The International Information Center for Geotechnical Engineers

Seismic Response and Stability Analysis of Landfills


Part II: Seismic Analysis of Geosynthetic Liner and Landfill Cover System

When performing seismic design of landfill and slope stability analyses, it is important to assess the performance of geosynthetic liner system and landfill covers. Most of the modern landfills are constructed with geosynthetics due to its low permeability and cushion. Although often, in engineering practice, one-dimensional (1-D) equivalent linear models are more preferred than two-dimensional (2-D) nonlinear models, 1-D models have a major drawback of not considering friction interface and shear strength. A comparison about two methods is required to determine whether slip along the geosynthetics may or may not affect the seismic estimations. 

Currently, methods of one-dimensional (1-D) decoupled seismic deformation analyses are applied to analysis of the geosynthetic liner system under seismic condition. Since the 1-D analysis doesn't consider the shear stresses and strains in the liner system and it ignores the impact of transient seismic deformation at the liner interface, a two-dimensional (2-D) non-linear time-domain numerical model of landfill seismic response has been developed. The main purpose of the 2-D model is to evaluate the adequacy of the one dimensional (1-D) decoupled seismic deformation analyses (e.g. Bray et al. 1998). Thus, A quarry fill and a canyon fill, shown in Figure 2.1, have been analyzed in both methods. Efforts have been made to find out the difference in the performance of the liner system in terms of liner stresses, strains and permanent displacement from 1-D and 2-D. The reason for using the finite difference numerical modeling code FLAC (Itasca 2008) to guide the seismic analyses is that it is able to consider both large displacements and relative displacement at liner system interfaces (Fowmes et al. 2005).


 Figure 2.1 Landfill Models Used in the Numerical Analysis: (a) Quarry-fill Model; (b) Canyon-fill Model 

The methodology applied to model the interaction between the waste and the geosynthetic liner system is a combination of the model that measures the impact of the waste settlement on side slope liner by Fowmes et al. (2005), the Mohr-Coulomb criterion and the zero moment of inertia. The Mohr-Coulomb model is able to accurately model the interface shear slip at the liner interface has been demonstrated by modeling of shaking table tests of a rigid block on both horizontal and inclined planes (Arab et al. 2009). The zero moment of inertia allows the geosynthetic element to buckle.

The two model landfills shown in Figure.2.1 were tested based on the records from the 1983 moment magnitude (Mw) 6.7 Coalinga earthquake with a peak horizontal ground acceleration (PHGA) of 0.4 g. This “outcrop” acceleration-time history was converted to a “within” rock motion using software, such as SHAKE2000 or STRATA. Then, the corresponding “within” shear time histories were applied at the base of the model in FLAC as the design ground motion. Two different cases are compared in the study based on friction angles and shear strength. Case A shows theanalysis with the same upper and lower interface shear strength, a friction angle of 20o at the base and a friction angle of 15o at the side slope.  Case B shows a case that the upper interface shear strength is higher than the lower interface shear strength, with a value of 15o for the lower interface friction angle at the base and 10o for the lower interface friction angle on the side slope. Results are shown in Figure 2.2. For the quarry fill analysis, the acceleration response spectrum(ARS) in the 2-D analysis has a greater spectral response at short periods than ARS in 1-D analysis. For the canyon fill, the ARS are similar. 


Figure 2.2 Acceleration Response Spectra on the Top Deck from Non-linear and Equivalent Linear Analysis (a) Quarry-fill Model; (b) Canyon-fill Model 

As mentioned before, one advantage is that the 2-D analysis predicts the stresses and strains in the geomembrane. After performing two different cases on two landfills, the maximum tensile forces and strains were at the crest of the landfill. Also, the strains and forces at the toe of the side slope were compressive in all cases. On the other hand, the relative displacement between the geomembrane and the underlying foundation material at different points for both quarry-fill and canyon-fill were computed. For the quarry-fill, the maximum permanent displacement was at the top of the slope and was about 0.15 m, which is much larger than 0 m from 1-D decoupled analysis. At mid-slope of the quarry fill, the permanent displacement is 0.06 m but a maximum transient relative displacement of about 0.09 m was estimated during the earthquake. For the canyon-fill, the top of slope experienced a permanent displacement of about 0.11 m while the mid-slope experienced about 0.05 m in permanent displacement and a maximum transient displacement of 0.09 m for the canyon-fill, which is close to 0.072 m from 1-D analysis. However, for the canyon-fill, at the toe of the landfill, a permanent displacement of about 0.81 m was estimated, which is much higher than 1-D analysis.

After comparing results between two methods, it is interesting that slip at the liner interface in the 2-D non-linear analyses did not significantly reduce the spectral response for any landfill configuration compared to the results of the 1-D equivalent liner analysis. The non-linear analyses indicated that the tensile forces and strains in the geomembrane were minimal when the interface shear strength was the same or greater at the bottom than at the top of the geomembrane.  Even the interface friction angle at the top of the slope was five degrees greater than at the bottom of the geomembrane, the seismic tensile forces were still within the allowable values. Also, the permanent seismic displacement at the crest of the side slope from the non-linear analysis matches the calculated permanent displacement from a conventional decoupled analysis. However, the permanent displacement at the toe of the canyon fill was significantly greater in the 2-D non-linear analysis compared to the decoupled analysis for both landfill configurations. Hence, with reasonable interface friction angles, the 1-D equivalent linear analyses are still reliable. Judgment needs to be made with the displacement at the toe of the canyon fill when using the 1-D methods. 



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