both upper and lower surfaces. The short-term data produced an internal friction angle of 301 with 9.8 kPa shear strength at 17 kPa normal stress. GCL-2 was a needle punched product with a nonwoven needle punched geotextile on one surface and a slit film woven geotextile on the other. The short-term data produced an internal friction angle of 251 with 7.9 kPa shear strength at 17 kPa normal stress. GCL-3 was a stitch bonded product (with stitching rows at 25 mm spacing) with a combined woven slit
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film and monofilament geotextile on both upper and lower surfaces. The short-term data produced an internal friction angle of 451 with 17.0 kPa shear strength at 17 kPa normal stress. Note that the products are not specifically identified since each of them have changed significantly since the field testing program was initiated in 1994. Needle punched GCL-1 was evaluated at 20%, 30%, 40% and 50% of its shortterm strength with each load held for 1000 h, see Fig. 5a. Using the Kelvin–Chain model, the 20%, 30% and 40% data was extrapolated to beyond 1 106 h (114 years) in Fig. 5b. Note that the 50% data was not used due to the anomalous step in the data at the end of the 40% test. From these graphs isochronous time curves were plotted in Fig. 5c for 1000 h (the actual data) and then for 1, 10 and 100 years. Needle punched GCL-2 was evaluated at 20%, 30%, 40%, 50% and 60% of its short-term strength with each load held for 1000 h, see Fig. 6a. Using the Kelvin– Chain model, the data was extrapolated to beyond 1 106 h (114 years) in Fig. 6b. Note that the 60% data required considered judgment in this regard. From these graphs isochronous time curves were plotted in Fig. 6c for 1000 h (the actual data) and then for 1, 10 and 100 years. Stitch bonded GCL-3 was evaluated at 20%, 30%, 40% and 50% of its short-term strength with each load held for 1000 h, see Fig. 7a. Using the Kelvin–Chain model, the data was extrapolated to beyond 1 106 h (114 years) in Fig. 7b. From these graphs isochronous time curves were plotted in Fig. 7c for 1000 h (the actual data) and then for 1, 10 and 100 years. A concern was expressed among the group regarding the reproducibility of the experimental data considering the long testing times that were involved. Thus, the needle punched GCL-2 product was retested for both the 20% and 30% loads. It was seen that the two sets of response curves were essentially identical to one another.
5. Discussion Concern by designers, owners and regulators has rightfully been expressed as to the long-term strength of the fiber or yarn components of reinforced GCLs. Thus, this effort has been undertaken to attempt to address the situation. The mechanical creep behavior of three reinforced GCLs under long-term laboratory creep testing has been investigated. In general, there were no ongoing creep deformations up to 30% of the short-term strength. Note that the initial deformations shown in Figs. 5a, 6a and 7a are elastic and of a short time period. At 40%, there was evidence of a slight amount of ongoing creep deformation and at 50% the deformation was more pronounced. At no time, however, was secondary creep (much less tertiary creep) evidenced in any of the test specimens. This gave impetus to extrapolation of the data to longer time periods. Using the Kelvin–Chain model, the data was extrapolated out to 1 106 h (114 years). The obvious target was 100 years which is a time period considered in some GCL applications. Having this data in Figs. 5b, 6b and 7b allowed for the plotting of isochronous time curves. They were presented in Fig. 5c, 6c and 7c for the three
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Fig. 5. (a) Creep strain date for needle punched GCL-1. (b) Kelvin–Chain extrapolated creep strain data for GCL-1. (c) Isochronous creep strain curves for GCL-1.
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Fig. 6. (a) Creep strain data for needle punched GCL-2. (b) Kelvin–Chain extrapolated creep strain data for GCL-2. (c) Isochronous creep strain curves for GCL-2.
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Fig. 7. (a) Creep strain data for needle punched GCL-3. (b) Kelvin–Chain extrapolated creep strain data for GCL-3. (c) Isochronous creep strain curves for GCL-3.
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products evaluated. All products appear to result in tolerable deformations up to loads equal to 30% of their short-term strengths, i.e., deformations of 10, 5 and 10 mm, respectively, for the three reinforced GCLs that were evaluated. It is suggested by these observations that the internal shear strength of both needle punched fibers and stitch bonded yarns used to reinforce the evaluated GCLs is adequate.
6. Conclusions and recommendations The creep deformation behavior of the fibers of needle punched reinforced GCLs and the yarns of stitch bonded GCLs was measured and furthermore extrapolated out to 100-year lifetimes. There was no evidence of fiber or yarn pullout or breakage in any of the tests. The extrapolation from 1000 h tests to 100-year lifetime is a three order of magnitude increase, which is indeed ‘‘bold’’. However, to do creep tests on hydrated GCLs for 10,000 h, or longer, is not without its own difficulties. Such operational problems such as rusting of equipment, biological algae growth, evaporation of water, and physical or vibrational disturbance of the test setup were all experienced within the 1000 h tests. They would probably be more difficult at considerably longer times. Possible changes in the bentonite component over time would also be a consideration, e.g., ion exchange as described by Daniel (2000). On a practical basis, the time and cost of such extremely long tests almost forces them to be put into a research classification. It should also be noted that fiber structure of both the needle punched and stitch bonded types of GCLs is very complex. It is indeed a textile engineering challenge complicated greatly by the encapsulating hydrated bentonite. The type of ‘‘yielding’’ confinement that the bentonite provides is clearly a topic for further research. The basic conclusion reached from these tests, however, is that the fiber structure maintained its integrity in all three of these GCL products over all loads that were evaluated. Even further, the deformations measured were very small and even with the extrapolation of the data out to 100-year lifetime the deformations are still within reasonable limits. Thus the polymers used (resin type, antioxidants, additives, etc.) appear to be appropriate. It seems necessary to develop specifications and testing guidelines to assure that the polymer formulation is consistent in light of this type of long-term testing. In the authors opinion, a generic specification should be developed.
Acknowledgements The financial assistant of the member organizations of the Geosynthetic Institute and its related institutes for research, information, education, accreditation and certification is sincerely appreciated. Their identification and contact number information is available on the institute’s web site at ‘‘geosyntheticinstitute.org’’.
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