Criticism of the Classical Model as Applied to MSW

Despite the fact that the classical model is the most used model for MSW settlement estimates and prediction, some criticism of it is presented below.

As presented in Section 3.3.1.1, the classical model hypotheses adopted for soils are not adequate for MSW. So, the Sowers Proposition, reviewed by other authors, must be understood as an empirical adjusted model, since it does not represent the phenomenon that occurs in reality. On the secondary compression representation, the C’α parameter is not constant with log-time.

Also, there are difficulties in establishing what the MSW initial thickness is (especially in old landfills), necessary to the formulation.

As pointed out in Section 3.2, the division into the settlement phases of initial, primary, and secondary causes confusion for the comprehension of settlement mechanisms as well as for settlement predictions.

That deficiency can be noted more when the initial and primary compressions are modeled together. The primary compression is determined by an expression in which there is no time variable (Equation 3.6), and must be considered as a final value; however, it is considered to last 30 days (Sowers, 1973). In practice, it is difficult to isolate the primary compression from secondary compression because, differently from most soils, for MSW there is not a clear distinction in the settlement curve as a function of time for the two processes.

Furthermore, the adoption of the time is somewhat vague when the primary compression is finished (ti, Equation 3.7). Some authors arbitrarily adopt

ti equal to 30 days, like Sowers (1973); others do not explain what ti to use

(Simoes et al., 1996).

Similarly, some authors utilize the initial thickness (H0, Equation 3.8) as

being the thickness at the beginning of instrumentation (Carvalho, 1999). Others use the thickness after the conclusion of primary compression (Morris and Woods, 1990), and the great majority of them do not explain which thickness was used. Using Equation 3.8, from the curve of relative settlements as a function of time, an angular coefficient C’α is obtained, which is dependent on the H0

adopted. Thus, the same data can furnish different values of C’α, depending on

the initial thickness adopted. C’α values can only be compared only if the same

criteria are applied, and the values presented in Table 3.2 and in Figure 3.8 must be reviewed with these restrictions.

Fasset et al. (Equation 3.10), as presented by Manassero et al. (1996) and Stulgis et al. (1995), has two components. One is load dependent and the other is time dependent. It must be noted that the equation is conceptually incorrect

because it is valid only for times tf larger than ti, and for a constant C’c, which is

not reported. Also, if C’α is constant with log-time, then the relative settlement

curve would be a straight line function with time. This is not true, as shown in Figure 3.8.

Figure 3.9 presented by Pinto (1999) shows the settlement as a function of time for a superficial mark on a Brazilian landfill, in which there is available data only between 196 to 685 days after closure. It can be noticed that when the curve is extrapolated for any date near to the landfill closure, a negative relative settlement is obtained, which is nonsense. Probably the real curve follows the behavior of the dashed curve.

Figure 3.9 – Non-linearity of the Relationship Relative Settlement as a Function of Log-Time (Pinto, 1999)

Similarly, the Bjarngard and Edgers expression (Equation 3.11), presented by Manassero et al. (1996) and Stulgis et al. (1995), is only valid for C’c constant

with the log of the applied stress and for times greater than tm (tm>ti). However,

the authors present the curve from the graph of the relative settlement as a function of time approximated by two straight lines with coefficients equal to C’α1

and C’α2. De Abreu (2000), Carvalho (1999), Stulgis et al. (1995), Boutwell Jr.

and Fiore (1995), and Manassero et al. (1996) verified the existence of two components exhibiting a quasi-linear behavior with log-time, with different inclinations.

Carvalho (1999), citing Konig and Jessberger (1997) and Manassero et al. (1996), presented the change in the behavior of the curve related to the first coefficient (C’α1) as being associated with the “creep” phenomenon, and the

second coefficient (C’α2) as being associated with the “creep” phenomenon plus

the effect of MSW degradation, and justifying why C’α2 would be much greater

than C’α1. However, this justification is not valid as explained in the following

comments:

• Innumerable functions that do not follow a logarithmic law (for example, linear, exponential, polynomial functions), present a distortion in their respective curves whenever presented in semi-logarithmic graphs, with two or more components very distinctive, which can be approximated by segments of straight lines. It does not have a physical meaning. It is a characteristic of the non-logarithmic functions.

• Which is the real meaning of C’α? According to Sowers (1973), Cα is an

index related to the biodegradation potential and to physical-chemical alterations, and its value can be as high as the organic contents present and how the degradation potential of the residues, given the environmental characteristics of the landfill (moisture, heat, oxygen presence, etc). However, and according to the literature (e.g., Palma, 1995), C’α is not constant and changes with time. As can be seen on

practically constant, while the settlement rate decreases (note that certainly after some time C’α obligatorily will decrease, otherwise the

settlement would be infinite, which is nonsense). That means that C’α does

not have a physical meaning. A landfill under unfavorable conditions to degradation can have a larger C’α than another one under favorable

conditions, and for that it is only necessary that the C’α of both landfills be

compared at different times.

In other words, in order to compare two C’α obtained in two different

landfills, it is necessary to know what is the time of the analysis. Furthermore, C’α must be considered as a parameter with an origin in a

mere adjustment of the curve relative settlement as a function of log-time.

Figure 3.10 – Graphs of MSW Relative Settlement and Settlement Rate (Carvalho, 1999)

Wall and Zeiss (1995) did not notice the influence of biodegradation on the development of secondary settlements during 225 days based on the observation of the behavior of MSW settlement through the use of cells under two different conditions (one favorable to biodegradation and the other unfavorable). Even so, one cannot consider anything regarding the physical meaning of the variation of C’α with time.

MSW settlements do not have an obligation to follow a logarithmic law and the truth is that they do not and cannot follow it. Since the settlement mechanisms between soils and MSW are different, it must be remembered that in several cases even soils do not follow a logarithmic law. It would be more reasonable to use other types of functions (for example, hyperboles or exponentials) than starting from a non-linear relationship, proceed to adjust it into a semi-log graph that also does not present linearity, and try to approximate it by segments of straight lines.