## Part 2: Static shear strength

### By Chris Athanassopoulos, P.E. and Patrick Fox, Ph.D., P.E.

## Introduction

Part 2 of our three-part series on geosynthetic clay liner (GCL) shear strength is devoted to static shear strength, which is the strength measured for relatively slow loading conditions. Internal and interface static shear tests have been conducted for a wide range of GCL materials and normal stress conditions (Gilbert et al., 1996; Fox et al., 1998; Triplett and Fox, 2001; Chiu and Fox, 2004; Fox and Stark, 2004; Zornberg et al., 2005; McCartney et al., 2009; Fox and Ross, 2011). Part 2 presents some of this past research as well as new strength data obtained for ultra-high normal stress conditions. The focus is hydrated needlepunch-reinforced (NP) GCLs and their interface with textured high-density polyethylene (HDPE) geomembranes (GMXs), which are common liner materials, particularly in North and South America. Most of the test results presented herein were obtained using a large dynamic direct shear machine described by Fox et al. (2006). The main capabilities of this machine include a 305mm × 1067mm specimen size, a maximum normal stress of 2071 kPa, and a maximum shear displacement of 254mm. Subsequent modifications have made it possible to test specimens measuring 152mm × 1067mm, and thereby double the maximum normal stress to more than 4100 kPa. Although previously unnecessary, such high normal stress levels are becoming relevant for design of large facilities. Shear strength data presented in this article, as well as any other publications, are suitable only for preliminary design purposes. Final design values must always be measured using project-specific tests.

## GCL internal shear strength

Hydrated sodium bentonite has very low shear strength. For example, Fox et al. (1998) sheared a hydrated unreinforced GCL and reported a peak friction angle φ_{p} = 10.2° and a residual friction angle φ_{r} = 4.7°. To increase the internal peak strength of a GCL, geosynthetic reinforcement is used to transmit shear stress across the weak hydrated bentonite layer. Reinforced GCLs can be manufactured as needlepunched or stitch-bonded. Needlepunching is now the preferred method and involves the use of barbed needles to pull nonwoven fibers from one geotextile through the bentonite core and the opposite geotextile. The industry uses the GCL peel strength index test (ASTM D6496) to assess the quality and strength of needlepunched reinforcement.

Figure 1 compares peak and residual failure envelopes for an unreinforced GCL, a stitch-bonded (SB) GCL, and two woven/nonwoven NP GCLs with different peel strengths(F_{p}). The peak strength (τ_{p}) envelopes indicate that reinforced GCLs are substantially stronger than unreinforced GCLs and that NP GCLs gain strength much faster than SB GCLs with increasing normal stress. The envelopes further indicate that higher peel strengths are associated with higher peak strengths for NP GCLs. Athanassopoulos and Yuan (2011) also found a correlation between peel strength and peak strength for a woven/nonwoven NP GCL. However, Zornberg et al. (2005) showed no clear trend between peel strengths and internal peak strengths for a large database of direct shear tests on the same type of NP GCL. Further work is needed to explain the inconsistency between these studies. The residual strength (τ_{r}) envelopes in Figure 1 are the same for all types of GCLs because any reinforcement is ruptured by the time a GCL reaches the residual shear condition.

More recently, Fox and Ross (2011) performed a series of internal shear tests on a nonwoven/nonwoven NP GCL for normal stresses ranging from 71.9 kPa to 2071 kPa. This GCL contained 3.7 kg/m^{2} of granular bentonite needlepunched between two 200 g/m^{2} nonwoven geotextiles and had an average peel strength of 2170 N/m. The resulting internal peak and residual failure envelopes are shown in Figure 2.

The peak envelope is bilinear and can be described by the following regression equations:

τ_{p} (kPa) = 83.7 kPa + σ_{n} tan 23.7° (71.9 ≤ σ_{n} ≤ 692 kPa)

τ_{p} (kPa) = 261.2 kPa + σ_{n} tan 9.9° (692 ≤ σ_{n} ≤ 2071 kPa)

Secant friction angles, defined as φ_{sec} = arctan(τ/ σ_{n}) , provide additional perspective on the variation of shear strength with changing normal stress. In this case, internal peak secant angles decreased from 57.6° at φ_{n} = 71.9 kPa to 16.8° at φ_{n} = 2071 kPa. The internal residual shear strength envelope is linear and is described by:

τ_{r} (kPa) = 1.3 kPa + σ_{n} tan 4.8° (71.9 ≤ σ_{n} ≤ 2071 kPa)

Corresponding internal residual secant angles decreased from 7.8° at σ_{n} = 71.9 kPa to 4.7° at σ_{n} = 2071 kPa. These values are consistent with Figure 1 and indicate that little to no NP reinforcement remains intact after 200 mm of shear displacement.

## GMX/GCL interface shear strength

GMX/NP GCL interface shear tests have been performed by various researchers (Gilbert et al., 1996; Triplett and Fox, 2001; Chiu and Fox, 2004; Vukelic et al., 2008; McCartney et al., 2009). General findings from this work show that peak shear strengths for GMX/NP GCL interfaces are lower than for NP GCLs at low to moderate normal stress conditions. Additionally, peak interface strengths for a GMX placed against the nonwoven side of a NP GCL are higher than those for the woven side due to extrusion of hydrated bentonite through the woven geotextile. The quantity of extruded bentonite typically increases with increasing normal stress and is greater when a GCL is hydrated under low normal stress conditions.

Fox and Ross (2011) also completed a series of interface shear tests between a GMX and the same nonwoven/nonwoven NP GCL as previously discussed. The GMX was a 1.5mm-thick HDPE geomembrane with structured texturing and an average asperity height of 0.72 mm. Results are presented in Figure 2. The peak strength failure envelope is described by:

τ_{p} (kPa) = 8.2 kPa + σ_{n} tan 18.4° (71.9 ≤ σ_{n} ≤ 692 kPa)

Corresponding interface peak secant angles decreased from 24.1° at φ_{n} = 71.9 kPa to 14.9° at φ_{n} = 2071 kPa. At low normal stress, the large displacement (200mm) envelope is described by:

τ_{200} (kPa) = 7.3 kPa + σ_{n} tan 10.5° (71.9 ≤ σ_{n} ≤ 692 kPa)

Residual secant angles decreased from 15.5° at σ_{n} = 71.9 kPa to 4.5° at σ_{n} = 2071 kPa. With increasing normal stress above 692 kPa, the failure mode transitioned from the GMX/GCL interface to GCL internal, and both the peak and large displacement envelopes became nonlinear. Partial internal failure occurred at 1382 kPa and complete internal failure occurred at 2071 kPa. As a result, the residual shear strength of the GMX/GCL interface test at 2071 kPa was equal to that of the GCL internal test because the NP reinforcement of the GCL was completely ruptured after 200mm of displacement.

The nonlinear failure envelopes in Figure 2 provide another example illustrating that linear extrapolation of measured data above or below the tested range of normal stress may overestimate shear strength and should not be attempted. Similar recommendations have been made by Thiel (2009) and others.

## Failure mode transition

At high normal stress, the interface strength between a GMX and a NP GCL can exceed the strength of the needlepunched reinforcement and failure of a GMX/NP GCL composite liner system can occur internally within the GCL. The critical normal stress associated with this failure mode transition depends on the specific materials (e.g., GCL peel strength, GMX texturing and asperity height) and testing conditions (e.g., hydration/consolidation, displacement rate) and, as such, can vary over a wide range. Triplett and Fox (2001) observed no GCL internal failures for GMX/NP GCL interface tests conducted at normal stresses as high as 486 kPa. McCartney et al. (2009) likewise reported no GCL internal failures in a database of 534 geomembrane/GCL interface tests performed at normal stresses as high as 965 kPa. Similarly, Athanassopoulos et al. (2009) did not observe GCL internal failure until the normal stress reached 2759 kPa. The variability of normal stress at failure mode transition highlights the need for project-specific shear tests using representative materials and conditions. Observations of internal shear failure of NP GCLs are thus far limited to the laboratory because there are no known cases of internal shear failure of NP GCLs in the field (Fox and Ross, 2011; Koerner, 2012). Nonetheless, the potential for both interface and internal failure should be considered for designs that subject hydrated NP GCLs to high normal stress levels.

## Shear strength at ultra-high normal stress

Athanassopoulos et al. (2012) and Thielmann et al. (2013) evaluated GMX/NP GCL interface strengths for normal stresses as high as 4144 kPa. The NP GCL contained 3.7 kg/m^{2} of granular bentonite needlepunched between two 200 g/m^{2} nonwoven geotextiles and had an average peel strength of 2224 N/m. The GMX was a 1.5mm-thick HDPE geomembrane with co-extruded texturing and asperity heights ranging from 0.51 to 0.58 mm. Two sets of tests were conducted: (1) GMX/NP GCL interface tests with the materials placed between rigid backing plates; and (2) GMX/NP GCL interface tests with the materials placed between a lower layer of sand and an upper layer of coarse gravel, to better replicate common field conditions. For the first test series, interface peak secant angles decreased from 21.6° at 348 kPa to 13.4° at 4144 kPa, and corresponding interface large displacement secant angles decreased from 7.1° to 3.5°. Internal GCL failures were observed for normal stress levels of 2072 kPa and above. Interestingly, as shown in Figure 3, repeating these tests with the GMX/NP GCL liner system placed between soil layers produced modest increases (up to 8.5%) in peak shear strength and dramatic increases (up to 83%) in large displacement shear strength.

The increase in strength is due to local out-of-plane deformation, or “dimpling,” of the liner components under the gravel particles, similar to those observed by Breitenbach and Swan (1999) and Parra et al. (2010). These results suggest that the common practice of performing direct shear tests using rigid backing plates is conservative with regard to shear strength of GMX/GCL composite liners that are overlain by gravelly soils.

## Summary and final comments

High quality data on static shear strengths of GCLs and GCL interfaces are needed for stability analyses of liner systems that incorporate these unique materials. The following conclusions are based on the foregoing review of selected research on this topic:

- Reinforced GCLs are substantially stronger than unreinforced GCLs. NP GCLs gain strength much faster with increasing normal stress than SB GCLs. Higher peel strengths are often associated with higher peak strengths for NP GCLs.
- Peak shear strengths for a GMX interface with the nonwoven side of a NP GCL are consistently higher than those for the woven side. The quantity of bentonite extruded to the interface typically increases with increasing normal stress and is less for nonwoven geotextiles than for woven geotextiles.
- Peak shear strengths for GMX/NP GCL interfaces are generally lower than for NP GCLs at low to moderate normal stress conditions.
- GMX/NP GCL interfaces can experience GCL internal failure at high normal stress. The critical normal stress at which such failure mode transition occurs is highly dependent on the specific materials and testing conditions, and has been shown to range from 692 to 2759 kPa in recent studies.
- Internal failures of NP GCLs have thus far been observed only in the laboratory. Fox and Ross (2011) and Koerner (2012) report that there are no known cases of internal shear failure of NP GCLs in the field. Nonetheless, the potential for both interface and internal

failure should be considered for designs that subject hydrated NP GCLs to high normal stress levels. - The widespread practice of conducting direct shear tests on single interfaces with rigid backing plates appears to be conservative with regard to shear strength, and especially large displacement shear strength, of GMX/GCL composite liners that are overlain by gravelly soils.
- The variability of static shear strengths of GCLs and GCL interfaces highlights the need for project-specific shear tests using representative materials and conditions.

Part 3 will conclude this series with a discussion of the dynamic shear strength of GCLs. This emerging area of research is an important consideration for GCL liner systems subject to earthquakes and other dynamic loadings.

### Chris Athanassopoulos, technical manager, CETCO, Hoffman Estates, Ill.; chris.athanassopoulos@amcol.com

Patrick Fox, professor, University of California-San Diego, La Jolla, Calif.; pjfox@ucsd.edu

#### Acknowledgements

Some of the data presented in this paper was obtained with funding provided by Grant No. CMMI-0800030 from the Geotechnical Engineering Program of the U.S. National Science Foundation and by CETCO of Hoffman Estates, Ill. This support is gratefully acknowledged.

#### References

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