puncture protection of geomembranes

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629 GEOSYNTHETICS INTERNATIONAL S 1996, VOL. 3, NO. 5 Technical Paper by D. Narejo, R.M. Koerner and R.F. Wilson-Fahmy PUNCTURE PROTECTION OF GEOMEMBRANES P ART II: EXPERIMENTAL ABSTRACT: Geomembrane protection materials should be considered in design if geomembranes are to properly serve the role of barrier materials. The type, thickness and properties of the required protection material are in significant need of a rational design method. This series of three papers provides a design method for the inclusion of geomembrane protection materials, geotextiles in particular. Part I focuses on theory, this paper, Part II, focuses on experiments, and Part III focuses on design examples. In this paper, truncated cone and stone puncture test results for both short and long term durations are presented. A 1.5 mm thick high density polyethylene (HDPE) geomem- brane, and various nonwoven needle-punched geotextiles with varying masses per unit area made from virgin polyester and polypropylene continuous and staple fibers were tested. Using the results of this testing program, a design methodology was developed for calculating the required mass per unit area of a puncture protection material for a given factor of safety. Conversely, the design can be used to determine the unknown factor of safety for a given type of protection material. KEYWORDS: Puncture protection, Cushioning, Geotextile, Geomembrane, Experimental. AUTHORS: D. Narejo, Research Associate, Carleton University, Ottawa, Ontario, Canada K1S 5B6, Telephone: 1/613-520-2600, Telefax: 1/613-520-3951; R.M. Koerner, Professor of Civil Engineering, Director, Geosynthetic Research Institute, Drexel University, Philadelphia, Pennsylvania 19104, USA, Telephone: 1/215-895-2343, Telefax: 1/215-895-1437; and, R.F. Wilson-Fahmy, Geotechnical Engineer, Parsons Brinckerhoff, 506 Carnegie Center Drive, Princeton, New Jersey 08540, USA, Telephone: 1/609-734-6969, Telefax: 1/609-734-6900. 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 20 June 1996, revised version received 22 October 1996 and accepted 31 October 1996. Discussion open until 1 July 1997. REFERENCE: Narejo, D., Koerner, R.M. and Wilson-Fahmy, R.F., 1996, “Puncture Protection of Geomembranes Part II: Experimental”, Geosynthetics International, Vol. 3, No. 5, pp. 629-653.

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Page 1: Puncture Protection of Geomembranes

629GEOSYNTHETICS INTERNATIONAL S 1996, VOL. 3, NO. 5

Technical Paper by D. Narejo, R.M. Koerner andR.F. Wilson-Fahmy

PUNCTURE PROTECTION OF GEOMEMBRANESPART II: EXPERIMENTAL

ABSTRACT: Geomembrane protection materials should be considered in design ifgeomembranes are to properly serve the role of barrier materials. The type, thicknessand properties of the required protection material are in significant need of a rationaldesign method. This series of three papers provides a design method for the inclusionof geomembrane protection materials, geotextiles in particular. Part I focuses on theory,this paper, Part II, focuses on experiments, and Part III focuses on design examples. Inthis paper, truncated cone and stone puncture test results for both short and long termdurations are presented. A 1.5 mm thick high density polyethylene (HDPE) geomem-brane, and various nonwoven needle-punched geotextiles with varying masses per unitarea made from virgin polyester and polypropylene continuous and staple fibers weretested. Using the results of this testing program, a design methodology was developedfor calculating the required mass per unit area of a puncture protection material for agiven factor of safety. Conversely, the design can be used to determine the unknownfactor of safety for a given type of protection material.

KEYWORDS: Puncture protection, Cushioning, Geotextile, Geomembrane,Experimental.

AUTHORS: D. Narejo, Research Associate, Carleton University, Ottawa, Ontario,Canada K1S 5B6, Telephone: 1/613-520-2600, Telefax: 1/613-520-3951; R.M.Koerner, Professor of Civil Engineering, Director, Geosynthetic Research Institute,Drexel University, Philadelphia, Pennsylvania 19104, USA, Telephone:1/215-895-2343, Telefax: 1/215-895-1437; and, R.F. Wilson-Fahmy, GeotechnicalEngineer, Parsons Brinckerhoff, 506 Carnegie Center Drive, Princeton, New Jersey08540, USA, Telephone: 1/609-734-6969, Telefax: 1/609-734-6900.

PUBLICATION: Geosynthetics International is published by the Industrial FabricsAssociation International, 345 Cedar St., Suite 800, St. Paul, Minnesota 55101-1088,USA, Telephone: 1/612-222-2508, Telefax: 1/612-222-8215. GeosyntheticsInternational is registered under ISSN 1072-6349.

DATES: Original manuscript received 20 June 1996, revised version received 22October 1996 and accepted 31 October 1996. Discussion open until 1 July 1997.

REFERENCE: Narejo, D., Koerner, R.M. and Wilson-Fahmy, R.F., 1996, “PunctureProtection of Geomembranes Part II: Experimental”, Geosynthetics International, Vol.3, No. 5, pp. 629-653.

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1 INTRODUCTION

In this paper, which is Part II of a three part series, an experimental approach isadopted to evaluate the puncture resistance of high density polyethylene (HDPE) geo-membranes with and without nonwoven needle-punched geotextiles as protection mat-erials. Rather than attempting to simulate the idealized geometry assumed in develop-ing the theoretical method of the analysis in Part I (Wilson-Fahmy et al. 1996), theexperimental program is conducted using conventional testing procedures. In thesetests, failure pressures rather than pressures causing yield of the HDPE geomembranesare measured. The reason for this is due to the existing test procedures and data baseon large scale puncture testing conducted to failure. It is feasible to develop a test meth-od to measure the onset of yield of an HDPE geomembrane, yet, the experimental de-vice would be intricate and the required effort would be enormous. A large scale para-metric evaluation such as the one developed in this paper could not be achieved in areasonable time frame using such an idealized test procedure. Thus, the focus of thispaper is on geomembrane failure, rather than geomembrane yield. However, the signifi-cance of measuring geomembrane failure instead of geomembrane yield will be ad-dressed further in the Part III of this series of papers (Koerner et al. 1996).

The test techniques used, the geomembrane and geotextile materials used, and thecorresponding test results are described in this paper. Tests evaluating geomembranethickness, geotextile mass per unit area, angularity of the protruding object, protrusionpacking density, nature of the applied pressure, and long term creep behavior are eva-luated. A set of design equations based upon these test results is then developed.

2 TESTING TECHNIQUES

2.1 Introduction

Various test methods have been used in the past to evaluate the puncture resistanceof geomembranes and the associated geomembrane protection materials. These testmethods can be grouped into three main categories: (i) index puncture tests; (ii) quasi-performance puncture tests; and (iii) performance puncture tests. For index puncturetests, a probe is pushed into a geomembrane specimen that is fixed in a circular configu-ration until failure occurs. Since this loading mode is not representative of field condi-tions, index tests are felt to be best suited for quality control and conformance purposes.Quasi-performance puncture tests, as the name implies, use idealized rather than actualfield conditions. For example, instead of using site specific stones, the protrusions usedhave idealized shapes in the form of truncated cones or truncated pyramids (e.g. thestandard test method ASTM D 5514), and the soil or waste overburden pressure is sub-stituted by hydrostatic pressure. However, the mode of puncture is similar to field con-ditions in that the geomembrane overlies a protrusion and is subjected to pressure untilfailure occurs. The mode of stress in performance puncture tests is similar to quasi-per-formance tests with the exception that the puncture resistance of the geomembrane isevaluated against a site specific soil. For example, geomembrane liners used in landfillsare tested using the specific overlying drainage stone of the leachate collection and re-moval system (Brummermann et al. 1994). Performance puncture tests are performed

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using either hydrostatic or geostatic pressures. Hydrostatic pressure simulates the in situcondition of a liquid overlying the geomembrane as in the case of surface impound-ments. Geostatic loading simulates overburden pressures in solid waste containmentapplications. Narejo (1994) gives a summary of the various geomembrane puncturetests reported in the literature.

Since one of the main objectives of this study is to simulate as closely as possible theloading condition in the field, index tests had to be excluded except to provide qualitycontrol puncture data. The remaining options were to use either quasi-performance orperformance puncture test methods. One of the major disadvantages of performancetests is that repeatability can be poor, because geomembrane puncture resistance ishighly sensitive to the precise orientation and packing arrangement of the protrudingobject. For example, an angular stone can be more damaging if its sharp edge is in con-tact with the geomembrane in contrast with the same stone lying flat. Also, a stone ar-rangement in which some stones are raised over the neighboring stones can be morecritical when compared to an arrangement with the tips of the stones being more or lessat the same height. Another disadvantage of performance tests is that the results cannotbe readily compared to test results obtained using different types of stones. For thesereasons, it was decided to use the truncated cone quasi-performance test for this study.The truncated cone test was chosen over the truncated pyramid test because a reason-able data base already exists (Hullings 1990); however, variations of the truncated conetest and a limited number of performance tests were also performed. Geostatic loadingwas also considered in order to investigate the possibility of arching within the soil me-dia that would result in a reduction of the pressure above the protrusion. In this case,sand was used as the loading medium above the geomembrane.

2.2 Short Term Hydrostatic Tests Using Truncated Cones

The hydrostatic puncture tests were performed according to the standard test method,ASTM D 5514. The pressure vessel and protrusions in this test consist of three truncatedcones with dimensions given in Figure 1b. The cones are mounted on a rigid steel plat-form in a triangular pattern at 250 mm centers, and the radius of curvature of the conetip is approximately 0.25 mm. The whole assembly is installed in the bottom sectionof a pressure vessel as illustrated in Figure 1a, and sand is placed on the base plate leav-ing the tips of the cones exposed and protruding above the sand surface. The heightsof the exposed tips above the sand surface can be varied to investigate the effect of theprotrusion height on puncture resistance. The geomembrane and its protection material,if any, are laid flat on the cone tips and the flange of the bottom portion of the pressurevessel. The top section of the pressure vessel is then secured in place thereby containingthe outer circumference of the test specimen. The geomembrane is loaded using hydro-static pressure applied through a water inlet in the top section of the pressure vessel ata rate of 7 kPa per minute. Failure of the geomembrane is detected via two electricallyconducting probes in an open circuit, embedded in the cones, and terminating at thecone tips. When geomembrane puncture occurs, the water penetrating the geomem-brane closes the circuit thereby activating a light bulb. A clock is also turned off to mea-sure the time to geomembrane failure. The failure time is particularly important for longterm tests in which a constant pressure is sustained until failure occurs.

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Figure 1. Details of the hydrostatic pressure truncated cone puncture test: (a) pressurevessel for the truncated cone and pyramid puncture tests; (b) protrusions for the truncatedcone puncture test.

28 mm

(a)

(b)Rounded to0.25 mm radius

Four cone heights of 12, 25, 38 and 50 mm were used. This choice was based on thefact that the critical cone height for an unprotected 1.5 mm thick HDPE geomembraneis approximately 12 mm (Hullings and Koerner 1991). The critical cone height is de-fined as the maximum cone height at which short term failure does not occur.

2.3 Long Term Hydrostatic Tests Using Truncated Cones

The same test set-up described in Section 2.2 was used for the long term hydrostatictests. In the tests, the geomembrane and its protection geotextile, if any, were subjected

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to a sustained pressure lower than the failure pressure measured in short term tests. Thepressure ranged between 25 to 85% of the short term failure pressure and was main-tained until failure occurred, or for 10,000 hours, whichever was reached first. As withthe short term tests, the targeted load level was obtained by applying the hydrostaticpressure at a rate of 7 kPa per minute.

2.4 Short Term Hydrostatic Tests Using Isolated Stones

These tests are performed using the same method as the hydrostatic truncated conepuncture test with the exception that the cones are substituted by isolated stones. Thepurpose of this test is to correlate the truncated cone test results to test results obtainedusing actual stones. Rounded, subrounded and angular stone shapes were used. The bot-tom portion of each stone was held inside a cup using epoxy; by doing so, the exposedheight and movement of the stone during a test could be easily controlled.

2.5 Short Term Hydrostatic Tests Using Packed Stones

The geomembrane in these tests was laid flat above a bed of stones. Standardized setsof stones corresponding to American Association of State Highway Transportation Of-ficials (AASHTO) No. 8, 57 and 3 stones (9 to 13, 25 to 38, and 50 to 64 mm, respective-ly) were used to simulate as closely as possible the field conditions of a continuous layerof stones. These stone sizes are often used in drainage layers above geomembranes. Theloading sequence was the same as that used for the truncated cones.

2.6 Geostatic Tests Using a Truncated Cone

A limited number of geostatic tests was also conducted. Geostatic means that soil wasthe pressurizing medium rather than water (water was used in all of the other tests inthis study). One cone was used instead of three and the diameter of the vessel was 300mm. A smaller device than that utilized in the hydrostatic test was used because loadingwas performed in a compression machine that could not accommodate a size greaterthan 300 mm. However, the radius of the initial unsupported area of the geomembranearound the cone is approximately the same in the two devices. A 150 mm thick layerof sand was placed above the flat geomembrane, and loading was applied via a rigidcircular plate resting on the sand surface. A schematic of the test setup is given in Figure2. A number of tests were conducted using a 150 mm diameter pressure cell embeddedat the same location as the geomembrane to evaluate the frictional stresses developingat the geomembrane-soil boundary. It was found that approximately 65% of the appliedpressure is transmitted to the level of the geomembrane. This value is used in evaluatingthe puncture resistance. It is recognized that the measurements obtained using this testdevice are not as accurate as those obtained in the hydrostatic test. This, in addition tothe fact that the two set-ups are somewhat different, is considered in the interpretationof the results.

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Figure 2. Test apparatus for geostatic truncated cone puncture tests.

3 MATERIALS USED

The geomembrane and associated protection materials used in the experimental in-vestigation are described in this section.

3.1 Geomembrane

A 1.5 mm thick HDPE geomembrane was used in all of the puncture tests performedwith a protection material, and in some of the puncture tests without a protection materi-al. Additional puncture tests using 1.0 and 2.0 mm thick HDPE geomembranes withoutprotection were also performed. Different geomembrane thicknesses were tested toassess the possibility of using thicker geomembranes instead of protection materials.

Selected physical and mechanical properties of the HDPE geomembranes tested aregiven in Table 1. Note that the yield stress is somewhat lower than the published valuesin the manufacturers’ literature, the reason being that testing was performed accordingto the wide width test, ASTM D 4885, that specifies a 100 mm long by 200 mm widespecimen. Index tension tests or axi-symmetric tension tests result in higher valuescompared to wide width tests as shown by data presented in the paper by Koerner(1994). Although the wide width test is possibly not the most convenient test, the resultsare necessary for comparison with the tensile properties of the protection geotextiles.

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Table 1. Selected physical and mechanical properties of the HDPE geomembranes used inthis study.

Geomembrane Thickness (mm) Yield load (kN/m) Yield strain (%) Puncture load (kN)

1 2.0 30 18 0.63

2 1.5 23 18 0.44

3 1.0 14 18 0.28

3.2 Nonwoven Needle-Punched Geotextile

The protection materials consisted of nonwoven needle-punched polyester and poly-propylene geotextiles with masses per unit area ranging between 130 and 1350 g/m2.The polyester geotextiles were manufactured from continuous fibers, whereas the poly-propylene geotextiles were made from staple fibers. Selected properties of these geo-textiles are given in Table 2. All of the geotextiles used were made from virgin polymer-ic materials.

4 TESTING PROGRAM

Table 3 presents the values of the various parameters used in the puncture tests. Thefollowing steps describe the procedure and basic concepts of the testing program:

S Determine the short term failure pressure of the geomembranes with and withoutprotection using hydrostatic truncated cone test data.S Determine the short term failure pressure of the geomembranes without protection

using hydrostatic puncture tests on isolated stones. Using the test results, establish acorrelation between the geomembrane failure pressure for truncated cones and angu-lar, subrounded and rounded stones.

Table 2. Selected physical and mechanical properties of the virgin polymer geotextileprotection materials.

Protectionmaterial

Mass/unit area(g/m2)

Thickness(mm)

Strength(kN/m)

Modulus(kN/m)

Strain(%)

Tapered pinpuncture loadmaterial (g/m2) (mm) (kN/m) (kN/m) (%) puncture load

(kN)

NW-NP-PET-1 130 1.3 10 37 60 0.2

NW-NP-PET-2 270 2.5 19 61 60 0.4

NW-NP-PET-3 550 4.8 41 69 60 0.8

NW-NP-PET-4 1080 9.6 75 142 70 1.5

NW-NP-PP-1 300 3.0 28 42 40 0.5

NW-NP-PP-2 680 5.6 51 78 40 1.1

NW-NP-PP-3 1350 11.0 96 137 40 2.3

Notes: Test methods used: mass/unit area, ASTM D 5261; thickness, ASTM D 5199; strength, modulus andstrain, ASTM D 4595; tapered pin puncture, FTMS 101C-M2065. NW = nonwoven; NP = needle-punched;PET = polyester; PP = polypropylene; FTMS = Federal Test Method Standard.

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Table 3. Puncture test program for geomembranes and protection materials.

Test method ProtrusionGeomembrane

thickness(mm)

Geotextilepolymer type

Geotextilemass/unit area

(g/m2)

Short term 3 truncated cones

(height: 12 - 50 mm) 1.0 -- --

1.5 -- --

2.0 -- --

1.5 PE 130

1.5 PE 270

1.5 PE 550

1.5 PE 1080

1.5 PP 300

1.5 PP 680

1.5 PP 1080

3 stones

(height: 12 - 50 mm)

- angular 1.5 -- --

- subrounded 1.5 -- --

- rounded 1.5 -- --

Bed of stones

- AASHTO #8 1.5 -- --

- AASHTO #57 1.5 -- --

- AASHTO #3 1.5 -- --

Short term 1 truncated cone --

geostatic tests (height: 12 - 50 mm) 1.5 -- --

Long term hydrostatic 3 truncated cones

truncated cone tests (height: 12 - 38 mm) 1.5 -- --

1.5 PE 270

1.5 PE 550

1.5 PE 1080

Notes: PE = polyethylene; PP = polypropylene; AASHTO = American Association of State Highway andTransportation Officials. AASHTO #8, #57 and #57 stone sizes = 9 - 13, 25 - 38 and 50 - 64 mm, respectively.

S Determine the failure pressure of geomembranes without protection using hydrostat-ic puncture tests on a layer of stones. Assuming the protrusion height is equal to halfthe maximum size of the stones (see the conclusions in Section 6, Part I, Wilson-Fahmy et al. 1996), establish a correlation between the geomembrane failure pressurefor isolated stones and packed stones.S Determine the failure pressure of geomembranes without protection using the geos-

tatic truncated cone test. Establish a correlation between the geomembrane failurepressure under hydrostatic and geostatic loading conditions.

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S Determine the long term puncture strength of geomembranes with and withoutprotection using long term hydrostatic truncated cone tests. Establish a correlationbetween the short term and long term puncture strength.

The established correlations are assumed to be independent of each other. Thus, thegeomembrane puncture resistance is determined by modifying the failure pressure fortruncated cone tests using one or more of the established correlations depending on theactual field conditions. The necessary design equations result directly from the abovedescribed process.

5 TEST RESULTS

This section presents the results of the various tests performed as per the testing pro-gram shown in Table 3.

5.1 Short Term Failure Pressure for Truncated Cones

5.1.1 Geomembrane Without Protection

Table 4 summarizes the test results for different thicknesses of geomembrane withoutprotection material.

It can be seen that increasing the geomembrane thickness results in an increase in fail-ure pressure at all cone heights; however, the magnitudes of the failure pressure are notlarge. For example, a failure pressure of 100 kPa corresponds to 8 m of municipal solidwaste having a unit weight of 12 kN/m3. Thus, from a practical point of view, and con-sidering the fact that pressure at yield can be much lower than the above values, the useof a protection material for HDPE geomembranes for cone heights greater than 12 mmappears to be necessary.

Table 4. Failure pressures from truncated cone puncture tests for different HDPE geomem-brane thicknesses.

GeomembraneFailure pressure (kPa)

Geomembranethickness

(mm)Cone height (mm)

(mm)50 38 25 12

1.0 21 28 28 110

1.5 34 55 69 140

2.0 48 62 100 310

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5.1.2 Geomembrane With Protection

Table 5 and Figure 3 give the failure pressures for 1.5 mm thick HDPE geomembraneswith various nonwoven needle-punched geotextiles having different masses per unitarea. The maximum pressure that can be applied in the device is 1100 kPa, and thus,no pressures higher than 1100 kPa could be reported. It is clear from this data that thefailure pressure is sensitive to the mass per unit area of the protection geotextile. Forexample, for a cone height of 25 mm, increasing the mass per unit area from 130 g/m2

(geotextile NW-NP-PET-1 in Table 5) to 1080 g/m2 (geotextile NW-NP-PET-4 in Table5) resulted in a six-fold increase in the failure pressure. In fact, the results in Figure 3show that for each cone height (CH), the relationship between mass per unit area andfailure pressure can be reasonably approximated by a straight line. The failure pressureis also an important function of the cone height. For example, reducing the height from50 to 25 mm resulted in an increase in failure pressure from 83 to 450 kPa for a geotex-tile with a mass per unit area of 550 g/m2 (geotextile NW-NP-PET-3 in Table 5). Thesame trend is also observed for all of the other geotextiles irrespective of their structure,i.e. geotextiles that are made of polyester continuous filament or polypropylene staplefiber geotextiles.

5.2 Correlation With Field Conditions

As mentioned previously, correlations between the short term hydrostatic truncatedcone test and field conditions are required in order to determine the in situ puncture re-sistance of the geomembrane with and without protection. These correlations are pre-sented in this section based on the test data.

Table 5. Failure pressures from hydrostatic pressure truncated cone puncture tests for a 1.5mm thick HDPE geomembrane with various types of virgin geotextile protection materials.

Failure pressure (kPa)Test

conditionCone height (mm)

condition50 38 25 12

GM alone(no protection)

34 55 69 140

NW-NP-PET-1 69 83 100 410

NW-NP-PET-2 69 83 320 830

NW-NP-PET-3 83 103 450 >1100

NW-NP-PET-4 150 365 610 >1100

NW-NP-PP-1 76 210 320 990

NW-NP-PP-2 120 280 500 >1100

NW-NP-PP-3 290 470 >1100 >1100

Notes: NW = nonwoven; NP = needle-punched; PET = polyester; PP = polypropylene; GM = geomembrane.

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Note: CH = cone height.

Figure 3. Linear variation of failure pressure with mass per unit area for nonwovenneedle-punched geotextiles at different cone heights (polyester continuous filament andpolypropylene staple fiber geotextiles).

5.2.1 Isolated Stones Versus Truncated Cones

Figure 4 shows the relationship between the exposed height of protrusions (stones)and the geomembrane failure pressure for angular, subrounded and rounded stone sha-pes. The truncated cone test results are also plotted in Figure 4 for comparison. Thetrend of results is the same for all stone shapes in that the failure pressure decreases asthe exposed height of the stone increases. The angular stone results closely follow thetruncated cone results, and produce lower geomembrane failure pressures than the sub-rounded and rounded stone results. In general, it can be assumed that the geomembranefailure pressures for subrounded stones are two times greater than those for angularstones, and the geomembrane failure pressures for rounded stones are four timesgreaterthan those for angular stones.

5.2.2 Packed Stones Versus Isolated Stones

Unlike the tests performed using isolated stones, failure could not be achieved for thepacked stone tests even under the maximum pressure capacity of the test device (1100kPa). Thus, it was decided to determine the minimum pressure causing yield of the geo-membrane. This was achieved by stopping the test at different increments of appliedpressure, opening the pressure vessel, and visually examining the geomembrane for any

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Figure 4. Failure pressure versus exposed height of protrusion.

signs of yield. Obviously, the pressure at yield can only be determined in an approxi-mate manner using this procedure. Nevertheless, the results indicate that the pressureat yield for packed stones is sensitive to the stone size. Table 6 shows that the pressureat yield increases as the stone size decreases.

To allow for comparisons with the behavior of a geomembrane over isolated protru-sions, it is assumed that the effective protrusion height for packed stones is equal to halfthe maximum stone size, which is in agreement with the conclusions in Section 6 of PartI of this series of papers (Wilson-Fahmy et al. 1996). It will also be assumed that thestone shape is angular; thus, if the stone acts as an isolated protrusion, it will give thesame failure pressure as a truncated cone. This assumption enables comparisons to bemade with the results of isolated protrusions. For example, a 12 mm effective protrusionheight results in a failure pressure of 140 kPa (Table 4) if it is an isolated protrusion,and in excess of 1100 kPa if it is a packed stone arrangement (Table 6). Thus, it can beconcluded that failure pressures for packed stones are much higher than for isolatedstones.

Table 6. Pressure at yield for packed stones.

AASHTOstone number

Maximum size(mm)

1/2 maximum size(mm)

d50(mm)

Pressure at yield(kPa)

Failure pressure(kPa)

3 50 - 64 25 - 32 38 70 >1100

57 25 - 38 13 - 19 12 170 >1100

8 9 - 13 5 - 7 10 690 >1100

Notes: AASHTO = American Association of State Highway and Transportation Officials; d50 = soil particlesize for which 50% of the sample is smaller.

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5.2.3 Hydrostatic Loading Versus Geostatic Loading

Table 7 gives the measured geostatic failure pressures for the geomembrane withoutand with protection using the device shown in Figure 2. Failure pressures above 700 kPacould not be reported as they exceeded the device capacity. Comparing the data in Table7 with those of Table 5 that were measured under hydrostatic conditions, it can be con-cluded that the failure pressures resulting from geostatic stresses are approximately sixtimes higher than those caused by hydrostatic pressures. This large difference is partial-ly attributed to soil arching which tends to alleviate the stresses transferred to the de-forming geomembrane and its protection material. The impact of this difference be-tween hydrostatic and geostatic loading on design is discussed later.

5.2.4 Short Term Versus Long Term Loading

The results for the long term (creep) tests are given in Table 8 and Figure 5. Whilethe data is sparse and is only for the test-specific temperature of 20°C ± 2°C, the trendof the test results is reasonably well defined. For the same percentage of the failure pres-sure, low cone heights results in longer failure times for geomembranes with and with-out protection. For example, at 75% of the failure pressure, increasing the cone heightfrom 12 to 38 mm for a geomembrane without protection resulted in a decrease in fail-ure time from 100 to 10 hours. The effect of increasing the mass per unit area of theprotection geotextile is shown to increase all failure times for the same cone height, andthe percentage of failure pressure. For example, for a cone height of 25 mm, the failuretime increased from 180 hours to more than 10,000 hours at 50% of the failure pressuredue to an increase of the geotextile mass per unit area from 270 to 1100 g/m2.

From Figures 5b, 5c and 5d it appears that the minimum required mass per unit areaof geotextiles for cone heights of 12, 25 and 38 mm are 270, 550 and 1100 g/m2, respec-tively. These values are used asdefault values in Part III of this series of papers (Koerneret al. 1996) where example problems and design tables are presented.

Table 7. Failure pressures from geostatic puncture tests for a 1.5 mm thick HDPE geomem-brane with various nonwoven needle-punched geotextiles.

Failure pressure (kPa)Test

condition Cone height (mm)condition50 38 25 12

GM alone(no protection)

240 310 450 700

NW-NP-PET-2 380 510 >700 >700

NW-NP-PET-3 580 >700 >700 >700

NW-NP-PET-4 >700 >700 >700 >700

Notes: NW = nonwoven; NP = needle-punched; PET = polyester; GM = geomembrane.

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Appliedpressure/Failurepressure(%)

Appliedpressure/Failurepressure(%)

Note: CH = cone height.

(a)

(b)

Figure 5. Percent ratio of applied pressure to failure pressure versus failure time forgeomembranes with and without protection material: (a) without protection material;(b) with a 270 g/m2 nonwoven needle-punched polyester geotextile.

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Appliedpressure/Failurepressure(%)

Note: CH = cone height.

Appliedpressure/Failurepressure(%)

(d)

(c)

Figure 5 (continued). Percent ratio of applied pressure to failure pressure versus failuretime for geomembranes with and without protection material: (c) with a 550 g/m2 nonwovenneedle-punched polyester geotextile; (d) with a 1100 g/m2 nonwoven needle-punchedpolyester geotextile.

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Table 8. Long term (creep) failure times for a 1.5 mm thick HDPE geomembrane with vari-ous nonwoven needle-punched polyester protection geotextiles.

Cone height(mm)

Protectiongeotextile

Failurepressure[

(kPa)

Applied pressure(% of failure

pressure)

Appliedpressure

(kPa)

Failure time(hours)

12 None 140 75 100 130

50 70 170

25 35 260

550 g/m2 1750* 75 1300 10,000**

1080 g/m2 3400* 40 1300 10,000**

25 None 69 75 52 24

50 34 42

25 17 68

270 g/m2 320 75 240 140

50 160 110

25 80 310

550 g/m2 450 85 380 240

70 310 390

60 270 1000**

1080 g/m2 610 75 460 10,000**

38 None 55 75 41 0.5

50 28 2.5

25 14 40

270 g/m2 83 75 62 3

50 41 12

25 21 200

550 g/m2 103 75 77 192

50 52 1000**

1080 g/m2 365 75 270 10,000**

Notes: *Calculated values using Equation 3. **Geomembrane showed signs of yield. [ From short termhydrostatic pressure truncated cone puncture tests.

6 DESIGN FORMULATION

6.1 Introduction

A design formulation is presented in this section based on the experimental puncturedata reported in the previous sections. The resulting equations predict the allowablefailure pressure for HDPE geomembranes both with and without geotextile protection.

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As previously explained, the logic behind the formulation is to first determine thefailure pressure based on the short term hydrostatic truncated cone test data. A seriesof modification factors are then applied to correlate the truncated cone data to actualfield conditions. The modification factors consider the stone shape, arrangement andsoil arching. All of these modification factors have a magnitude of 1.0 or less since theexperiments were conducted on a worst-case basis. Partial factors of safety are then in-corporated into the design equations to account for creep and chemical/biological de-gradation. These partial factors of safety are equal to 1.0 or greater since longer periodsof time are typically required for these factors to have an effect. Finally, a global factorof safety is applied to account for uncertainties in the formulation. The above describedempirical formulation is presented in a step-by-step manner in order to emphasize thevarious factors involved.

6.2 Basic Design Equation

The formulation for predicting geomembrane failure pressure, p, is based on Figure3 where it is seen that for each cone height, the failure pressure varies linearly with re-spect to the mass per unit area of the geotextile. Note that this failure pressure from theexperiments is assumed to be the maximum allowable design pressure with an impliedglobal factor of safety of 1.0. Thus, the maximum allowable pressure can be expressedas follows:

(1)pallow= d×MA

where: pallow = maximum allowable pressure (with an implied factor of safety of 1.0);MA = mass per unit area of the protection geotextile (g/m2); and d = constant. From Fig-ure 3, it is found that the parameter d can be related to the cone height, H, accordingto the following equation:

(2)d= 450H2

where H is in millimeters.Combining Equations 1 and 2, the failure pressure can be determined in terms of the

cone height and mass per unit area of the protection geotextile as follows (a minimumpressure of 50 kPa is imposed which conservatively corresponds to the failure pressureof the 1.5 mm thick HDPE geomembrane without any protection material):

(3)pallow= 450MA

H2≥ 50 kPa

The accuracy of the above equation is depicted in Figure 6 which shows the relation-ship between the measured failure pressure and the failure pressure predicted usingEquation 3. The data in Figure 6 are for polyester geotextiles made from continuousfilaments, and polypropylene geotextiles made of staple fibers. Hence, Equation 3 ap-plies to essentially all of the polymer and fiber types used in the nonwoven needle-punched geotextiles.

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Figure 6. Measured versus empirically predicted failure pressures using Equation 3 for allnonwoven needle-punched geotextiles evaluated with a 1.5 mm thick HDPE geomembrane.Note: R = correlation coefficient.

6.3 Modification Factors

A series of modification factors is now sequentially applied to Equation 3 in orderto arrive at a pressure representing field conditions. The modified pressure will be re-ferred to as piallow .

6.3.1 Modification Factor for the Protrusion Shape

It was previously shown that the failure pressure depends on the protrusion shape.Rounded stones gave the highest failure pressure followed by subrounded stones. Thelowest failure pressure is associated with angular stones and is approximately equal tothe failure pressure of truncated cones. In order to account for the effect of stone shape,a modification factor is introduced into Equation 3 as follows:

(4)p′allow= pallow 1MFS

where MFS is the modification factor for the protrusion shape. Hereafter, piallow refersto the empirically modified value of pallow as is illustrated in Figure 6.

Based on the analysis of the data presented in Section 5.2.1, the modification factorsfor different stone shapes are presented in Table 9.

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Table 9. Modification factor for protrusion shape.

Stone shape Modification factor, MFS

Angular 1.00

Subrounded 0.50

Rounded 0.25

6.3.2 Modification Factor for Packing Density

It is shown in Section 5.2.2 that the allowable pressure for packed stones is muchhigher than for isolated stones. Unfortunately, within the capacity of the experimentaldevice, no failure could be achieved with the packed stones, and hence, no direct cor-relation with isolated stones could be made. However, using the theoretical analysispresented in Part I of this series of papers (Wilson-Fahmy et al. 1996), the pressure atyield for packed stones (Ro/H = 2) could be compared with the pressure at yield for iso-lated stones (Ro/H = 4) where Ro is the horizontal distance from a undeformed geomem-brane point of tangency with the protrusion tip to the undeformed geomembrane pointof tangency with the soil subgrade. The analysiswas performed for geomembraneswithand without protection. Based on the results, a modification factor of 0.5 is suggestedwhich provides a conservative estimate of the effect of packing density. Thus, Equation4 can be rewritten after introducing a modification factor for packing density as follows:

(5)p′allow= pallow 1MFS×MFPD

where MFPD is the modification factor for packing density. The modification valuespre-sented in Table 10 can be used for isolated protrusions and packed stone arrangements.

6.3.3 Modification Factor for Soil Arching

Equation 5 can be further modified as follows to include the effect of soil arch-ing:

(6)p′allow= pallow 1MFS×MFPD×MFA

where MFA is the modification factor for soil arching.

Table 10. Modification factors for packing density.

Protrusion arrangement Modification factor, MFPD

Isolated protrusions 1.00

Packed stones 0.50

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It is shown in Section 5.2.3 that geostatic loading can lead to an increase in failurepressure by a factor of six in comparison with hydrostatic loading. This corresponds toa modification factor of 0.17. It may be noted, however, that the effect of soil archingon the pressure at yield may not be as great as the effect on the failure pressure. Thedeformations of the geomembrane up to yield may not be large enough to mobilize thesoil arching effect; therefore, caution must be exercised when using the data in Table7 for design. It is recommended that the values in Table 11 be used when soil archingis anticipated.

6.4 Partial Factors of Safety

After introducing the various modification factors (all of which are 1.0 or less), sever-al partial factors of safety should be applied in order to determine the allowable pressureon the geomembrane. The partial factors of safety are equal to 1.0 or greater. Two fac-tors are considered below, a partial factor of safety for long term creep and a partial fac-tor of safety to account for long term chemical/biological degradation of the materialsinvolved.

6.4.1 Partial Factor of Safety for Creep

A partial factor of safety for creep is incorporated into Equation 6, and the allowablepressure is now calculated as follows:

(7)p′allow= pallow 1MFS×MFPD×MFA

1FSCR

where FSCR is the partial factor of safety for creep. Based on the creep data presentedin Table 8, the recommended partial factors of safety for creep are given in Table 12.

Table 11. Modification factors for soil arching.

Soil arching effect Modification factor, MFA

None 1.00

Moderate 0.75

Maximum 0.50

Table 12. Partial factors of safety for creep.

Geotextile mass Partial factors of safety for creepGeotextile massper unit area

2Protrusion height (mm)pe u t a ea

(g/m2) 38 25 12 6No geotextile N/R N/R N/R >>1.5

270 N/R N/R >1.5 1.5

550 N/R 1.5 1.3 1.2

1100 1.3 1.2 1.1 1.0

>1100 ~1.2 ~1.1 ~1.0 1.0

Note: N/R = not recommended.

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It may be noted that the above partial factors of safety values for creep are relativelylow in comparison with the factors of safety found in the literature for creep of geotex-tiles in tension. This may be explained by the fact that, in the puncture mode, the geo-membrane and its protection material will conform more to the subgrade as they creepand hence the unsupported length will decrease with time. It was shown in Part I of thisseries of papers (Wilson-Fahmy et al. 1996) that for the same applied pressure the maxi-mum stress mobilized at the protrusion tip will decrease as the unsupported length de-creases. Thus, a decrease in stress in the geomembrane and its protection material isexpected with time. Accordingly, a lower factor of safety for creep is required for thepuncture mode in comparison to the stress mode in which the material is subjected toa constant tensile stress.

6.4.2 Partial Factor of Safety for Chemical/Biological Degradation

The partial factor of safety against chemical/biological degradation, FSCBD , is in-cluded in Equation 7 as follows:

(8)p′allow= pallow 1MFS×MFPD×MFA

1FSCR× FSCBD

Although not assessed in this study, the value of FSCBD is felt to range between 1.0 and2.0 with an average value of 1.5; see Koerner (1994) for discussion and details.

6.5 Global Factor of Safety

After determining an allowable pressure that is suitably adjusted for modificationfactors and partial factors of safety (Equation 8), a global factor of safety is determinedby dividing the allowable pressure by the required pressure as follows:

(9)FS= p′allowpreqd

where: preqd = maximum stress required on the geomembrane; and FS = desired globalfactor of safety for uncertainties related to site specific conditions.

It is felt that the global factor of safety should never be less than 3.0. Higher valuesmay be used depending on site specific conditions. For example, a high factor of safetyshould be used in situations where large isolated stones are frequently encountered onthe subgrade. Also, a tightly installed geomembrane may also require a larger globalfactor of safety compared to a geomembrane installed with slack. Furthermore, no mo-dification has been included for in situ temperatures different from the test proceduretemperature, i.e. ≃ 20°C. More definitive recommendations for the global factor ofsafety are made in Part III of this series of papers (Koerner et al. 1996).

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7 SUMMARY OF EXPERIMENTAL INVESTIGATION

An experimental investigation is presented that involves testing unprotected geo-membranes and geomembranes protected with nonwoven needle-punched geotextilesunder various idealized and field simulated conditions. The test results are used to de-velop an empirical design method for the protection of HDPE geomembranes. The fol-lowing points summarize the basic features of the experimental data and the empiricaldesign method:

S The puncture resistance of a geomembrane increases as the mass per unit area of theprotection geotextile increases. The relationship is linear for all protrusion heights.S The puncture resistance of geomembranes using angular stones (e.g. quarried stone)

is assumed equal to the puncture resistance of geomembranes using the truncatedcones in the experimental investigation. Subrounded stones result in two times thepuncture resistance of geomembranes using angular stones, while rounded stones re-sult in four times the puncture resistance of geomembranes using angular stones.S An increase in the protrusion height causes a decrease in the puncture resistance of

the geomembranes. For any mass per unit area protection geotextile, the puncture re-sistance of the geomembrane is inversely proportional to the square of the protrusionheight.S The puncture resistance of a geomembrane over a bed of stones is greater than that

over isolated stones for the same effective protrusion height. It may be conservativelyassumed that the puncture resistance of a geomembrane in the former case is twotimes that of the latter case.S The puncture resistance of a geomembrane under geostatic loading can be up to six

times greater than that under hydrostatic loading, the reason being attributed to theeffect of soil arching. However, the effect of soil arching at yield may not be as greatas the effect of soil arching on the failure pressure. The deformation of the geomem-brane up to yield may not be large enough to mobilize the soil arching effect. There-fore, it is advisable in design to limit the puncture resistance under geostatic loadingto a maximum of two times that under hydrostatic loading.S Puncture resistance of a geomembrane decreases with time, while the effect of time

is more pronounced with a decrease in the mass per unit area of the protection geotex-tile and an increase in the protrusion height.S The factor of safety values for creep are relatively low in comparison to the factors

of safety found in the literature for creep of geotextiles in tension. This can be ex-plained by the fact that in puncture mode the geomembrane and its protection mater-ial conform more to the subgrade as they creep and hence the unsupported length de-creases with time. Since, for the same applied pressure, the maximum stressesmobilized at the protrusion tip decrease with the decrease of the unsupported lengthof the geomembrane, a decrease in stress is expected with time. Thus, lower factorsof safety for creep are required in the puncture mode compared to the same geotex-tiles subjected to a constant tensile stress.S Although not investigated in this study, the effect of chemical and biological degrada-

tion should be included when determining the geomembrane puncture resistance.Since puncture is basically a result of tension failure at the protrusion tip, it would

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be logical to assume that chemical and biological degradation affect the puncturestrength as they do the tensile strength of geomembranes. Partial factor of safety val-ues for chemical and biological degradation cited in the literature are used in thisstudy.S All of the above factors are considered in the empirical formulation presented in Sec-

tion 6 with the purpose of determining an allowable pressure for the geomembraneand its protection material. Additionally, a global factor of safety is introduced thatis consistent with standard design practice to account for any uncertainties.S The effect of temperatures that are significantly higher or lower than≃ 20°C corre-

sponding to the test procedure have not been included.S The design method is illustrated in Part III of this series of papers (Koerner et al. 1996)

using example problems and design charts.

REFERENCES

ASTM D 4595, “Standard Test Method for Tensile Properties of Geotextiles by theWide-Width Strip Method”, American Society for Testing and Materials, West Con-shohocken, Pennsylvania, USA.

ASTM D 4885, “Standard Test Method for Determining Performance Strength of Geo-membranesby the Wide Strip Tensile Method”, American Society for Testing and Ma-terials, West Conshohocken, Pennsylvania, USA.

ASTM D 5199, “Test Method for Measuring Nominal Thickness of Geotextiles andGeomembranes”, American Society for Testing and Materials, West Conshohocken,Pennsylvania, USA.

ASTM D 5261, “Test Method for Measuring Mass PerUnit Area of Geotextiles”, Amer-ican Society for Testing and Materials, West Conshohocken, Pennsylvania, USA.

ASTM D 5514, “Standard Test Method for Large Scale Hydrostatic Puncture Testingof Geosynthetics”, American Society for Testing and Materials, West Conshohocken,Pennsylvania, USA.

Brummermann, K., Blümel, W. and Stoewahse, C., 1994, “Protection Layers for Geo-membranes: Effectiveness and Testing Procedures”, Proceedings of the Fifth Inter-national Conference on Geotextiles, Geomembranes and Related Products, Vol. 3,Singapore, September 1994, pp. 1003-1006.

Daniel, F. and Daniel, L., 1984, “The Behavior of Geomembranes in Relation to Soil”,Proceedings of the International Conference on Geomembranes, IFAI, Vol. 1, Den-ver, Colorado, USA, pp. 175-180.

Frobel, R., Youngblood, W. and Vandervoort, J., 1983, “The Composite Advantage inthe Mechanical Protection of Polyethylene Geomembranes - A Laboratory Study”,Proceedings of Geosynthetics ‘87, IFAI, Vol. 2, New Orleans, Louisiana, USA, Feb-ruary 1987, pp. 565 -576.

FTMS 101C Method 2065, “Puncture Resistance and Elongation Test (1/8-inch ProbeMethod)”, Federal Test Method Standard, U.S. General Services Administration,Washington, DC, USA.

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Hullings, D.E., 1990, “Puncture Behavior and Protection of Geomembranes UsingLarge Scale Hydrostatic Facility”, Master’s Thesis, Drexel University, Philadelphia,Pennsylvania, USA, 71 p.

Hullings, D.E. and Koerner, R.M., 1991, “Puncture Resistance of Geomembranes Us-ing a Truncated Cone Test”, Proceedings of Geosynthetics ‘91, IFAI, Vol. 1, Atlanta,Georgia, USA, February 1991, pp. 273-285.

Koerner, R.M., 1994, “Designing with Geosynthetics”, Third Edition, Prentice Hall,Englewood Cliffs, New Jersey, USA, 783 p.

Koerner, R.M., Wilson-Fahmy, R.F. and Narejo, D., 1996, “Puncture Protection of Geo-membranes Part III: Examples”, Geosynthetics International, Vol. 3, No. 5, pp.655-675.

Murphy, V.P. and Koerner, R.M., 1988, “CBR Strength (Puncture) of Geosynthetics”,Geotechnical Testing Journal, Vol. 11, No. 3, pp. 164-172.

Narejo, D.B, 1994, “Puncture Behavior of HDPE Geomembranes”, Ph.D. Thesis,Drexel University, Philadelphia, Pennsylvania, USA, 137 p.

Narejo, D.B., Wilson-Fahmy, R.F. and Koerner, R.M., 1993, “Geomembrane PunctureEvaluation and Use of Geotextile Protection Layers”, Progress in Geotechnical Engi-neering Practice, Pennsylvania Department of Transportation, proceedings of a con-ference held in Hershey, Pennsylvania, USA, April 1993, pp. 1-16.

Wilson-Fahmy, R.F., Narejo, D. and Koerner, R.M., 1996, “Puncture Protection of Geo-membranes Part I: Theory”, Geosynthetics International, Vol. 3, No. 5, pp. 605-628.

ACKNOWLEDGEMENTS

This paper and Parts I and III of this series were made possible by co-funding by theU.S. Environmental Protection Agency under Cooperative Agreement No. CR-815692and the member organizations of the Geosynthetic Research Institute. Their sponsor-ship and interactions are sincerely appreciated.

NOTATIONS

Basic SI units are given in parentheses.

CH = cone height (m)d = constant (Pa/kg/m2)d50 = soil particle size for which 50% of the sample is smaller (m)FS = global factor of safety (dimensionless)FSCR = partial factor of safety for long term creep (dimensionless)FSCBD = partial factor of safety for chemical/biological degradation

(dimensionless)H = protrusion height (m)

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MA = geotextile mass per unit area (kg/m2)MFA = modification factor for soil arching (dimensionless)MFPD = modification factor for packing density (dimensionless)MFS = modification factor for protrusion shape (dimensionless)p = geomembrane failure pressure (Pa)pallow = maximum allowable pressure on the geomembrane with an implied

factor of safety of 1.0 (Pa)piallow = allowable pressure on the geomembrane for site specific conditions (Pa)preqd = maximum pressure required on the geomembrane (Pa)Ro = horizontal distance from the undeformed geomembrane point of

tangency with the protrusion tip to the undeformed geomembrane pointof tangency with the soil subgrade (m)

ABBREVIATIONS

AASHTO: American Association of State Highway Transportation OfficialsASTM: American Society for Testing and MaterialsFTMS: Federal Test Method StandardGM: geomembraneHDPE: high density polyethyleneNP: needle-punchedNW: nonwovenPE: polyethylenePET: polyesterPP: polypropylene