«Technical Paper by S.M. Merry and J.D. Bray GEOMEMBRANE RESPONSE IN THE WIDE STRIP TENSION TEST ABSTRACT: The geomembrane wide strip tension test is ...»
Technical Paper by S.M. Merry and J.D. Bray
GEOMEMBRANE RESPONSE IN THE
WIDE STRIP TENSION TEST
ABSTRACT: The geomembrane wide strip tension test is a performance test that provides test data from which the stress-strain response of a geomembrane may be calculated. However, the volumetric response of the geomembrane must be accounted for
when processing the test data to obtain the geomembrane stress-strain properties. This paper presents the results of strain controlled, uniaxial tension tests performed on two common polymeric geomembranes. During the tests, measurements were taken at specific locations on the geomembrane specimen. These measurements, combined with results from photographic analyses, allowed the specimen width and thickness to be determined during the tests. The measured values corresponded well with the theoretical values, assuming that the geomembrane is incompressible. The test results were not sensitive to the aspect ratio of the test specimen. The wide strip tension test should be considered a uniaxial (not a plane strain) tension test. It was also shown that modeling the stress-strain response of polymeric geomembranes with a constant cross sectional area instead of a constant volume significantly underestimates the actual stress-strain response of the geomembrane, particularly at large strains.
KEYWORDS: Geomembrane, Stress-Strain, Uniaxial tension test, Wide strip tension test, Volumetric strain, Failure.
AUTHORS: S.M. Merry, Assistant Professor of Civil and Environmental Engineering, 3220 Merrill Engineering Building, University of Utah, Salt Lake City, Utah 84112, USA, Telephone: 1/801-581-6931, Telefax: 1/801-585-5477; and J.D.
Bray, Associate Professor of Civil and Environmental Engineering, 440 Davis Hall,
University of California, Berkeley, California 94720-1710, USA, Telephone:
1/510-642-9843, Telefax: 1/510-642-7476.
PUBLICATION: Geosynthetics International is published by the Industrial Fabrics Association International, 345 Cedar St., Suite 800, St. Paul, Minnesota 55101-1088, USA, Telephone: 1/612-222-2508, Telefax: 1/612-222-8215. Geosynthetics International is registered under ISSN 1072-6349.
DATES: Original manuscript received 30 April 1996, revised version received 9 August 1996 and accepted 12 August 1996. Discussion open until 1 May 1997.
REFERENCE: Merry, S.M. and Bray, J.D., 1996, “Geomembrane Response in the Wide Strip Tension Test”, Geosynthetics International, Vol. 3, No. 4, pp. 517-536.
GEOSYNTHETICS INTERNATIONAL S 1996, VOL. 3, NO. 4 MERRY AND BRAY D Geomembrane Response in the Wide Strip Tension Test
1 INTRODUCTIONIn this paper, the mechanical response of two polymeric geomembranes, a 0.75 mm thick polyvinyl chloride (PVC) and a 1.5 mm thick high density polyethylene (HDPE), are evaluated using the American Society for Testing and Materials (ASTM) standard geomembrane wide strip tension test, ASTM D 4885. First, the uniaxial tension test apparatus is described. Next, photographs of a PVC test specimen that show typical response characteristics during a wide strip tension test are presented. Equations are derived that use the data collected during the wide strip tension tests to calculate the geomembrane specimen stresses and strains depicted in the photographs. The stress and strain values obtained using the derived equations are compared to values calculated using equations available in the literature. Over the entire test strain range the difference between the values obtained using the derived equations and those in the literature is shown to be significant. However, over small strain ranges that are typical in design, the difference is judged to be minimal.
2 UNIAXIAL TENSION TESTS
2.1 Description of Apparatus The uniaxial tension test system is shown in Figure 1. The main components of this system are the clamps, the load frame and the data acquisition system. The clamps are made of 25.4 mm wide × 50.8 mm thick × 304.8 mm long billet aluminum. The clamps were machined with a 0.13 mm high raised area that extends over the entire
length of the clamp, and is approximately 15 mm wide (Figure 2). This was done to increase the clamping stress in this area so as to minimize slippage of the geomembrane.
In order to further minimize slippage, striations from the machining process on the raised area of the clamps are perpendicular to the geomembrane pulling direction. Six 10 mm diameter high strength, stainless steel tensile bolts for each clamp ensure adequate restraint of the geomembrane during testing. The bolts were tightened to a minimum torque of 80 N-m. Although the clamps used in this study were not fabricated to the exact details shown in ASTM D 4885, they do conform to the requirements discussed in Section 6 of the standard in that the clamping system does “minimize slippage, damage to the specimen, and uneven stress distribution.”. Serrated clamps are are less prone to slippage, yet, they may damage the geomembrane and cause premature failure of the specimen. The primary difference between the clamps used in this study and those detailed in ASTM D 4885 is the time required to change test specimens. The ASTM clamps are designed for quick specimen setup, whereas the bolts in the clamps for this study must be systematically torqued, which requires more time.
A Wykeham Farrance load frame comprising a motor-driven gear system was used to provide a constant rate of deformation. The gears can be changed to provide 30 different discrete deformation rates. The available deformation rates played an important role in the determination of specimen length as a strain rate of approximately 1%/ minute during shearing was desired (ASTM D 4885). The total travel of the load frame is limited to 110 mm. For specimen lengths conforming to ASTM D 4885 (specimen length = 100 mm), the maximum strain obtainable is approximately 110%. The load
cell is an Eaton model 3174 that is rated to 22 kN. The load cell was calibrated to provide a 0 to 10 volt signal for approximately a 0 to 22 kN tensile load. At 4096 bits/N, a load resolution of approximately 5.3 N was achieved. Data acquisition was performed with ATS software for Windows (Sousa and Chan 1991). A temperature probe was mounted approximately 1 m from the test specimen.
2.2 Description of a Typical Test
In this section, a typical test performed on a 0.75 mm (30 mil) thick PVC specimen using the test apparatus described in Section 2.1 is presented. The clamped length of the specimen was 110.8 mm and the untensioned width was 218.4 mm. The specimen was slightly larger than 100 mm long × 200 mm wide as required in ASTM D 4885 because a strain rate of 1%/minute was desired and the loading frame is not capable of providing continuously variable crosshead speeds. The crosshead speed for this test was
1.25 mm/minute, thus providing an engineering strain rate of approximately 1%/minute. Additional tests for photographic analyses are summarized in Table 1.
Figure 3 shows the PVC specimen clamped into the test apparatus prior to the start of a test. This test is typical of the three other tests performed for photographic analyses that are not reported in this paper. To aid with the photographic analyses, a reference line was placed on the clamps, and a reference grid was drawn on the specimen. The reference grid on the specimen (25.4 mm × 25.4 mm) was centered vertically and horizontally. The grid blocks ABCD and OPQR are slightly wider (29.2 mm) than the other grid blocks. Prior to the load application, both the grid lines on the specimen and the vertical edges of the specimen formed straight lines.
Figure 4a shows the test specimen at an axial engineering strain of approximately 5% (Figure 4 is offered for illustrative purposes only, and strain definitions are discussed in Section 3.2). While the grid lines on the specimen still appear as straight lines, a small amount of deformation can be detected along the vertical edges, particularly near the top and bottom of the specimen. Figure 4b shows the specimen at an axial engineering strain of approximately 10%. The lateral deformation along the vertical edges has become more distinct with a slight amount of curvature along the specimen edges. The lower horizontal line of the reference grid has started to become distorted with more strain in the vertical direction at the center of the specimen than at the edge. Figures 4c and 4d show the PVC specimen at greater levels of axial engineering strain (i.e. 20 and 50%, respectively). At the increased levels of strain, the distances between the interior vertical grid lines and vertical edges of the specimen have become increasingly narrower. Thus, the assumption that the specimen responds under plane strain boundary conditions in the reference grid area is inappropriate. In fact, the middle portion of the specimen is better represented by uniaxial (laterally unrestrained) boundary conditions.
Table 1. Summary of properties of uniaxial test specimens used for photographic analyses.
Figure 5 shows the bottom of a 1.5 mm (60 mil) thick HDPE specimen following removal from the clamps. The approximate original edge of the clamps is shown as a dotted line. Figure 5 also shows an imprinted line at a distance of approximately 15 mm from the clamp edge that was formed by the transition of the raised area on the clamp face. Only a small amount of strain accumulated within the raised area near the vertical edges of the specimen from drawing the geomembrane. The clear, largely undisturbed trace left by the raised area of the clamp indicates that the specimen was adequately restrained, thus limiting the strains within the specimen to the portion of the specimen between the clamps. This trace was also evident in the tested PVC specimens and showed only a slight deviation from that shown in Figure 5, even though the PVC specimens were tested to significantly higher strains than the HDPE specimens (approximately 100 and 30%, respectively).
3 CALCULATION OF GEOMEMBRANE STRAINS AND STRESSES
3.1 General The standard test method, ASTM D 4885, does not explicitly provide equations to calculate geomembrane strains and stresses for the uniaxial tension test. While this may appear somewhat trivial, stress is calculated as the force, F, divided by the area, A, which raises the question whether or not the geomembrane stress should be based on the original or deformed cross sectional area. Several sources (ASTM D 4885; Giroud
et al. 1990; Gourc and Perrier 1991) suggest that the geomembrane tension, Τ, be calculated as the force, F divided by the original (untensioned) width. Division of Τ by the original geomembrane thickness, t, results in the stress being calculated as a function of the original area, which is the procedure also proposed by Koerner (1994). Yet, using the original thickness and width of the geomembrane does not represent the actual stress during the test. Therefore, the equations presented in this paper are used to interpret strains and stresses based on the deformed geomembrane geometry.
3.2 Strains Using the uniaxial tension testing system described in Section 2.1, the axial strain is
typically formulated as an engineering strain, εa, as follows:
where: Lo = original (untensioned) length of the geomembrane specimen between the clamps; and ∆L = specimen elongation. It is assumed that there is no slippage or straining of the geomembrane within the clamps. The engineering strain definition is most appropriate at small strains. When larger strains are of interest, the strain may be better evaluated on an incremental basis where the length, L, is taken as the observed length
at the previous increment or measurement. This strain formulation, referred to as natural (or true) strain, is defined as:
For the sake of consistency with normal design practice, the engineering strain definition (Equation 1), which is suitable for infinitesimal strains, will be used primarily in this paper. The consequences of using Equation 2 in lieu of Equation 1 will be discussed in Section 6.
Thinning of the geomembrane during testing is due to the Poisson’s ratio effect. The
thickness, t, of the geomembrane at any strain may be calculated as:
where: ν = engineering Poisson’s ratio, which is the ratio of the transverse and axial engineering strains, εt and εa, respectively; and, εa is calculated using Equation 1. Likewise, the strain-dependent width of the geomembrane, w(ε), may be calculated as:
For an isotropic, homogeneous material, the volume throughout the test, Vf, may be expressed in terms of the original volume, Vi, the engineering Poisson’s ratio, and the
axial engineering strain as:
Figure 6 shows a plot of the theoretical engineering Poisson’s ratio (based on Equation 6), versus axial engineering strain and Poisson’s ratio values based on measured width and thickness changes during a test (i.e. ν = - εt /εa ). The plot shows excellent agreement between the measured and theoretical values of ν over the entire strain range.
The natural Poisson’s ratio, νn, is the ratio of the transverse and axial natural strains,
εnt and εna, respectively:
The natural Poisson’s ratio is constant over large strain ranges for homogeneous, isotropic materials, and has a value of 0.50 for incompressible materials.