Our project is a literature review of scholarly papers and will attempt to cover select topics in the realm of earthquakes and landfills with a condensed discussion of the topic at hand. An attempt to compile and organize information from several papers will be made as well throughout the course of the paper. The first part of this paper is focused on a general overview of seismic design. The second part of this paper will converge to a discussion regarding geomembranes and liner systems in the context of seismic activity.
In 1993, Resource Conservation and Recovery Act or RCRA’s Title 40 CFR Subtitle D initiated interest in the field of seismic performance of landfills. Subtitle D provided the Federal minimum for seismic design criteria and was assumed to be applicable to Subtitle C landfills since Subtitle C had no direct mention of anything relating to seismic design criteria. As a result, there was a noticeably disproportionate discussion about Subtitle D versus Subtitle C in our literature review as reflected in our paper. Note, however that, states such as California, a state prone to earthquakes, has much more stringent and specific requirements regarding landfill seismic design (Kavazanjian & Matasovic, 2001).
With this said, seismic design of landfills is heavily dependent on project and site specificities. With dependence on project-specific data comes uncertainty associated with waste composition which are overcome by utilizing parametric and sensitivity numerical studies (Kavazanjian & Matasovic, 2001).
The primary cause of damage of landfills stems from the induced seismic hazards from strong ground motions. These damages include landfill slope instability, liquefaction of the landfill foundation, lateral spreading, foundation settlement, landslides, disruptions of liner and cover system, gas emission control system, and water drainage control system (Krishna, 2009).
The performance philosophy of landfills under seismic loading is either “withstand without harmful discharge” or “withstand without damage.” Subtitle D outlines that the waste containment system must be able to withstand MHA or the maximum horizontal acceleration. This can be evaluated by means of using the peak horizontal ground acceleration (PHGA) with a 90 percent chance of not being exceeded in the next 250 years or, once again, based off site-specific analysis (Kavazanjian & Matasovic, 2001).
The damage associated with a landfill from seismic loading has been classified in five categories by Matasovic et al, 1995. Matasovic classified the damages on a I-V scale, as per the nature of the damage, from little/no damage as category I to major damage as category V. Please refer to Figure 1.1 for specifics as outlined by Matasovic et al. (1995).
Figure 1.1: Seismic landfill damage categories I - V (Matasovic et al, 1995)
An observation made from the literature review was the repeating references to the Operating Industries, Inc (OII). This project will utilize this groundbreaking case study to exemplify the topics being discussed. This is an instrumented landfill which provided significant insight during the event of the Northridge earthquake. Most papers reviewed had mention of this site and seemingly provided a basis for future research and design criteria based on the empirical data gathered from OII. This allowed some of the first major observations of a landfill’s response under seismic loading (Anderson & Kavazanjian, 1995).
In context, the OII landfill is in California and a Maximum Credible Earthquake (MCE) event was used for its design. MCE is the maximum earthquake capable of impacting the site and is a more stringent design consideration for earthquake events than the Maximum Probable Earthquake (MPE). MCE is used for hazardous waste sites and MPE is used for MSW. As discussed earlier, of the two design philosophies, “without damage” was deemed impossible for the site given its location and thus the final cover system was catered to withstand an earthquake without the release of contaminants (Kavazanjian & Matasovic, 2001). It is important to note that in the consideration of an MCE, it is common to design the landfill to prevent the release of contaminants since designing for no damage is practically not feasible.
Based on our review, the dynamic or seismic analysis of a landfill comprises of the following steps:
Special sections will be dedicated to (1), (2), and (6) in the following three sections.
The following information critical for an earthquake resistant landfill design are to be determined prior to the design of a landfill:
A special note on liquefaction: liquefaction is a factor that must be paid careful attention to during siting. Liquefaction is a phenomenon that occurs when loose sandy material is seismically loaded, causing a transient increase in pore water pressure. This causes loss of soil strength and can lead to major failures. Liquefaction may cause severe damage to the structural integrity of the landfills, like localized bearing capacity failures, lateral spreading, excessive settlements, and damage to liner and cover systems, and drainage systems. Sandy soils below the groundwater table are prone to liquefaction. When siting for the landfill or evaluating the soil conditions of the vicinity, liquefiable soils must be either avoided or mitigated. If liquefaction conditions are present or unavoidable, ground improvement methods, or other mitigation techniques, may need to be implemented.
As mentioned earlier, landfill seismic analysis is often heavily site-specific. Evaluating the solid waste material properties is critical when designing a landfill for seismic criteria. With landfill solid waste characterization comes uncertainty, variability, and heterogeneity. Thus, the evaluation of waste materials’ properties are performed in conjunction with the parametric and sensitivity studies to compensate for these issues (Kavazanjian et al. 2001).
The intrinsic properties of the landfill required for dynamic analyses include the following (Murali Krishna, 2009):
As mentioned earlier, this paper will use the OII case study to demonstrate examples of results for the properties mentioned above in Figures 1.2 – 1.6 taken from Kavazanjian & Matasovic, 1998. OII will serve as a thematic case study to show real-world application of seismic design of landfills.
Figure 1.2: (i) Unit weight variation with depth
Figure 1.3: (ii) Shear wave velocity versus depth
Figure 1.4: (iii) Shear strength
Figure 1.5: (iv) Shear strain versus damping ratio
Figure 1.6: (v) Shear strain versus normalized shear modulus
Figures 1.2 to 1.6 -
Figure 1.2 shows the unit weights obtained from multiple boreholes obtained from the gravel displacement method. An average unit weight is then calculated.
Figure 1.3 shows the shear wave velocity profiles from Spectral Analysis of Surface Waves (SASW) testing. In general, the shear wave velocity increases with depth. This is natural considering it increases with higher stresses, which exist as greater depths. A greater shear wave velocity is desirable since this means there is less amplification. The solid red line is the calculated mean and the two dotted lines are the standard deviation of one sigma.
Figure 1.4 shows the shear strength. The two dashed plots represent material that passed the 19 mm screen and material that didn’t. The percentages show the amount of refuse, or not-soil material in the sample.
Figure 1.5 and Figure 1.6 show two cyclic shear strain relationships on a log scale. The damping ratio increases while normalized shear modulus decreases with increasing cyclic shear strain. The two graphs agree with the notion that material damping ratio is inversely proportionate to dynamic shear modulus. The shear modulus upper bound and the damping lower bound values were developed from field data and laboratory testing and are commonly used in the industry to this day. The curves were calculated using back-analysis of landfill seismic response (Matasovic & Kavazanjian, 1998).
The two conventional approaches to evaluate the stability of landfill structural systems consist of the pseudo-static method of analysis and the Newmark Sliding-Block analysis.
The pseudo-static method yields the limit state equilibrium expressed in terms of factor of safety of slopes during seismic loading. A minimum FS of 1 is desired and essentially means that the driving force is equal to the resisting force since,
FS = 1 = resisting force / driving force
thus, resisting force = driving force if FS = 1
FS = ( ( W * cos(α) – k * W * sin(α) * tan(φ) ) / ( W * sin(α) + k * W * cos(α) )
where k = ah / g
ah = pseudo-static acceleration in horizontal direction
k = coefficient for the horizontal direction
W = weight of failure mass
g = Earth’s gravitational constant
φ = Friction angle of soil
α = Angle of toe up to failure surface of sliding mass. See Figure 1.8
Selecting the k coefficients is based on very subjective criteria and descriptions. This can significantly affect the accuracy of this method.
Also, the seismic accelerations exist in the horizontal and vertical directions, however, the horizontal component is the only one considered in design since the vertical forces average out to 0 and are typically not in-sync with horizontal motion (Kramer,1996).
Figure 1.8: Force diagram depicting a sliding mass on an inclined plan. Force diagram of a landslide mass sitting on an inclined planar slip surface (Terzaghi, 1950).
As per the diagram,
W = weight / unit length of landslide mass
k = seismic coefficient
s = shear resistance along slip surface
α = angle of slip surface inclination
Note in this scenario, the whole landslide mass is considered as a whole, from the toe of the slope to the surface above.
The sliding-block analysis was introduced by Nathan Newmark in 1965. The Newmark analysis yields the cumulative, permanent displacement of the slopes during seismic loading. The method utilizes the basic physics scenario of the rigid block on an inclined plane, as shown in Figure 1.9 (Kramer, 1996). Just as there is a certain amount of friction that a wooden block on an inclined surface will need to overcome to slide likewise, the yield acceleration is the acceleration required for the landslide mass to initiate motion, or sliding. The yield acceleration is ay = kyg. When the ay is exceeded, permanent deformation occurs. This method is used to compare between the displacement of the slopes and allowable displacement of the landfill components in the event of a major earthquake. This method is more refined than the pseudo-static method and as it provides an indicative estimate of amount of displacement when the material slides.
Figure 1.9: Forces acting on a block on an inclined plane in dynamic conditions. (Kramer, 1996)
Figure 1.10: Illustrated the integration of the accelertion above the yield acceleration to render the velocity which is integrated again to obtain the displacement (Krishna, 2009).
The following passage will review the computer programs encountered. With the aid of finite element analysis, computer programs have been developed to model seismic response of earth materials. For the OII site, QUAD4M was used to conduct a two-dimensional equivalent-linear finite element seismic response analysis for the final cover system. Example programs used in dynamic analysis are listed below in the diagram shown:
Figure 1.7: Computer programs for seismic scenarios in landfills (Created by Mowar)
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.
The Olympic View Sanitary Landfill (OVSL) is located approximately 15 km southwest of Port Orchard, Washington. The site started receiving municipal solid waste and construction debris in the 1960s, transitioning from an unlined waste disposal site to a modern lined sanitary landfill. The Phase I area of the landfill was founded in the glacial moraine that underlies the entire site, and three areas were lined with composite liners. Three types of composite landfill cover were used in Phase I. Cover types A and B apply native soil mixed with bentonite as the low permeability soil layer beneath the geomembrane. Cover types C employs a needle-punched reinforced geosynthetic clay liner (GCL) as the low permeability soil layer instead of the native soil mixing with bentonite.
The reason why the OVSL landfill is selected is that it is the first recorded case history of a composite cover system shaken by strong ground motions. On February 28th, 2001, a moment magnitude (Mw,) of 6.8, Nisqually earthquake happened. The main shock occurred at the interface of the Juan De Fuca and North American tectonic plates, approximately 52 km below the ground surface. According to The Pacific Northwest Seismograph network (2001), the OVSL site was approximately 39 km away from the earthquake epicenter (the point on the ground surface directly above the focus) and 65 km from the zone of energy release. There is a station called Kitsap County Moderate Risk Waste (KIMR), which is located at 1 km from the OVSL site. It is founded on “soft rock/dense soil”, defined as Site Class C per the NEHRP (BSSC 1998) Site Classification system. Soft rock/dense soil is defined as a site with a shear wave velocity over the upper 30 m of between 360 and 720 m/s or an average standard penetration test (SPT) below count (N60) in excess of 50. The NEHRP Site Classification is made upon geologic maps for Kitsap County, where the KIMR station and the OVSL are located. During the Nisqually earthquake, the KIMR station recorded acceleration time histories in three orthogonal directions. The recorded PHGA values in the north-south (KIMR-NS) and east-west (KIMR-EW) directions were 0.15 g and 0.16 g. Based on the current stability analysis of earth structures and seismic design landfill, the vertical components of ground motions were not necessary for the seismic analysis of the landfill cover.
The landfilling operations were in progress at the OVSL site when the Nisqually earthquake happening. Reports from the operators at the site working on the ground surface indicated that they were immediately alarmed by the earthquake. However, operators working on the solid waste fill reported that they barely noticed that the ground was shaking. 5 days after the earthquake, a formal reconnaissance team arrived at the OVSL site. Neither the landfill crews nor the team found any evidence of seismically induced damage including permanent lateral displacement of the composite landfill cover. However, they discovered that many landfill gas risers had moved laterally relative to the cover by up to approximately 30 mm. Two and half years after the Nisqually earthquake, a spectral analysis of surface waves (SASW) geophysical survey was conducted at OVSL site. The results of the site-specific SASW measurements conducted on top of each of the landfill areas covered by a composite cover are shown in Figure. 2.3. The results indicate that the shear wave velocity of the OVSL site is stress dependent, as it is greater at depth than the near surface in all three profiles.
Figure 2.3 – Results of SASW measurements at OVSL Site
Four different methods were applied to analysis the seismic effects on the composite landfill cover of the OVSL site. Method 1 and 2 were evaluated using two simple chart solutions outlined in the United States Environmental Protection Agency (EPA) guidance document on seismic design of solid waste landfills (Richardson et al. 1995). Method 3 is a more rigorous screening procedure proposed by Bray et al. (1998). Method 4 is a conventional decoupled equivalent-linear site response/Newmark-type (Newmark 1965) permanent seismic deformation analysis. The results of four methods are shown in Table 2.1
Table 2.1 – Summary of Seismic Response and Deformation Analysis
Method 1 and 2 are intended to be most conservative because the larger displacement would cause failure.For the OVSL site, they overestimated the response of the OVSL landfill. Estimation from Method 3 was lower but still greater than the method 4 values and is still too conservative. Hence, method 4 is more accurate in the case. Based on method 4, the range of maximum transient displacement of 35 to 55mm is consistent with the observed relative movement between the cover and landfill gas risers of up to 30 mm.
Both geosynthetics and composite landfill cover are commonly used in modern landfills. At the OVSL landfill, it is important to not only perform seismic design procedures, such as slope stability or liquefaction but know what performance of geosynthetics and landfill cover are expected under certain shear strength and period. So, engineering judgment is needed to select appropriate methods to analyze the geosynthetics and landfill covers under seismic conditions.
The primary goal of seismic design of a landfill is to ensure that the landfill sustains an earthquake without damage or without leaking contaminant. With the onset of the Subtitle D regulation, research and interest in the seismic criteria of landfill design has been of interest. The lack of specification from the Subtitle C and D may root from the fact that seismic design is heavily specific to region and site-specificities. This puts the onus on the designer to ensure the project at hand is fully understood and evaluated before designing a landfill for seismic loading. Choosing which design philosophy and specifications are met is paramount with careful consideration needed. In areas such as Washington State and California, where seismic activity is imminent, and populations are ever-growing, landfill design for seismic criteria is becoming evermore important.
About the Authors:
The Part I: Seismic Design part of this paper was authored by Oscar Mowar. He is from Seattle, Washinton. and an undergraduate Civil Engineering student focusing on Geotechnical Engineering at the University of Michigan '18.
The Part II: Geosynthetics and Cover System chapters were authored by Michael Liu. He is from Shanghai, China and a graduate Geotechnical Engineering at the University of Michigan.