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Long-term allowable tensile stresses for polyethylene geomembranes
Geotextiles and Geomembranes 12 (1993) 287-306
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Long-Term Allowable Tensile Stresses for Polyethylene Geomembranes Ryan R. Berg Consultant, 2190 Leyland Alcove, Woodbury, Minnesota 55125, USA
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Rudolph Bonaparte GeoSyntec Consultants, 5775 Peachtree Dunwoody Road, Suite 200F, Atlanta, Georgia 30342, USA (Received 14 July 1992; accepted 24 November 1992)
ABSTRACT The objective of this paper is to present a rational methodology for establishing long-term allowable tensile stresses for polyethylene geomembranes used in waste-containment applications. Procedures currently used in the USA do not account for all of the factors that may significantly affect this parameter. The proposed procedure is intended to address this limitation by providing a framework to account for time, temperature, exposure environment, seam response, and boundary-stress and deformation conditions. The proposed procedure is conceptually similar to procedures used to establish the long-term allowable tension for geosynthetic reinforcement. An example of the use of the procedure is provided.
INTRODUCTION Polyethylene geomembranes are widely used in the United States (USA) as low-permeability barrier layers in liner and cover systems at landfills, liquid impoundments, and other waste-containment facilities. Typical examples of geomembrane usage at these facilities are shown in Fig. 1. The primary function of the geomembrane in all of these applications is liquid 287 Geotextiles and Geomembranes 0266-1144/93/$06-00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Great Britain.
Ryan R. Berg, Rudolph Bonaparte
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(a)
(b)
LEGEND LINERORCOVER SYSTEM GEOMEMBRANE
(c)
~" LINER SYSTEM
Fig. 1. Geomembrane application in: (a) landfill; (b) liquid impoundment; and (c) ore-
leachingpad. barrier. In order to satisfy this function, the integrity of the geomembrane, including welded seams between adjacent geomembrane panels, must be maintained. Tensile rupture has a deleterious effect on integrity, and thus stresses within geomembranes should be maintained below levels that cause rupture. The purpose of this paper is to review and evaluate current practice in the USA for establishing allowable tensile stresses for polyethylene (PE) geomembranes, and to recommend a new, more rational approach. The remainder of this paper is organized as follows. A discussion of current USA practice with respect to establishing allowable tensile stresses for PE geomembranes is presented first. This discussion is followed by an evaluation of the limitations of the current approach. A new procedure is then proposed for establishing allowable tensile stress. The proposed procedure is based on the use of constant-load tension tests (i.e. creep tests) and is similar to procedures currently used to evaluate long-term allowable stresses for geosynthetic reinforcement. Results of creep-testing of a specific PE geomembrane are used to illustrate the application of the proposed procedure. The paper concludes with a discussion on the implications of applying the proposed procedure in practice.
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STATE-OF-PRACTICE Description The safest approach to the design of PE geomembrane liners is to minimize or eliminate the potential for tensile stresses within the geomembrane. This goal can be accomplished by controlling the various elements of design, such as total and differential settlements of the foundation, slope stability, anchor-trench stability, and details associated with geometric discontinuities and penetrations of the geomembrane by pipes. In some applications, however, it may not be possible to totally eliminate the potential for applied or induced tensile stresses. When the design of a facility necessitates consideration of an allowable geomembrane tensile stress, current practice frequently consists of selecting a value based on the results of short-term tension tests, such as tests conducted in accordance with the American Society for Testing and Materials D 638, Standard Test Method for Tensile Properties of Plastics (ASTM, 199 la). This method involves testing a dumbbell-shaped specimen in uniaxial tension at 23°C and a deformation rate of 50 mm/min. ASTM D 638 is a short-term index test that generates data primarily for qualitycontrol and comparative-study purposes. In fact, the following statement is provided in the Significance and Use section of the test method: '... data obtained by this test method cannot be considered valid for applications involving load-time scales or environments widely different from those of this test method. In cases of such dissimilarity, no reliable estimation of the limit of usefulness can be made for most plastics. This sensitivity to rate of straining and environment necessitates testing over a broad load-time scale (including impact and creep) and range of environmental conditions if tensile properties are to suffice for engineering design purposes.' Notwithstanding this caution, practitioners frequently use short-term test results to establish long-term allowable stress. Uniaxial tension-strain curves for PE geomembranes, obtained from short-term tests, typically exhibit ductile behavior with strains at rupture of several hundred percent or more. The curves also typically exhibit a distinct yield point followed by a transition in which the materials exhibit strainsoftening behavior. Giroud (1984) showed that the softening behavior of PE geomembranes in uniaxial loading results in material sensitivity to notches and other geometric discontinuities. He recommended that, to avoid this sensitivity, PE geomembranes be designed to carry tensile stresses less than the yield stress. In a uniaxial test, such as ASTM D 638, the yield stress of most medium- and high-density PE geomembranes occurs at a tensile strain between 10 and 15 percent.
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Based on the work of Giroud (1984), the present state-of-practice in the USA for the design of PE geomembranes is to limit the allowable geomembrane tensile strain to the short-term yield strain divided by a factor of safety. Factors of safety of 1.5-2 are typical, resulting in allowable tensile strains for design in the range of about 5-10%. With this approach, the design engineer implicitly assumes that the long-term stress associated with this short-term strain level is acceptable and that rupture will not occur. This approach has been accepted by some environmental-regulatory agencies and utilized by many design engineers (e.g. Stephens & Bodner, 1991; Tieman et al., 1990). In the past few years, the state-of-practice described above was augmented by growing consideration of the stress-crack resistance of PE geomembranes (e.g. Peggs & Carlson, 1990; Halse et al., 1988). Stress cracking is defined in ASTM D 883 as 'an external or internal rupture in a plastic caused by tensile stress less than its short-term mechanical strength' (ASTM, 1991b). Today, there is an awareness that resin selection is of primary importance in obtaining a stress-crack-resistant PE geomembrane. Shortcomings of existing standardized tests for identifying stress-crackresistant materials, such as ASTM D 1693 (ASTM, 1988a), have been described in the literature (Halse et al., 1990). New tests, particularly the notched constant-tension load (NCTL) test proposed by Halse et al. (1990), are now being used to identify stress-crack-resistant materials better. The development of these new tests as a means of selecting stress-crack-resistant resins is an important step in addressing the long-term mechanical performance of PE geomembranes. However, once a resin is selected and the geomembrane is manufactured, there remains a need to quantify longterm allowable tensile stresses for those projects in which the geomembrane will be subjected to boundary tensile loads or deformations. Limitations
The state-of-practice described in the preceding section for establishing allowable stresses for PE geomembranes neglects to account for a number of important factors, including time, temperature, exposure environment, presence of seams, stress and boundary-installation damage or deformation conditions. Each of these factors is briefly described below. Time
Polyethylene geomembranes are thermoplastic materials that exhibit timedependent responses to applied boundary stresses or deformations. For example, the creep tensile stress at rupture of a PE geomembrane decreases with increasing duration of load application, as illustrated in Fig. 2.
Long-term tensile stressesfor polyethylene geomembranes
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LOG TIME (s) Fig. 2. Rupture stress-time-temperature relationship for a PE geomembrane.
Furthermore, as also illustrated in this figure, PE geomembranes subjected to constant tensile stress may exhibit either a ductile or a brittle failure mode.
Temperature The influence of temperature on the response of a PE geomembrane subjected to a constant tensile stress is also illustrated in Fig. 2. For a given stress, the time to failure decreases as the temperature increases. Moreover, the transition time from a ductile to a brittle failure mode decreases as the temperature increases.
Exposure environment PE geomembranes are resistant to degradation in most environments encountered in waste containment. Under certain conditions of exposure to chemicals or radiation, however, the stress-strain characteristics of a PE geomembrane may be affected. Seams With current practice, the shear strength of PE geomembrane seams is not typically accounted for in design. Design specifications (NSF, 1991; EPA, 1988) usually require that the short-term shear strength of the seam be equal to some fraction (e.g. 90%) of the short-term tensile strength of the geomembrane. No attempt is typically made, however, to evaluate longterm seam response. There is currently very little information available on the long-term behavior of seams under stress, on the behavior of seams subjected to complex stress states, and on the effect of the seaming technique or process.
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Ryan R. Berg, Rudolph Bonaparte
Installation damage
As with other geosynthetics, H D P E geomembranes can be damaged during the installation process. The importance of this factor is probably less for geomembranes than for other geosynthetics, as a primary design goal is to protect the geomembrane from damage that could result in holes. Boundary-stress a n d deformation conditions
Boundary stress and deformation conditions in the field may be simple and well-defined or quite complex. In the laboratory, plane-strain boundary conditions are typically approximated to by using wide-strip tension tests (ASTM, 1988b), while axisymmetric boundary conditions are approximated to by using burst-type tension tests (GRI, 1990b; Koerner et al., 1990a; Frobel, 1991). The influence of the boundary-stress conditions on a PE geomembrane stress-strain response is illustrated in Table 1. It should also be recognized that boundary conditions in many geomembrane applications are deformation-controlled, not stress-controlled. An example of a stress-controlled boundary condition is a covered geomembrane on a slope having unbalanced shear stresses on its upper and lower surfaces (Fig. 3). An example of a deformation-controlled boundary condition is a foundation settlement that leads to geomembrane distortions at the base of a landfill (Fig. 4). In stress-controlled applications, the geomembrane is free to strain in response to the application of an external stress. If the external stress is sustained, the internal stress within the geomembrane will also be sustained, and the geomembrane will creep. In deformation-controlled applications, the geomembrane develops internal stresses in response to deformations in the surrounding environment. As Table 1
Results of Short-Term Tension Testsa Test
Dumbbell specimenb
Narrow specimenc
Wide specimena
Circular specimene
Yield stress (N/mm2) Yield strain (%) Ultimate stress (N/mm2) Ultimate strain (%)
22 11 28 700
21 13 24 600
19 15 21 500
16 47 16 47
~Data are for product identified as HDPE geomembrane and are taken from Koerner 099o). lT)umbbellspecimen, 6 mm wide, pulled at 50 mm/min. eNarrow-str/p specimen, 25 mm wide, pulled at 50 mm/min. dWide-strip specimen, 200 mm wide, pulled at 50 mm/min. eSpecimenplaced over a 200 mm diameter circular void filled with compressible foam and subjected to hydrostatic pressure on top side. Stress and strain were estimated by assuming an elliptical deformed shape.
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i SOIL
W F
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Fig. 3. Load-controlledboundary condition.(Note: T = geomembrane tension (N/m); Fs = shear force per unit width on top surface of geomembrane (N/m); Fr = shear resistanceper unitwidth on bottom surfaceof geomernbrane(N/m); and P = passiveforce per unitwidth (N/m); W = weight(N/m); and N = normal force(N/m)).
soon as deformations stop, gcomembrane strain becomes constant, and stress relaxation begins. Ideally, the procedure for establishing the allowable stress for gcomcmbrane liners should account for all of the above-mentioned factors.
PROPOSED PROCEDURE Overview The proposed procedure for establishing allowable tensile stresses for P E geomcmbranes draws heavily from conceptually similar procedures currently used to evaluate long-term allowable tensile stresses for geosynthetic reinforcement (e.g. Bonaparte & Berg, 1987; Jewell & Greenwood, 1988; A A S T H O - A G C - A R T B A , 1990; GRI, 1990a, 1991, 1992; Allen, 1991). The procedure requires that creep-testing be performed on the geomembrane at a range of temperatures and that the test resultsbe extrapolated to the in-service temperature and design life.Testing should simulate the nature of the applied loads (i.e.uniaxial or multiaxial, and deformation- or stress-controlled) as rupture occurs in the nonlinear viscoelastic range of response. The procedure described in this section of the paper is applicable only to stress-controlled boundary conditions; it is not directly applicable to situations where the geomembrane will substantially relax. Although work is underway on the subject (e.g. Koerner et al., 1990b, 1992), there are at present insufficient data to develop a full understanding of the stress-
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WASTE
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relaxation behavior of PE geomembranes. When additional data are available, the proposed procedure should be generalized. A discussion of each step in the proposed procedure is presented below. Step 1: Establish in-service conditions The allowable tensile stress for a PE geomembrane is a function of both the in-service environment and the required design life. In-service environmental conditions that should be defined include temperature, chemical exposure, and, if applicable, radiation exposure. Step 2: Establish stress-strain and rupture characteristics Long-term creep tests should be performed for each specific geomembrane (i.e. for each combination of resin, additive package, and manufacturer) for which the long-term allowable tensile stress is required. Ideally, the duration of creep-testing should equal or exceed the design life. It is impracticable, however, to perform tests for more than a few years. Various techniques (see Mruk, 1984; Koerner et al., 1992; and others) have been proposed for using limited-duration test data to estimate long-term design life. The techniques typically require that testing be performed at several temperatures, with the highest temperature being significantly above the expected in-service temperature (e.g. 20 to 60°C, assuming an in-service temperature of 20°C). The test results are then used to establish empirically or theoretically based relationships between tensile stress, time to rupture, and temperature. It is suggested that, even with the use of these techniques, the minimum duration of testing should be 10 000 hours, which is consistent with previous recommendations for geosynthetic reinforcement. The use of elevated-temperature testing as described above is valid only within limited ranges of temperature. For PE geomembranes, this range of temperature is approximately from -80°C to + 80°C, which corresponds to the region between glass- and melting-temperature transition zones. At
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each test temperature, a series of tests should be performed, at load levels ranging from approximately 20 to 80% of the short-term yield strength of the geomembrane, to establish the relationship between rupture stress and time. The test configuration that should be employed will depend on the boundary-loading conditions. For applications involving or approaching plane-strain conditions, wide-width-strip tension tests can be employed. For other applications, axisymmetric burst-type tests may be suitable. Data of the type described above have recently been presented by DuvaU and Edwards (1992) and Duvall (1993). The data are from axisymmetric burst-type tests involving specimens of a widely available 1.5 mm thick PE geomembrane. Three sets of specimens were tested under each condition listed in Table 2. Both ductile and brittle failure modes were observed in the tests. Stress-rupture-time relationships derived from the results of tests at temperatures of 60 and 80°C are presented in Fig. 5. A predicted stressrupture-time relationship for a temperature of 23°C, derived from regression analysis of the 60°C and 80°C test results, is also presented in Fig. 5. A rupture stress of 7.2 N/mm 2 at 50 years and 23°C is obtained for the tested geomembrane product under the assumed conditions. The failure mode corresponding to this rupture stress is brittle. It is interesting to note that, if testing had been stopped prior to the onset of brittle rupture (i.e. prior to about 5000 hours), only ductile failures would have been observed in the elevated-temperature tests. If only the ductile-rupture data are used to predict a geomembrane rupture stress at 23°C and 50 years, a value of 13-6 N/mm 2 is obtained. Table 2 Conditions for Long-Term Axisymmetric Rupture Testsa
Internal pressure (kPa) 205 275 345 415 485 550 690 830 550 620 690 415 485 550
Temperature (°C) 23 23 23 23 23 23 23 23 60 60 60 80 80 80
aFrom Duvall and Edwards (1992).
d verage stress (gPa) 5.0 6.0 7.0 8.0 8.8 9.7 11.6 13.4 9.1 10.2 11-5 6-9 8.1 9-5
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TIME (hours) Fig. 5. Rupture stress-time-temperature relationship of PE geomembrane under axisymmetric loading (from Duvall, 1993).
Duvall and Edwards (1992) and Duvall (1993) derived geomembrane stress-strain relationships from their test results by using the tensionmembrane model of Giroud (1981). The isochronous (i.e. constant-time) stress-strain relationships for the 23°C test results are shown in Fig. 6. Using regression analysis, Duvall and Edwards extrapolated the test data to develop a predicted 50-year isochronous stress-strain relationship, also shown in Fig. 6. Ideally, long-term tests should be conducted with the geomembrane in the expected chemical (and radiation) environment and with test specimens containing representative geomembrane seams. However, owing to experimental difficulty and cost, these factors will typically not be accounted for in the type of performance testing considered under Step 2. Steps 3 and 4, below, provide an alternative approach to account for these factors, though the approach results in an uncoupled evaluation of effects.
Long-term tensile stressesfor polyethylene geomembranes
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Step 3: Quantify an exposure
factor
A partial stress-reduction factor to account for geomembrane exposure to chemicals (or radiation) should be defined. Whereas PE is stable in many chemical environments, certain exposures will affect geomembrane properties. The resistance of a PE geomembrane to chemical attack will be product-specific, since resin characteristics, additive packages, and process techniques vary between manufacturers. In the absence of long-term testing, relatively short-term tests may be used to estimate a chemical-exposure factor. The US Environmental Protection Agency (EPA), for example, has developed Method 9090 (EPA, 1986), which involves exposing geomembrane specimens to the expected inservice chemical environment for up to 120 days at temperatures of up to 50°C. After prescribed exposure times of 30, 60, 90, and 120 days, the specimens are tested in short-term tension tests. This procedure should be extended to include testing at two different elevated temperatures (e.g. 35°C and 50°C) so that the results can be used to establish a relationship between
Ryan R. Berg, Rudolph Bonaparte
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short-term tensile strength, time of exposure, and temperature. From the relationship, an estimate can be developed for the short-term tensile strength of the geomembrane, ~cf, at the in-service temperature, environment, and design life. A stress-reduction factor to account for chemical degradation is then derived from the following equation: FC = --°~cr
(1)
O~ci
where FC ~cf 0~ci
= reduction factor for chemical (or radiation) exposure (dimensionless); = final predicted tensile strength of incubated specimen at the in-service temperature and design life; and = initial tensile strength of non-incubated specimen.
Limitations on the use of eqn (1) should realized. First, specimens are incubated in an unstressed condition. It is inherently assumed that the response of unstressed, incubated geomembrane specimens is similar to that of specimens incubated under stress. Second, the proposed approach assumes that the test exposure causes effects similar to those that would occur at the in-service temperature and design life. Third, the proposed approach does not recognize that the effects of chemical exposure may be manifested in stages, as stabilizers within the geomembrane are consumed. Step 4: Quantify a seam factor
A partial stress-reduction factor to account for differences in strength between geomembrane seams and geomembrane sheet material should be defined. As previously noted, design specifications in USA practice typically require that PE geomembrane seam-peel and shear strength be equal to a percentage of the short-term strength of the geomembrane material. These short-term test results could be used to develop a 'weld' factor. However, owing to the current absence of any data establishing a correlation between long-term seam behavior and short-term test results, such an approach is insupportable. John and Hessel (1985) reached a similar conclusion. Hessel and John (1987) reported that long-term weld factors can be derived from the results of creep tests on geomembrane specimens submerged in surfactants and subjected to elevated temperatures. Geomembrane sheet and seam specimens are tested to rupture under similar conditions. A weld factor, FW, is obtained by dividing the seamspecimen rupture stress by the sheet-specimen rupture stress, as illustrated in Fig. 7. Hessel and John have shown that weld factors derived in this
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manner are approximately equal to weld factors derived from longer-term tests in water. Testing, as described above, should be considered for the development of weld factors for specific geomembrane products and installers. Such testing would entail the use of specimens seamed under varying conditions to address weld methods, operator variations, site moisture and dust variations, geomembrane-material variations, weld temperatures, rate of welding, etc. At present, published data on the long-term strength of PE-geomembrahe seams are extremely limited. Most published information on this subject is from the German technical literature (Diedrich & Gaube, 1970; John & Hessel, 1985; Hessel & John, 1987; Koch et al., 1988; MQnk et al., 1989). Hessel and John (1987) performed testing to evaluate weld factors for PE geomembrane seams under conditions reported to be representative of those in the field. Their results are summarized in Table 3. Long-term weld factors from their investigation ranged from 0.3 to 0.8. These values are low compared with the weld factors of 0.8-0.9 they reported for extrusion welds produced under optimal conditions by the plasticcontainer industry.
Step 5: Quantify an installation-damage factor A partial stress-reduction factor to account for geomembrane scratches or gouges caused by installation should also be considered. Current practice
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Ryan R. Berg, Rudolph Bonaparte Long-Term
TABLE 3 Weld Factors Geomembranes ~
Seaming method
for
PE
Weldfactor
Extrusion welding Heated-tool welding Hot-gas welding
0.4-0.8 0-3-0.75 0.4-0.7
~Fest data are from preliminary work by Hessel and John (1987).
for evaluating this factor for geosynthetic reinforcement involves retrieving specimens from actual or prototype installations, subjecting the specimens to short-term (rapid) tensile tests, and then developing reduction factors for use on subsequent projects. Limited evidence indicates that short-term tensile tests can be used to estimate long-term reduction factors for geosynthetic reinforcement (Bush & Swan, 1988). With this approach, a stress-reduction factor is calculated by using the following equation: FI = --°gif
(2)
o~ii
where FI = reduction factor for installation damage (dimensionless); ~if = final tensile strength of exhumed specimen; and aii = initial tensile strength of undamaged specimen. An approach similar to that described above can be used for PE geomembranes. Specimens of PE geomembranes can be exhumed from project or test installations. These specimens can then be tested as indicated above to establish general reduction factors for future PE-geomembrane installations. It is expected that, in many cases, FI will be 1.0, or nearly so, since a primary design goal is geomembrane protection.
Step 6: Select over-all factor of safety An over-all factor of safety against geomembrane rupture should be established to account for uncertainties associated with applied loads, geometry, and construction. The selected factor of safety should also reflect judgement applied in making design assumptions and construction control, and in the consequences of failure. Over-all factors of safety of 1.35-1-5 are typically recommended in geosynthetic-reinforcement practice. These factors are, however, applied to a limit stress, which is less than the rupture stress considered here. In USA practice (Mruk, 1984; PPI, 1989), PE pipes are designed with the factor of
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safety applied to the rupture stress. The Plastic Pipe Institute (PPI, 1990) recommends an over-all factor of safety of 2.0 for water-conveyance applications and higher factors for natural-gas pipelines. An over-all factor of safety of 3.1 for gas distribution is called for in the Code for Pressure Piping of the American Society of Mechanical Engineers (ASME, 1989) and by the US Department of Transportation (DOT, 1989). It is noted that these factors of safety for pipes account for the normal effects of pipe installation. Selection of an over-all factor of safety for a specific project should be made by the design engineer. However, based on the present practice for gas pipelines, over-all factors of safety in the range of 2-3 appear reasonable for load-controlled applications in which the design analysis is based on unfactored loads.
Step 7: Compute allowable tensile stress An allowable long-term tensile stress may be computed by using eqn (3): aa =
tTr x FC x FW x FI FS
(3)
where aa
= allowable tensile stress at the given in-service temperature and design hfe (N/minE); ~rr = rupture stress at the given in-service temperature and design life (N/minE); FC = reduction factor to account for chemical (or radiation) degradation over the design life (dimensionless); FW = reduction factor (i.e. weld factor) to account for long-term seam strength (dimensionless); FI = reduction factor to account for installation damage (dimensionless); and FS = overall factor of safety (dimensionless).
Equation (3) defines a long-term allowable tensile stress for a specific geomembrane subject to a constant boundary tensile stress over a given design life. The strain corresponding to the allowable tensile stress is a function of the duration of loading and can be obtained from isochronous stress-strain relationship derived from the test results obtained in Step 2. EXAMPLE The test results shown in Figure 5 provide geomembrane rupture stresses for a range of conditions. The test results are used below, along with
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Ryan R. Berg, Rudolph Bonaparte
assumed values for the various reduction factors, to illustrate the application of the proposed procedure.
Example of appfication of the proposedprocedure Step 1: Establish in-service environment and design life. Assumption: service temperature is 23°C. Assumption: design life equals 50 years. Step 2: Establish stress-strain and rupture characteristics. From Fig. 6, O" r ----- 7-2 N/mm 2 Step 3: Quantify a chemical-exposure factor. Assumption: chemical-exposure factor, FC = 1. Step 4. Quantify a seam factor. Assumption: long-term seam factor, FW = 0.7. Step 5. Quantify an installation-damage factor. Assumption: installation-damage factor, FI = 1.0. Step 6. Select an over-all factor of safety. Assumption: over-all factor of safety against rupture, FS = 2-0. Step 7.
Calculate long-term allowable tensile stress. 7.2 MPa x 1-0 x 0.7 x 1-0 = 2.5 N/mm 2 aa = 2.0
Step 8. Evaluate tensile strain at allowable stress and design life. From Fig. 6, e ,,~ 1.5%. The values of allowable tensile stress and strain given in the above example can be compared with values obtained by utilizing the present state-of-practice in the USA. For current practice, a yield strain for a PEgeomembrane dumbbell-test specimen of 11% was assumed (Table 1), along with a factor of safety of 2.0. The resulting allowable strain (i.e. yield strain divided by factor of safety) is 5.5%. The corresponding allowable tensile stress, based on Table 1 and assuming a linear stress-strain response, is 11 N/mm 2. Clearly, the proposed procedure may result in a much lower allowable stress than that obtained by using the current stateof-practice. It is also interesting to note that, if the stress-rupture-time line in Fig. 5 had not exhibited a brittle 'knee', an allowable stress of 3.8 N/ram 2 and a corresponding tensile strain of 2.9% would have been obtained. This allowable stress, based on the ductile-stress rupture line in Fig. 5, is 5 0 0 higher than that obtained from the brittle-stress rupture line. This simple
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comparison highlights the importance of identifying the potential for a particular geomembrane to undergo brittle rupture when loaded, and the benefit to be gained by using a geomembrane resin not susceptible to this failure mode during the specified design life. Finally, it is noted that if the geomembrane was able to relax, a larger initial allowable stress would be acceptable.
CONCLUSIONS The USA state-of-practice for evaluating long-term allowable stresses for PE geomembranes at waste-containment facilities was reviewed, and the limitations of the practice were identified. A new, more rational procedure for evaluating long-term allowable tensile stress was presented. The proposed procedure accounts for time, temperature, ductile and brittle fracture, chemical environment, welded seams, installation damage, and an over-all factor of safety. Laboratory testing and engineering judgement are required at each step of the procedure. The procedure as presented here is limited to stress-controlled boundary conditions~ The use of the procedure was illustrated by an example. The allowable stress obtained in the example was significantly lower than the allowable stress obtained by using current USA practice. The testing requirements inherent in the proposed procedure may be viewed by some as being excessive or unduly expensive. The requirements are, however, no more extensive than those for other types of geosynthetics used to carry loads in permanent, critical applications. Programs of the type described here have previously been carried out for several different geosynthetic-reinforcement products. Furthermore, for a given product made from a specific resin, much of the required testing need be performed only once. When it is realized that a given product may be used on hundreds of projects involving millions of square meters of installation, the testing requirements indeed appear reasonable. The proposed procedure requires that extensive performance testing be conducted. Consequently, a system for ensuring that materials used in a particular project are the same as those tested is also required. Present quality-control test programs are not sufficiently sensitive to identify variations in polymer characteristics. Hence, consistent with the approach advocated in this paper, quality-control programs should include resinsource, resin-property, and geomembrane-property certification. Until these testing and certification programs are in place, design engineers will be faced with uncertainty in evaluating long-term allowable stresses for PE geomernbranes.
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Ryan R. Berg, Rudolph Bonaparte
ACKNOWLEDGEMENTS The authors are grateful to Professor Grace Hsuan, Dr Donald G. Bright, Mr Donald E. Duvall and Dr Majdi A. Othman for their input to this paper. The authors are also indebted to Dr Jean-Pierre Giroud and Professor Robert M. Koerner for their review of the paper.
REFERENCES AASTHO-AGC-ARTBA (1990). Design guidelines for use of extensible reinforcements (geosynthetic) for mechanically stabilized earth walls in permanent applications. In In-Situ Soil Improvement Techniques, Task Force 27 Report, AASHTO-AGC-ARTBA Joint Committee, Washington, DC, USA. Allen, T. M. (1991). Determination of long-term tensile strength of geosynthetics: a state-of-the-art review. In Proceedings of the Geosynthetics '91 Conference, Vol 1. Industrial Fabrics Association International, MN, USA, pp. 351-79. ASME (1989). Gas transmission and distribution piping systems - - codefor pressure piping, B31.8. American Society of Mechanical Engineers, New York, USA. ASTM (1988a). Standard Test Method for Environmental Stress-Cracking of Ethylene Plastics, D 1693. American Society for Testing and Materials, Philadelphia, PA, USA. ASTM (1988b). Standard Test Method for Determining Performance Strength of Geomembranes by the Wide Strip Tensile Method, D 4885. American Society for Testing and Materials, Philadelphia, PA, USA. ASTM (1991a). Standard Test Method for Tensile Properties of Plastics, D638. American Society for Testing and Materials, Philadelphia, PA, USA. ASTM (1991b). Terminology Relating to Plastics, D883. American Society for Testing and Materials, Philadelphia, PA, USA. Bonaparte, R. & Berg, R. R. (1987). Long-term allowable tension for geosynthetic reinforcement. In Proceedings of the Geosynthetics '87 Conference, Vol. 1. Industrial Fabrics Association International, MN, USA, pp. 181-92. Bush, D. I. & Swan, D. B. G. (1988). An assessment of the resistance of Tensar SR2 to physical damage during the construction and testing of a reinforced soil wall. In Polymeric Reinforcement in Soil Retaining Structures (NATO Advanced Study Institute Series). Kluwer Academic Publishers, London, England, pp. 173-80. Diedrieh, G. & Gaub¢, E. (1970). Welding methods for rigid polyethylene pipe and sheet: creep rupture strength and long term welding factors. Kunstsoffe, 60, 7480. Translated by SCITRAN. DOT (1989). Transportation of natural gas and other gas by p~eline: minimum safety standards. Title 49, US Code of Federal Regulations (CFR), Part 192. US Department of Transportation, Research and Special Programs Administration, Office of Pipeline Safety, Washington, DC, USA. Duvall, D. E. (1993). Creep and stress rupture testing of a polyethylene geomembrane under equal biaxial tensile stress. Proceedings of the Geosynthetics '93 Conference, Vol. 2. Industrial Fabrics Association International, MN, USA, 1993, pp. 817-30.
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DuvaU, D. E. & Edwards, D. B. (1992). Creep and stress rupture testing of polyethylene sheet under equal biaxial tensile stresses. In Proceedings of the Society of Plastics Engineers 50th Annual Technical Conference. Society of Plastic Engineers, CT, USA, pp. 128-31. EPA 0986). Method 9090, Compatibility test for wastes and membrane liners. In Tests Methods for Evaluating Solid Waste, Vol. 1A: Laboratory Manual, Physical/Chemical Methods, US Environmental Protection Agency, Washington, DC, USA. EPA 0988). Lining of waste containment and other impoundment facilities, EPA/ 600/2-88/052. US Environmental Protection Agency, Washington, DC, USA. Frobel, R. K. (1991). Geosynthetic material response to landfill cap settlement and subsidence. In Proceedings of the Geosynthetics '91 Conference, Vol. 1. Industrial Fabrics Association International, MN, USA, pp. 175-86. Giroud, J. P. (1981). Designing with geotextiles. Materieux et Constructions, 14, 257-72. Giroud, J. P. (1984). Analysis of stresses and elongations in geomembranes. In Proceedings of the International Conference on Geomembranes, Vol. 2. RILEM, Paris, France, pp. 481--6. GRI (1990a). Determination of the Long-Term Design Strength of Stiff Geogrids, GRI Test Method GG4(a). Geosynthetic Research Institute, Drexel University, Philadelphia, PA, USA. GRI (1990b). Three Dimensional Geomembrane Tension Test, GRI Test Method GM4. Geosynthetic Research Institute, Drexel University, Philadelphia, PA, USA. GRI (1991). Determination of the Long-Term Design Strength of Flexible Geogrids, GRI Test Method GG4(b). Geosynthetic Research Institute, Drexel University, Philadelphia, PA, USA. GRI (1992). Determination of the Long-Term Design Strength of Geotextiles, GRI Test Method GT7. Geosynthetic Research Institute, Drexel University, Philadelphia, PA, USA. Halse, Y. H., Koerner, R. M. & Lord, A. E., Jr. (1988). Laboratory evaluation of stress cracking in HDPE geomembrane seams. In Aging and Durability of Geosynthetics, ed. R. M. Koerner. Elsevier Applied Science, London, England, pp. 177-94. Halse, Y. H., Lord, A. E., Jr. & Koerner, R. M. 0990). Ductile-to-brittle transition time in polyethylene geomembrane sheet. In Geosynthetic Testing for Waste Containment Applications (STP1081) ed. R. M. Koerner. American Society for Testing and Materials, Philadelphia, PA, USA, pp. 95-109. Hessel, J. & John, P. (1987). Long-term strength of welded joints in polyethylene water proofing sheets for refuse dumps. Materialwissenschaft Und Werkstofftech, 18, 228-31. Translated by SCITRAN. Jewell, R. A. & Greenwood, J. H. (1988). Long term strength and safety in steep slopes reinforced by polymer materials. Geotextiles and Geomembranes, 7, 81118. John, P. & Hessel, J. (1985). Heated plate welding of HDPE pipes and sheets. Kunstsoffe, 75, 770-2. Translated by SCITRAN. Koch, P., Gaube, E., Hessel, J., Gondro, C., & Heil, H. (1988). Long-term strength of dump lining sheets made of polyethylene. Muell and Abfall, 8, 3-12. Translated by SCITRAN. Koerner, R. M. (1990). Designing with Geosynthetics (2nd edition). Prentice Hall, Englewood Cliffs, NJ, USA.
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Koerner, R. M., Koerner, G. R. & Hwu, B. L. (1990a). Three-dimensional, axisymmetric geomembrane tension test. In Geosynthetic Testing for Waste Containment Applications (STP 1081) ed. R. M. Koerner. American Society for Testing and Materials, Philadelphia, PA, USA, pp. 170-84. Koerner, R. M., Halse, Y. H. & Lord, A. E. (1990b). Long-term durability and aging of geomembranes. In Waste Containment Systems: Construction, Regulation, and Performance, Geotechnical Special Publication No. 26, ed. R. Bonaparte, American Society of Civil Engineers, New York, NY, USA, pp. 106-34. Koerner, R. M., Hsuan, Y. & Lord, A. E. (1992). Remaining technical barriers to obtain general acceptance of geosynthetics. 1992 Mercer Lecture, International Geotextile Society, Mfink, G., Hegler, R. P. & Mennig, G. (1989). Lining of waste landfills. Kunstsoffe, 79, 352-8. Translated by SCITRAN. Mruk, S. A. (1984). Polyethylene piping systems for gas distribution/past, present, and future. Presented at the Pacific Gas Association Distribution Conference, Irvine, CA, USA. NSF (1991). Flexible Membrane Liners, NSF 54 Standard. National Sanitation Foundation, Ann Arbor, Michigan, USA. Peggs, I. D. & Carlson, D. S. (1990). Brittle fracture in polyethylene geomembranes. In Geosynthetics: Microstructure and Performance (STP 1076), ed. I. D. Peggs. American Society for Testing and Materials, Philadelphia, PA, USA, pp. 57-77. PPI (1989). Policies and procedures for developing recommended hydrostatic design stresses for thermoplastic pipe materials. (Technical Report TR3). Plastic Pipe Institute, Wayne, N J, USA. PPI (1990). Recommended hydrostatic strengths and design stresses for thermoplastic pipe and fittings compounds. (Technical Report TR4). Plastic Pipe Institute, Wayne, NJ, USA. Stephens, A. & Bodner, R. (1991). Geogrid liner support at Empire sanitary landfill. In Proceedings of the Geosynthetics '91 Conference, Vol. 1. Industrial Fabrics Association International, MN, USA, pp. 15-22. Tieman, G. E., Druback, G. W., Davis, K. A. & Weidner, C. H. (1990). Stability considerations of vertical landfill expansions. In Geotechnics of Waste Fills - Theory and Practice (STP 1070), eds. A. Landva & G. D. Knowles. American Society for Testing and Materials, Philadelphia, PA, USA, pp. 285-302.
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Long-Term Allowable Tensile Stresses for Polyethylene Geomembranes Ryan R. Berg Consultant, 2190 Leyland Alcove, Woodbury, Minnesota 55125, USA
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Rudolph Bonaparte GeoSyntec Consultants, 5775 Peachtree Dunwoody Road, Suite 200F, Atlanta, Georgia 30342, USA (Received 14 July 1992; accepted 24 November 1992)
ABSTRACT The objective of this paper is to present a rational methodology for establishing long-term allowable tensile stresses for polyethylene geomembranes used in waste-containment applications. Procedures currently used in the USA do not account for all of the factors that may significantly affect this parameter. The proposed procedure is intended to address this limitation by providing a framework to account for time, temperature, exposure environment, seam response, and boundary-stress and deformation conditions. The proposed procedure is conceptually similar to procedures used to establish the long-term allowable tension for geosynthetic reinforcement. An example of the use of the procedure is provided.
INTRODUCTION Polyethylene geomembranes are widely used in the United States (USA) as low-permeability barrier layers in liner and cover systems at landfills, liquid impoundments, and other waste-containment facilities. Typical examples of geomembrane usage at these facilities are shown in Fig. 1. The primary function of the geomembrane in all of these applications is liquid 287 Geotextiles and Geomembranes 0266-1144/93/$06-00 © 1993 Elsevier Science Publishers Ltd, England. Printed in Great Britain.
Ryan R. Berg, Rudolph Bonaparte
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(a)
(b)
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~" LINER SYSTEM
Fig. 1. Geomembrane application in: (a) landfill; (b) liquid impoundment; and (c) ore-
leachingpad. barrier. In order to satisfy this function, the integrity of the geomembrane, including welded seams between adjacent geomembrane panels, must be maintained. Tensile rupture has a deleterious effect on integrity, and thus stresses within geomembranes should be maintained below levels that cause rupture. The purpose of this paper is to review and evaluate current practice in the USA for establishing allowable tensile stresses for polyethylene (PE) geomembranes, and to recommend a new, more rational approach. The remainder of this paper is organized as follows. A discussion of current USA practice with respect to establishing allowable tensile stresses for PE geomembranes is presented first. This discussion is followed by an evaluation of the limitations of the current approach. A new procedure is then proposed for establishing allowable tensile stress. The proposed procedure is based on the use of constant-load tension tests (i.e. creep tests) and is similar to procedures currently used to evaluate long-term allowable stresses for geosynthetic reinforcement. Results of creep-testing of a specific PE geomembrane are used to illustrate the application of the proposed procedure. The paper concludes with a discussion on the implications of applying the proposed procedure in practice.
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STATE-OF-PRACTICE Description The safest approach to the design of PE geomembrane liners is to minimize or eliminate the potential for tensile stresses within the geomembrane. This goal can be accomplished by controlling the various elements of design, such as total and differential settlements of the foundation, slope stability, anchor-trench stability, and details associated with geometric discontinuities and penetrations of the geomembrane by pipes. In some applications, however, it may not be possible to totally eliminate the potential for applied or induced tensile stresses. When the design of a facility necessitates consideration of an allowable geomembrane tensile stress, current practice frequently consists of selecting a value based on the results of short-term tension tests, such as tests conducted in accordance with the American Society for Testing and Materials D 638, Standard Test Method for Tensile Properties of Plastics (ASTM, 199 la). This method involves testing a dumbbell-shaped specimen in uniaxial tension at 23°C and a deformation rate of 50 mm/min. ASTM D 638 is a short-term index test that generates data primarily for qualitycontrol and comparative-study purposes. In fact, the following statement is provided in the Significance and Use section of the test method: '... data obtained by this test method cannot be considered valid for applications involving load-time scales or environments widely different from those of this test method. In cases of such dissimilarity, no reliable estimation of the limit of usefulness can be made for most plastics. This sensitivity to rate of straining and environment necessitates testing over a broad load-time scale (including impact and creep) and range of environmental conditions if tensile properties are to suffice for engineering design purposes.' Notwithstanding this caution, practitioners frequently use short-term test results to establish long-term allowable stress. Uniaxial tension-strain curves for PE geomembranes, obtained from short-term tests, typically exhibit ductile behavior with strains at rupture of several hundred percent or more. The curves also typically exhibit a distinct yield point followed by a transition in which the materials exhibit strainsoftening behavior. Giroud (1984) showed that the softening behavior of PE geomembranes in uniaxial loading results in material sensitivity to notches and other geometric discontinuities. He recommended that, to avoid this sensitivity, PE geomembranes be designed to carry tensile stresses less than the yield stress. In a uniaxial test, such as ASTM D 638, the yield stress of most medium- and high-density PE geomembranes occurs at a tensile strain between 10 and 15 percent.
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Based on the work of Giroud (1984), the present state-of-practice in the USA for the design of PE geomembranes is to limit the allowable geomembrane tensile strain to the short-term yield strain divided by a factor of safety. Factors of safety of 1.5-2 are typical, resulting in allowable tensile strains for design in the range of about 5-10%. With this approach, the design engineer implicitly assumes that the long-term stress associated with this short-term strain level is acceptable and that rupture will not occur. This approach has been accepted by some environmental-regulatory agencies and utilized by many design engineers (e.g. Stephens & Bodner, 1991; Tieman et al., 1990). In the past few years, the state-of-practice described above was augmented by growing consideration of the stress-crack resistance of PE geomembranes (e.g. Peggs & Carlson, 1990; Halse et al., 1988). Stress cracking is defined in ASTM D 883 as 'an external or internal rupture in a plastic caused by tensile stress less than its short-term mechanical strength' (ASTM, 1991b). Today, there is an awareness that resin selection is of primary importance in obtaining a stress-crack-resistant PE geomembrane. Shortcomings of existing standardized tests for identifying stress-crackresistant materials, such as ASTM D 1693 (ASTM, 1988a), have been described in the literature (Halse et al., 1990). New tests, particularly the notched constant-tension load (NCTL) test proposed by Halse et al. (1990), are now being used to identify stress-crack-resistant materials better. The development of these new tests as a means of selecting stress-crack-resistant resins is an important step in addressing the long-term mechanical performance of PE geomembranes. However, once a resin is selected and the geomembrane is manufactured, there remains a need to quantify longterm allowable tensile stresses for those projects in which the geomembrane will be subjected to boundary tensile loads or deformations. Limitations
The state-of-practice described in the preceding section for establishing allowable stresses for PE geomembranes neglects to account for a number of important factors, including time, temperature, exposure environment, presence of seams, stress and boundary-installation damage or deformation conditions. Each of these factors is briefly described below. Time
Polyethylene geomembranes are thermoplastic materials that exhibit timedependent responses to applied boundary stresses or deformations. For example, the creep tensile stress at rupture of a PE geomembrane decreases with increasing duration of load application, as illustrated in Fig. 2.
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Furthermore, as also illustrated in this figure, PE geomembranes subjected to constant tensile stress may exhibit either a ductile or a brittle failure mode.
Temperature The influence of temperature on the response of a PE geomembrane subjected to a constant tensile stress is also illustrated in Fig. 2. For a given stress, the time to failure decreases as the temperature increases. Moreover, the transition time from a ductile to a brittle failure mode decreases as the temperature increases.
Exposure environment PE geomembranes are resistant to degradation in most environments encountered in waste containment. Under certain conditions of exposure to chemicals or radiation, however, the stress-strain characteristics of a PE geomembrane may be affected. Seams With current practice, the shear strength of PE geomembrane seams is not typically accounted for in design. Design specifications (NSF, 1991; EPA, 1988) usually require that the short-term shear strength of the seam be equal to some fraction (e.g. 90%) of the short-term tensile strength of the geomembrane. No attempt is typically made, however, to evaluate longterm seam response. There is currently very little information available on the long-term behavior of seams under stress, on the behavior of seams subjected to complex stress states, and on the effect of the seaming technique or process.
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Ryan R. Berg, Rudolph Bonaparte
Installation damage
As with other geosynthetics, H D P E geomembranes can be damaged during the installation process. The importance of this factor is probably less for geomembranes than for other geosynthetics, as a primary design goal is to protect the geomembrane from damage that could result in holes. Boundary-stress a n d deformation conditions
Boundary stress and deformation conditions in the field may be simple and well-defined or quite complex. In the laboratory, plane-strain boundary conditions are typically approximated to by using wide-strip tension tests (ASTM, 1988b), while axisymmetric boundary conditions are approximated to by using burst-type tension tests (GRI, 1990b; Koerner et al., 1990a; Frobel, 1991). The influence of the boundary-stress conditions on a PE geomembrane stress-strain response is illustrated in Table 1. It should also be recognized that boundary conditions in many geomembrane applications are deformation-controlled, not stress-controlled. An example of a stress-controlled boundary condition is a covered geomembrane on a slope having unbalanced shear stresses on its upper and lower surfaces (Fig. 3). An example of a deformation-controlled boundary condition is a foundation settlement that leads to geomembrane distortions at the base of a landfill (Fig. 4). In stress-controlled applications, the geomembrane is free to strain in response to the application of an external stress. If the external stress is sustained, the internal stress within the geomembrane will also be sustained, and the geomembrane will creep. In deformation-controlled applications, the geomembrane develops internal stresses in response to deformations in the surrounding environment. As Table 1
Results of Short-Term Tension Testsa Test
Dumbbell specimenb
Narrow specimenc
Wide specimena
Circular specimene
Yield stress (N/mm2) Yield strain (%) Ultimate stress (N/mm2) Ultimate strain (%)
22 11 28 700
21 13 24 600
19 15 21 500
16 47 16 47
~Data are for product identified as HDPE geomembrane and are taken from Koerner 099o). lT)umbbellspecimen, 6 mm wide, pulled at 50 mm/min. eNarrow-str/p specimen, 25 mm wide, pulled at 50 mm/min. dWide-strip specimen, 200 mm wide, pulled at 50 mm/min. eSpecimenplaced over a 200 mm diameter circular void filled with compressible foam and subjected to hydrostatic pressure on top side. Stress and strain were estimated by assuming an elliptical deformed shape.
Long-term tensile stressesfor polyethylene geomembranes
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soon as deformations stop, gcomembrane strain becomes constant, and stress relaxation begins. Ideally, the procedure for establishing the allowable stress for gcomcmbrane liners should account for all of the above-mentioned factors.
PROPOSED PROCEDURE Overview The proposed procedure for establishing allowable tensile stresses for P E geomcmbranes draws heavily from conceptually similar procedures currently used to evaluate long-term allowable tensile stresses for geosynthetic reinforcement (e.g. Bonaparte & Berg, 1987; Jewell & Greenwood, 1988; A A S T H O - A G C - A R T B A , 1990; GRI, 1990a, 1991, 1992; Allen, 1991). The procedure requires that creep-testing be performed on the geomembrane at a range of temperatures and that the test resultsbe extrapolated to the in-service temperature and design life.Testing should simulate the nature of the applied loads (i.e.uniaxial or multiaxial, and deformation- or stress-controlled) as rupture occurs in the nonlinear viscoelastic range of response. The procedure described in this section of the paper is applicable only to stress-controlled boundary conditions; it is not directly applicable to situations where the geomembrane will substantially relax. Although work is underway on the subject (e.g. Koerner et al., 1990b, 1992), there are at present insufficient data to develop a full understanding of the stress-
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relaxation behavior of PE geomembranes. When additional data are available, the proposed procedure should be generalized. A discussion of each step in the proposed procedure is presented below. Step 1: Establish in-service conditions The allowable tensile stress for a PE geomembrane is a function of both the in-service environment and the required design life. In-service environmental conditions that should be defined include temperature, chemical exposure, and, if applicable, radiation exposure. Step 2: Establish stress-strain and rupture characteristics Long-term creep tests should be performed for each specific geomembrane (i.e. for each combination of resin, additive package, and manufacturer) for which the long-term allowable tensile stress is required. Ideally, the duration of creep-testing should equal or exceed the design life. It is impracticable, however, to perform tests for more than a few years. Various techniques (see Mruk, 1984; Koerner et al., 1992; and others) have been proposed for using limited-duration test data to estimate long-term design life. The techniques typically require that testing be performed at several temperatures, with the highest temperature being significantly above the expected in-service temperature (e.g. 20 to 60°C, assuming an in-service temperature of 20°C). The test results are then used to establish empirically or theoretically based relationships between tensile stress, time to rupture, and temperature. It is suggested that, even with the use of these techniques, the minimum duration of testing should be 10 000 hours, which is consistent with previous recommendations for geosynthetic reinforcement. The use of elevated-temperature testing as described above is valid only within limited ranges of temperature. For PE geomembranes, this range of temperature is approximately from -80°C to + 80°C, which corresponds to the region between glass- and melting-temperature transition zones. At
Long-term tensile stressesfor polyethylene geomembranes
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each test temperature, a series of tests should be performed, at load levels ranging from approximately 20 to 80% of the short-term yield strength of the geomembrane, to establish the relationship between rupture stress and time. The test configuration that should be employed will depend on the boundary-loading conditions. For applications involving or approaching plane-strain conditions, wide-width-strip tension tests can be employed. For other applications, axisymmetric burst-type tests may be suitable. Data of the type described above have recently been presented by DuvaU and Edwards (1992) and Duvall (1993). The data are from axisymmetric burst-type tests involving specimens of a widely available 1.5 mm thick PE geomembrane. Three sets of specimens were tested under each condition listed in Table 2. Both ductile and brittle failure modes were observed in the tests. Stress-rupture-time relationships derived from the results of tests at temperatures of 60 and 80°C are presented in Fig. 5. A predicted stressrupture-time relationship for a temperature of 23°C, derived from regression analysis of the 60°C and 80°C test results, is also presented in Fig. 5. A rupture stress of 7.2 N/mm 2 at 50 years and 23°C is obtained for the tested geomembrane product under the assumed conditions. The failure mode corresponding to this rupture stress is brittle. It is interesting to note that, if testing had been stopped prior to the onset of brittle rupture (i.e. prior to about 5000 hours), only ductile failures would have been observed in the elevated-temperature tests. If only the ductile-rupture data are used to predict a geomembrane rupture stress at 23°C and 50 years, a value of 13-6 N/mm 2 is obtained. Table 2 Conditions for Long-Term Axisymmetric Rupture Testsa
Internal pressure (kPa) 205 275 345 415 485 550 690 830 550 620 690 415 485 550
Temperature (°C) 23 23 23 23 23 23 23 23 60 60 60 80 80 80
aFrom Duvall and Edwards (1992).
d verage stress (gPa) 5.0 6.0 7.0 8.0 8.8 9.7 11.6 13.4 9.1 10.2 11-5 6-9 8.1 9-5
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Duvall and Edwards (1992) and Duvall (1993) derived geomembrane stress-strain relationships from their test results by using the tensionmembrane model of Giroud (1981). The isochronous (i.e. constant-time) stress-strain relationships for the 23°C test results are shown in Fig. 6. Using regression analysis, Duvall and Edwards extrapolated the test data to develop a predicted 50-year isochronous stress-strain relationship, also shown in Fig. 6. Ideally, long-term tests should be conducted with the geomembrane in the expected chemical (and radiation) environment and with test specimens containing representative geomembrane seams. However, owing to experimental difficulty and cost, these factors will typically not be accounted for in the type of performance testing considered under Step 2. Steps 3 and 4, below, provide an alternative approach to account for these factors, though the approach results in an uncoupled evaluation of effects.
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Step 3: Quantify an exposure
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A partial stress-reduction factor to account for geomembrane exposure to chemicals (or radiation) should be defined. Whereas PE is stable in many chemical environments, certain exposures will affect geomembrane properties. The resistance of a PE geomembrane to chemical attack will be product-specific, since resin characteristics, additive packages, and process techniques vary between manufacturers. In the absence of long-term testing, relatively short-term tests may be used to estimate a chemical-exposure factor. The US Environmental Protection Agency (EPA), for example, has developed Method 9090 (EPA, 1986), which involves exposing geomembrane specimens to the expected inservice chemical environment for up to 120 days at temperatures of up to 50°C. After prescribed exposure times of 30, 60, 90, and 120 days, the specimens are tested in short-term tension tests. This procedure should be extended to include testing at two different elevated temperatures (e.g. 35°C and 50°C) so that the results can be used to establish a relationship between
Ryan R. Berg, Rudolph Bonaparte
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short-term tensile strength, time of exposure, and temperature. From the relationship, an estimate can be developed for the short-term tensile strength of the geomembrane, ~cf, at the in-service temperature, environment, and design life. A stress-reduction factor to account for chemical degradation is then derived from the following equation: FC = --°~cr
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O~ci
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= reduction factor for chemical (or radiation) exposure (dimensionless); = final predicted tensile strength of incubated specimen at the in-service temperature and design life; and = initial tensile strength of non-incubated specimen.
Limitations on the use of eqn (1) should realized. First, specimens are incubated in an unstressed condition. It is inherently assumed that the response of unstressed, incubated geomembrane specimens is similar to that of specimens incubated under stress. Second, the proposed approach assumes that the test exposure causes effects similar to those that would occur at the in-service temperature and design life. Third, the proposed approach does not recognize that the effects of chemical exposure may be manifested in stages, as stabilizers within the geomembrane are consumed. Step 4: Quantify a seam factor
A partial stress-reduction factor to account for differences in strength between geomembrane seams and geomembrane sheet material should be defined. As previously noted, design specifications in USA practice typically require that PE geomembrane seam-peel and shear strength be equal to a percentage of the short-term strength of the geomembrane material. These short-term test results could be used to develop a 'weld' factor. However, owing to the current absence of any data establishing a correlation between long-term seam behavior and short-term test results, such an approach is insupportable. John and Hessel (1985) reached a similar conclusion. Hessel and John (1987) reported that long-term weld factors can be derived from the results of creep tests on geomembrane specimens submerged in surfactants and subjected to elevated temperatures. Geomembrane sheet and seam specimens are tested to rupture under similar conditions. A weld factor, FW, is obtained by dividing the seamspecimen rupture stress by the sheet-specimen rupture stress, as illustrated in Fig. 7. Hessel and John have shown that weld factors derived in this
Long-term tensile stresses for polyethylene geomembranes
299
manner are approximately equal to weld factors derived from longer-term tests in water. Testing, as described above, should be considered for the development of weld factors for specific geomembrane products and installers. Such testing would entail the use of specimens seamed under varying conditions to address weld methods, operator variations, site moisture and dust variations, geomembrane-material variations, weld temperatures, rate of welding, etc. At present, published data on the long-term strength of PE-geomembrahe seams are extremely limited. Most published information on this subject is from the German technical literature (Diedrich & Gaube, 1970; John & Hessel, 1985; Hessel & John, 1987; Koch et al., 1988; MQnk et al., 1989). Hessel and John (1987) performed testing to evaluate weld factors for PE geomembrane seams under conditions reported to be representative of those in the field. Their results are summarized in Table 3. Long-term weld factors from their investigation ranged from 0.3 to 0.8. These values are low compared with the weld factors of 0.8-0.9 they reported for extrusion welds produced under optimal conditions by the plasticcontainer industry.
Step 5: Quantify an installation-damage factor A partial stress-reduction factor to account for geomembrane scratches or gouges caused by installation should also be considered. Current practice
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I
I td
LOG TIME (s) Fig. 7. W e l d factor f o r PE-geomcmbran¢ seam.
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Ryan R. Berg, Rudolph Bonaparte Long-Term
TABLE 3 Weld Factors Geomembranes ~
Seaming method
for
PE
Weldfactor
Extrusion welding Heated-tool welding Hot-gas welding
0.4-0.8 0-3-0.75 0.4-0.7
~Fest data are from preliminary work by Hessel and John (1987).
for evaluating this factor for geosynthetic reinforcement involves retrieving specimens from actual or prototype installations, subjecting the specimens to short-term (rapid) tensile tests, and then developing reduction factors for use on subsequent projects. Limited evidence indicates that short-term tensile tests can be used to estimate long-term reduction factors for geosynthetic reinforcement (Bush & Swan, 1988). With this approach, a stress-reduction factor is calculated by using the following equation: FI = --°gif
(2)
o~ii
where FI = reduction factor for installation damage (dimensionless); ~if = final tensile strength of exhumed specimen; and aii = initial tensile strength of undamaged specimen. An approach similar to that described above can be used for PE geomembranes. Specimens of PE geomembranes can be exhumed from project or test installations. These specimens can then be tested as indicated above to establish general reduction factors for future PE-geomembrane installations. It is expected that, in many cases, FI will be 1.0, or nearly so, since a primary design goal is geomembrane protection.
Step 6: Select over-all factor of safety An over-all factor of safety against geomembrane rupture should be established to account for uncertainties associated with applied loads, geometry, and construction. The selected factor of safety should also reflect judgement applied in making design assumptions and construction control, and in the consequences of failure. Over-all factors of safety of 1.35-1-5 are typically recommended in geosynthetic-reinforcement practice. These factors are, however, applied to a limit stress, which is less than the rupture stress considered here. In USA practice (Mruk, 1984; PPI, 1989), PE pipes are designed with the factor of
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301
safety applied to the rupture stress. The Plastic Pipe Institute (PPI, 1990) recommends an over-all factor of safety of 2.0 for water-conveyance applications and higher factors for natural-gas pipelines. An over-all factor of safety of 3.1 for gas distribution is called for in the Code for Pressure Piping of the American Society of Mechanical Engineers (ASME, 1989) and by the US Department of Transportation (DOT, 1989). It is noted that these factors of safety for pipes account for the normal effects of pipe installation. Selection of an over-all factor of safety for a specific project should be made by the design engineer. However, based on the present practice for gas pipelines, over-all factors of safety in the range of 2-3 appear reasonable for load-controlled applications in which the design analysis is based on unfactored loads.
Step 7: Compute allowable tensile stress An allowable long-term tensile stress may be computed by using eqn (3): aa =
tTr x FC x FW x FI FS
(3)
where aa
= allowable tensile stress at the given in-service temperature and design hfe (N/minE); ~rr = rupture stress at the given in-service temperature and design life (N/minE); FC = reduction factor to account for chemical (or radiation) degradation over the design life (dimensionless); FW = reduction factor (i.e. weld factor) to account for long-term seam strength (dimensionless); FI = reduction factor to account for installation damage (dimensionless); and FS = overall factor of safety (dimensionless).
Equation (3) defines a long-term allowable tensile stress for a specific geomembrane subject to a constant boundary tensile stress over a given design life. The strain corresponding to the allowable tensile stress is a function of the duration of loading and can be obtained from isochronous stress-strain relationship derived from the test results obtained in Step 2. EXAMPLE The test results shown in Figure 5 provide geomembrane rupture stresses for a range of conditions. The test results are used below, along with
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assumed values for the various reduction factors, to illustrate the application of the proposed procedure.
Example of appfication of the proposedprocedure Step 1: Establish in-service environment and design life. Assumption: service temperature is 23°C. Assumption: design life equals 50 years. Step 2: Establish stress-strain and rupture characteristics. From Fig. 6, O" r ----- 7-2 N/mm 2 Step 3: Quantify a chemical-exposure factor. Assumption: chemical-exposure factor, FC = 1. Step 4. Quantify a seam factor. Assumption: long-term seam factor, FW = 0.7. Step 5. Quantify an installation-damage factor. Assumption: installation-damage factor, FI = 1.0. Step 6. Select an over-all factor of safety. Assumption: over-all factor of safety against rupture, FS = 2-0. Step 7.
Calculate long-term allowable tensile stress. 7.2 MPa x 1-0 x 0.7 x 1-0 = 2.5 N/mm 2 aa = 2.0
Step 8. Evaluate tensile strain at allowable stress and design life. From Fig. 6, e ,,~ 1.5%. The values of allowable tensile stress and strain given in the above example can be compared with values obtained by utilizing the present state-of-practice in the USA. For current practice, a yield strain for a PEgeomembrane dumbbell-test specimen of 11% was assumed (Table 1), along with a factor of safety of 2.0. The resulting allowable strain (i.e. yield strain divided by factor of safety) is 5.5%. The corresponding allowable tensile stress, based on Table 1 and assuming a linear stress-strain response, is 11 N/mm 2. Clearly, the proposed procedure may result in a much lower allowable stress than that obtained by using the current stateof-practice. It is also interesting to note that, if the stress-rupture-time line in Fig. 5 had not exhibited a brittle 'knee', an allowable stress of 3.8 N/ram 2 and a corresponding tensile strain of 2.9% would have been obtained. This allowable stress, based on the ductile-stress rupture line in Fig. 5, is 5 0 0 higher than that obtained from the brittle-stress rupture line. This simple
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303
comparison highlights the importance of identifying the potential for a particular geomembrane to undergo brittle rupture when loaded, and the benefit to be gained by using a geomembrane resin not susceptible to this failure mode during the specified design life. Finally, it is noted that if the geomembrane was able to relax, a larger initial allowable stress would be acceptable.
CONCLUSIONS The USA state-of-practice for evaluating long-term allowable stresses for PE geomembranes at waste-containment facilities was reviewed, and the limitations of the practice were identified. A new, more rational procedure for evaluating long-term allowable tensile stress was presented. The proposed procedure accounts for time, temperature, ductile and brittle fracture, chemical environment, welded seams, installation damage, and an over-all factor of safety. Laboratory testing and engineering judgement are required at each step of the procedure. The procedure as presented here is limited to stress-controlled boundary conditions~ The use of the procedure was illustrated by an example. The allowable stress obtained in the example was significantly lower than the allowable stress obtained by using current USA practice. The testing requirements inherent in the proposed procedure may be viewed by some as being excessive or unduly expensive. The requirements are, however, no more extensive than those for other types of geosynthetics used to carry loads in permanent, critical applications. Programs of the type described here have previously been carried out for several different geosynthetic-reinforcement products. Furthermore, for a given product made from a specific resin, much of the required testing need be performed only once. When it is realized that a given product may be used on hundreds of projects involving millions of square meters of installation, the testing requirements indeed appear reasonable. The proposed procedure requires that extensive performance testing be conducted. Consequently, a system for ensuring that materials used in a particular project are the same as those tested is also required. Present quality-control test programs are not sufficiently sensitive to identify variations in polymer characteristics. Hence, consistent with the approach advocated in this paper, quality-control programs should include resinsource, resin-property, and geomembrane-property certification. Until these testing and certification programs are in place, design engineers will be faced with uncertainty in evaluating long-term allowable stresses for PE geomernbranes.
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ACKNOWLEDGEMENTS The authors are grateful to Professor Grace Hsuan, Dr Donald G. Bright, Mr Donald E. Duvall and Dr Majdi A. Othman for their input to this paper. The authors are also indebted to Dr Jean-Pierre Giroud and Professor Robert M. Koerner for their review of the paper.
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