## Part 3: Dynamic strength

### By Patrick J. Fox and Chris Athanassopoulos

### View Part 1 and Part 2.

## Introduction

The final segment of our three-part series on geosynthetic clay liner (GCL) shear strength is devoted to dynamic strength, the strength measured for rapid loading conditions. Static shear strengths have been reported for a wide variety of GCLs and GCL interfaces (e.g., Fox and Stark, 2004; Zornberg et al., 2005; McCartney et al., 2009; Fox and Ross, 2011); however only sparse data are available on the dynamic shear strength of these materials (Lai et al., 1998; Fox et al., 2006; Nye and Fox, 2007). Such information is important for design and long-term performance assessment of facilities in seismic regions that contain GCLs.

A research program has been completed on dynamic internal and interface shear strengths for needle-punched (NP) GCLs and textured geomembranes, as these are common liner materials, particularly in North and South America. Tests were performed for a wide range of normal stress using the large dynamic direct shear machine described by Fox et al. (2006). The main features of this machine include a specimen size of 305mm × 1067mm, a maximum normal stress of 2071 kPa, a maximum shear displacement of 254mm, and a maximum shear displacement rate of 30,000mm/min. The shearing surfaces prevent specimens from slipping and thereby avoid associated progressive failure effects (Fox and Kim, 2008). Monotonic tests consisted of a single shear thrust at a specified displacement rate. Cyclic shear tests consisted of back-and-forth shear motion at a specified frequency and displacement amplitude. Part 3 presents some of these results to illustrate internal shear strength of NP GCLs under rapid loading conditions. Published strength data, as in this article, are suitable only for preliminary design purposes. Final design strengths must always be measured using project-specific tests.

## Monotonic shear tests

Monotonic internal shear tests were conducted on hydrated specimens of a W/NW NP GCL for various combinations of normal stress σ_{n} and shear displacement rate R. Shear stress τ vs. shear displacement Δ relationships obtained for σ_{n} = 141 kPa are shown in **Figure 1**. Failure occurred at or just inside the woven geotextile/bentonite interface in each case. Similar to the static shear relationships discussed in Part 1 of this series, these relationships indicate shear resistance that rises rapidly to a well-defined peak strength and then undergoes large post-peak strength reduction as a result of reinforcement failure to ultimately reach a residual condition. Values of peak shear strength τ_{p}, displacement at peak Δ_{p}, and residual shear strength τ_{r} are shown in **Figure 2** as a function of displacement rate. An average static peak strength of 156 kPa was measured for R = 0.1 mm/min. With increasing displacement rate, peak strength increased approximately 20% to 186 kPa at R = 1000mm/min and then decreased to 151 kPa at R = 30,000 mm/min. Displacements at peak strength were approximately 30 mm for the slow rates and progressively decreased to 21 mm for the fastest rate. Residual shear strengths were relatively constant at 11 kPa for R ≤ 10 mm/min and then increased to 24 kPa at R = 30,000 mm/min. The static secant residual friction angle is 4.5°, which is in good agreement with values obtained in previous investigations (Fox et al., 1998). The dynamic secant residual friction angle at the fastest rate is 9.7°, which corresponds to an average increase of approximately 1° for each log cycle of displacement rate. The effect of displacement rate in **Figure 2** is more complex than suggested by previous studies and cannot be explained solely on the basis of pore pressure effects (Nye and Fox, 2007).

Peak shear strengths obtained for three higher normal stress levels are shown in **Figure 3** along with the corresponding data from **Figure 2**. At each normal stress, peak strength increases with increasing displacement rate to a maximum at R = 100 to 10,000 mm/min. These maximum τ_{p} values are about 15% to 20% higher than the corresponding static strengths measured at R = 0.1 mm/min. At the highest displacement rates, peak strengths decrease from these maximum values. Figure 3 indicates that, in general, static peak strengths are conservative at each normal stress level. The only exception is the data for σ_{n} = 141 kPa, in which average peak strengths measured at the highest displacement rate were slightly less than those measured at 0.1 mm/min. The trends in **Figure 3** suggest the resistance of reinforcing fibers increases and then decreases with increasing displacement rate for monotonic shear.

## Cyclic shear tests

Cyclic internal shear tests were conducted on hydrated specimens of the same W/NW NP GCL for various combinations of normal stress, displacement amplitude Δ_{a}, and frequency ƒ. An example of the data obtained for σ_{n} = 141 kPa is shown in **Figure 4**. This specimen was subjected to 50 cycles of sinusoidal displacement with Δ_{a} = 15mm and ƒ = 1Hz. Measured shear stress for the duration of the test is shown in **Figure 4a**. Each loading cycle produced a maximum shear stress τ_{m} , which was equal to 130 kPa for the first cycle and then decreased nonlinearly during subsequent cycles to a near-steady value of 37 kPa for the 50th cycle.

The stress-displacement relationship, shown in **Figure 4b**, also indicates strength degradation during cyclic loading. The hysteretic response is broadly similar to that for natural soils, although some differences are observed. The first quarter-cycle of loading (Δ = 0 to 15mm) is similar to a monotonic shear test with shear stress rising to τ_{m} as more needle-punched fibers become engaged with increasing displacement. Depending on the displacement amplitude, some fibers rupture or pull out of the geotextiles during this first stroke while others remain partly to fully intact. Upon reversal, the reinforcement relaxes and provides little resistance until it becomes engaged in the other direction during the third quarter-cycle (Δ = 0 to -15mm). As in **Figure 4a**, the progressive decrease of τ_{m} indicates that the reinforcement experiences additional damage with continued cycling.

Shear resistance during the middle part of each cycle corresponds to the dynamic shear strength of hydrated bentonite. Close inspection of **Figure 4** indicates that this strength decreases slightly with increasing number of cycles, which may reflect progress toward a residual shear condition or the generation of pore pressures along the shearing surface. Dynamic bentonite strength was 24 kPa during the 50th cycle which, similar to the monotonic shear data at the same normal stress (**Figure 2**), yields a dynamic secant residual friction angle of 9.7°.

Cyclic loading can reduce the subsequent static shear strength of a NP GCL. To investigate this effect, six cyclic shear tests were conducted for σ_{n} = 141 kPa, ƒ = 1 Hz, and Δ_{a} ranging from 2mm to 25mm. After cyclic loading, each specimen was subjected to monotonic shear with R = 0.1mm/min. Peak and residual static shear strengths are shown in **Figure 5** along with the corresponding data from a static shear test with no prior cycling (Δ_{a} = 0). Higher cyclic displacement amplitude yields progressively lower post-cyclic static peak strengths, which is due to greater levels of damage to the needle-punched reinforcement. The reinforcement was almost completely ruptured for Δ_{a} = 25mm, leaving the specimen with little more than residual shear strength afterward. Post-cyclic residual shear strengths were unaffected by previous cyclic loading and yield a static secant residual friction angle of 4.9°.

## Summary and conclusions

The following conclusions are based on the above tests results for internal shear of a hydrated W/NW NP GCL under dynamic loading conditions:

- Dynamic loading can significantly affect GCL shear strength.
- Similar to static shear tests, stress-displacement relationships for monotonic (i.e., single direction) tests display well-defined peak and residual shear strengths and large post-peak strength reduction.
- Peak shear strengths for monotonic tests first increase and then decrease with increasing displacement rate R. The highest peak strengths occurred for R = 100 to 10,000 mm/min and were approximately 15% to 20% larger than corresponding static peak strengths (R = 0.1 mm/min). Static peak strengths were generally conservative at each normal stress level.
- Cyclic shear tests performed at constant displacement amplitude Δ
_{a}indicate hysteretic shear behavior and GCL strength degradation with continued cycling. - Larger cyclic displacement amplitude yields progressively lower post-cyclic static peak strength due to greater levels of damage to the needle-punched reinforcement. A GCL specimen subjected to 50 cycles with Δ
_{a}= 25mm was left with little more than residual shear strength.

The preceding data and discussions pertain to GCL internal shear strength. Dynamic stability analyses involving GCLs must also consider dynamic interface strengths between the GCL and adjacent materials, which are likely to control for low normal stress conditions.

###
Patrick Fox, Ph.D., P.E., professor, geotechnical engineering, *University of California-San Diego*, La Jolla, Calif.

Chris Athanassopoulos, P.E., technical manager, CETCO, Hoffman Estates, Ill.

**Acknowledgement**

This research was supported, in part, 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

Fox, P. J., Sura, J. M., Ross, J. D., and Olsta, J. T. (2009). “Rapid shear response of a needle-punched GCL,” Proceedings, Geosynthetics 2009, Salt Lake City, Utah, 386-391.

Fox, P. J., Nye, C. J., Morrison, T. C., Hunter, J. G., and Olsta, J. T. (2006). “Large dynamic direct shear machine for geosynthetic clay liners,” *Geotechnical Testing Journal*, 29(5), 392-400.

Fox, P. J., and Kim, R. H. (2008). “Effect of Progressive Failure on Measured Shear Strength of Geomembrane/GCL Interface,” *Journal of Geotechnical and Geoenvironmental Engineering*, 134(4), 459-469.

Fox, P. J., and Ross, J. D. (2011). “Relationship between GCL Internal and GMX/GCL Interface Shear Strengths,” *Journal of Geotechnical and Geoenvironmental Engineering*, 137(8), 743-753.

Fox, P. J., Rowland, M. G., and Scheithe, J. R. (1998). “Internal Shear Strength of Three Geosynthetic Clay Liners,” *Journal of Geotechnical and Geoenvironmental Engineering*, 124(10), 933-944.

Fox, P. J., and Stark, T. D. (2004). “State-of-the-Art Report: GCL Shear Strength and its Measurement,” *Geosynthetics International*, 11(3), 141-175.

Lai, J., Daniel, D. E., and Wright, S. G. (1998). “Effects of cyclic loading on internal shear strength of unreinforced geosynthetic clay liner,” *Journal of Geotechnical and Geoenvironmental Engineering*, 124(1), 45-52.

McCartney, J. S., Zornberg, J. G., Swan, R. H., Jr. (2009). “Analysis of a Large Database of GCL-Geomembrane Interface Shear Strength Results,” *Journal of Geotechnical and Geoenvironmental Engineering*, 135(2), 209-223.

Nye, C. J., and Fox, P. J. (2007). “Dynamic shear behavior of a needle-punched geosynthetic clay liner,” *Journal of Geotechnical and Geoenvironmental Engineering*, 133(8), 973-983.

Zornberg, J. G., McCartney, J. S., and Swan, R. H. (2005). “Analysis of a Large Database of GCL Internal Shear Strength Results,” *Journal of Geotechnical and Geoenvironmental Engineering*, 13 (3), 367-380.