Several researches have been developed, since the 1970s, to determine the behavior of landfills. An example of these studies is the application of mathematical models to predict settlements. This work aimed to develop a mathematical model for prediction of settlements, applied to the landfill in the city of São Leopoldo - RS, Brazil, managed by the Companhia Riograndense de Valorização de Residuos (CRVR). A mathematical model was developed to predict the landfill settlements under study, by means of a Multiple Linear Regression (MLR) statistical analysis, including Factor Analysis by the Principal Components method, via Varimax Rotation. The model used the CRVR leachate monitoring parameters, dated from 2014 to 2018, and presented an adherence of 80% to the actual settlement data. It was found that the use of settlement prediction models, through MLR analysis, is adequate for estimating the lifecycle of landfills, as long as some adjustments are made in monitoring the data (frequency of monitoring and continuous monitoring of parameters). It must also be considered that each landfill has its particularities, being necessary a case-by-case analysis in order to make sure that the model meets the landfill under study.
Method Article
Development of a mathematical model of Multiple Linear Regression, with Factor Analysis, to predict the settlement of a landfill in Southern Brazil
https://doi.org/10.21203/rs.3.rs-1522611/v1
This work is licensed under a CC BY 4.0 License
Version 1
posted 05 Apr, 2022
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Sanitary Landfill
Southern Brazil
Settlement
Mathematical model
Settlement prediction
Lifecycle
Multiple Linear Regression
MLR
The use of landfills as a final disposal system of solid waste is common in many countries and in Brazil, is the most widely used alternative. According to information from the Municipalities that responded to the survey of the National Sanitation Information System (SNIS) in 2019, the System are aware of the final destination of 92.1% of the mass of waste collected in the country, 75.1% of which are destined to landfills. (BRASIL, 2020). Unfortunately, the areas used for landfills have a useful life of 20 to 30 years only, requiring studies that propose an increase in the useful life of these units.
Municipal Solid Waste (MSW), when grounded, exhibits mechanical, physical, chemical and biological behaviors over time, which directly influence their operating conditions, such as leachate generation, biogas, and settlements. All of these characteristics modify the structure of the landfill. (DENARDIN, 2013; MELO et al., 2014; SOUTO, 2009).
The leachate generation occurs during the lifetime of the landfill. Its composition is influenced by the physical, chemical and biological characteristics of the waste, the latter being the predominant one. For this reason, it is necessary to carry out studies to characterize MSW and to monitor leachate in order to understand the behavior of the landfill in the long term. (AMARAL et al., 2008; SOUTO, 2009).
The settlements occur due to the compaction of MSW by mechanical processes of landfill operation; decomposition of grounded mass; leachate level; waste characteristics such as specific mass and organic matter content; drainage system and uncontrollable environmental factors. The grounding time of the waste and its composition can determine the possible occurrence of settlements, and the older the landfill, the lower this potential. (ALCÂNTARA; JUCÁ, 2010). The occurrence of settlements (due to several factors such as operation method, degradation of landfilled waste and leachate generation), shows to be a solution to reduce the occupation of new landfill areas, due to the use of it for this purpose.
One way of previously monitoring the occurrence of settlements is the application of mathematical prediction models, which use the characteristics of the landfills in order to monitor the change in the height and volume of the grounded mass, depending on the physical, chemical and biological processes that occur in the site. (GOMES; CAETANO, 2010).
Thus, the prediction of settlements in landfills, where there are significant reductions in the volume of landfilled mass due to the decomposition and compression of waste, is an important contribution tool in the area of geotechnics. (ALCÂNTARA; JUCÁ, 2010).
In this context, the present work sought to develop a settlement prediction model, applied to the landfill of Companhia Riograndense de Valorização de Residuos (CRVR), in the city of São Leopoldo - RS, Brazil. Geotechnical monitoring and leachate analysis data from the landfill were used and analyzed over time, seeking to apply these properties to the developed model, based on existing models and based on the characteristics that most influence the occurrence of settlement, through statistical analysis using correlation and linear regression.
This study was carried out at the CRVR Sanitary Landfill, in the city of São Leopoldo, Rio Grande do Sul, Brazil. CRVR is a subsidiary of the Solví holding company, which operates in Brazil and abroad. The São Leopoldo unit has a licensed area of approximately 119,000 m² for waste disposal, with a capacity of 1000 tons/day and a useful life of approximately 20 years, and a total licensed area of approximately 384,000 m². (FEPAM, 2020).
The landfill started its activities in late 2011 and currently has six phases closed and is operating the seventh phase, which started in April/2019 and is being operated above the previous phases. Every month, 31,000 m³ of waste are received, on average. The area has four leachate storage ponds for further treatment by an outsourced company. And it has monthly monitoring of vertical and horizontal settlements; quarterly leachate monitoring; and surface and groundwater sampling points.
Gravimetric characterization of waste received at the landfill
The CRVR landfill in São Leopoldo receives waste from several cities in the Vale do Sinos region, from municipalities that generate from 1000 to 100000 t/month of waste. Gravimetry was calculated through monthly reports issued by the company that manages the landfill, containing quantities and origins of waste received. The origin was subdivided into two categories: regular municipal collections and other generators (companies, industries, supermarkets, cooperatives).
For the waste received from the municipalities, the gravimetry contained in the Municipal Plans was used, while the purpose of each was observed in the other generators. Thus, companies that handle plastic entered gravimetry as plastic generators. Likewise, waste generated by paper trading establishments was classified 100% as Paper. In the Metal category, the residues generated by industries and commerce that work with metals, as well as the auto parts industry, were determined. In the Organic Matter (OM) category, such as food waste, pruning, branches and similar, 100% of the waste coming from universities, supermarkets and CEASA (State Supply Center) was classified. As waste or biological contaminant (BC), it was considered the ISW (Industrial Solid Waste) and the SWHS (Solid Waste from Health Services) autoclaved and decontaminated, waste from the rubber, tire and ceramic industries, builders/pavers and companies transportation, material not usable in recycling cooperatives and other materials received by the landfill without description or with missing information. The “Others” category is mostly made up of Long-Life Packaging (LLP).
Leachate monitoring
The parameters for monitoring the raw leachate, collected at the entrance of the first storage pond, carried out quarterly by CRVR, with analyzes dated from October/2014 to September/2018, were investigated.
The parameters analyzed quarterly are: Total Alkalinity, Aluminum, Arsenic, Barium, Boron, Cadmium, Lead, Chlorides, Copper, Thermotolerant Coliforms, Total Coliforms, Conductivity, Total Chromium, BOD, COD, BOD/COD, Iron, Total Phosphorus, Manganese, Mercury, Nickel, Nitrate, Nitrite, Ammoniacal Nitrogen, Kjeldahl total nitrogen, Mineral oils and greases, Vegetable and animal oils and greases, Dissolved oxygen, pH, Sedimentable solids, Total suspended solids, Total solids, Total dissolved solids, Sulfate, Sulfide , Temperature, Turbidity, Zinc.
Monitoring of settlements
The monitoring of settlements, through superficial landmarks, was carried out by CRVR from October/2014 to September/2018. The superficial landmarks used in this study were: SL 11, SL 12, SL 15, SL 16, SL 20, SL 21, SL 23, SL 24 and SL 25.
Statistical analysis
The statistical method chosen for this study was Correlation and Linear Regression. According to Hair et al. (2009), the minimum proportion of observations for each independent variable must be 5 to 1, with the most suitable being 15 to 1. In this study, the dependent variable considered was Settlement (using only data from one of the superficial landmarks because the number of observations was the most coherent for the study). Initially, the independent variables considered were all the monitoring parameters of the CRVR/SL raw leachate, but after the development of the work, it was verified the need to use the Factor Analysis tool, considering, from there on, the factors generated by the Factor Analysis as the independent variables.
For the available data, it was possible to reach a total of 49 observations, replicating the leachate monitoring data to the months in which there was no analysis.
For the development of the mathematical model, the IBM® SPSS Statistics® Software, version 22, was used. Data from the SL 12 superficial landmark and the leachate monitoring parameters were used, both dated from Oct/2014 to Sept/2018.
Figure 2 explains the model development stages and, after that, what was done in each stage is described.
First, with all SL 12 leachate and settlement monitoring data, a Correlation Analysis was performed to assess Collinearity, considering that there were gaps in monitoring referring to a few months in which some parameters had not been monitored. Subsequently, Linear Regression Analysis was performed, using the “insert” method, which proved to be inefficient for generating the model, as it showed that no parameter was significant.
After the first attempt, it was decided to run the Regression Analysis only with the parameters that had all the observations, without any missing values. These were: Total Alkalinity, Chlorides, Conductivity, Total Chromium, BOD, COD, BOD/COD, Nickel, DO, pH, Sulfate, Temperature and Time.
Reviewing the Correlation Matrix, it was found that several independent variables had a Pearson Correlation Coefficient greater than 0.3, therefore, they showed signs of being related (HAIR et al., 2009). In an attempt to perform the Regression Analysis again, without these variables, no success was achieved. Then, the characteristic of Multicollinearity of the data was verified.
To solve the data Multicollinearity, it was necessary to apply a Factor Analysis, where the main objective is to gather two or more parameters into a common factor, which represents the analyzed parameters, and is created according to the correlation of the parameters it contains.
Then, it was applied the Orthogonal Factor model to the data, using the Principal Components Method via Varimax Rotation. It was decided to suppress coefficients smaller than 0.5, in order to evaluate only stronger correlations.
The rotating component matrix generated four factors, which were used in Multiple Linear Regression. The regression showed that two of the factors were significant, which were used to develop the model.
In the equation generated from the first model (Regression 1), considering the adjusted R², it was not possible to obtain a good representation of the independent variables by their coefficients. It was then decided to run the regression analysis again, this time for each of the two generated factors (Regression 2 and 3), with their corresponding independent variables, in order to obtain coefficients with a higher percentage of explanation for the relationship of the independent variables with the dependent variable. Thus, the generated equation was the sum of the three regression analyzes performed.
Gravimetric characterization of waste received at the landfill
The gravimetric characterization of the waste from the CRVR São Leopoldo landfill was carried out and is shown in Figure 3.
Leachate monitoring
Quarterly raw leachate monitoring data, made available by CRVR, dated from October/2014 to September/2018, were analyzed.
Figures 4 and 5 show the charts for some parameters that were monitored in the period from Oct/2014 to Sept/2018, for CRVR's raw leachate.
In the literature, it is commonly mentioned that the characteristics of the leachate are variable throughout the life of a landfill, and that its age actively influences its composition. Figure 4 shows the behavior of the BOD and COD curves, during the monitoring from Oct/14 to Sept/18, as well as the BOD/COD ratio of the leachate. In this study, the BOD values were between 620 and 3,160 mg.L-1, and the COD values in the range of 3,053 to 9,085 mg.L-1, the value for the BOD/COD ratio was between 0.069 and 0.644, and the average was 0.316 .
Lange and Amaral (2009), present BOD values in the range of 115 to 7,830 mg.L-1, while the COD is between 1,319 and 9,777 mg.L-1, for leachate from São Leopoldo city . Gomes and Caetano (2010) verified values in the range of 152 to 5,700 mg.L-1 of COD, for the T1 landfill, in the city of Presidente Lucena. In the study by Naveen et al. (2017), the authors presented BOD/COD ratio values between 0.1 and 0.5 for a medium-age landfill - between 5 and 10 years; while Abreu and Vilar (2017) observed the ratio in the range of 0.14 – 0.22; considering waste with a high degree of degradation. Barlaz et al. (2010) verified the mean value of 0.45 (± 0.28) of the BOD/COD ratio, showing the influence of the new waste on these values.
Authors such as Abreu and Vilar (2017); Barlaz et al. (2010), Kjeldsen et al. (2002) and Naveen et al. (2017), among others, comment that the longer the waste grounding time, the lower the BOD/COD ratio, considering values above 0.5 for new waste landfills, with great potential for degradation, and in the range of 0.1 to 0.5 for landfills already in the stable methanogenesis stage, with less degradation potential. Considering this, it was observed that the landfill under study had an average age (7 years, in 2018 – average BOD/COD ratio = 0.316) and was at the beginning of the stable methanogenic phase. (KJELDSEN et al., 2002).
The pH values for this study (Figure 5), remained between 7.3 and 8.65, the leachate also showed high alkalinity (6,779 and 16,690 mg.L-1 CaCO3), confirming the characteristic of the stable methanogenic phase, found by the relation BOD/DQO, previously, as presented by Alcântara (2007) and Kjeldsen et al. (2002).
In the literature, Naveen et al. (2017) also presented a value above neutrality (pH of 7.5) and highly alkaline leachate (11,000 mg.L-1 CaCO3), for a middle-aged landfill, similar to this study. Gomes and Caetano (2010) verified pH values in the range of 6.1 to 7.4 but did not monitor alkalinity for the small-sized T1 landfill. Fei, Zekkos and Raskin (2014), observed pH values around 6.0 for both reactors studied in their research, and alkalinity of 2,000 and 3,000 mg.L-1 CaCO3 for reactors 1 and 2, respectively, reporting that the initial phase of acidification of the leachate did not occur, passing directly to the initial methanogenic phase. Lange and Amaral (2009) reported pH values in the range of 7.0 to 9.0; and alkalinity in the range of 589 to 13,048 mg.L-1 CaCO3 for leachate from São Leopoldo city.
Assessing the secondary data, monitored by CRVR/SL, in comparison with the literature studied, it is possible to verify the characteristic of a leachate that is already in the beginning of its stabilization, characterized by the initial methanogenic phase, with high pH and alkalinity values corroborating the BOD/COD ratio found in this study.
For metal monitoring data (Figure 5), more accentuated values are noted for Iron, Zinc, Manganese, Total Chromium and Lead. Naveen et al.(2017), Gomes and Caetano (2010) and Barlaz et al.(2010) also monitored metals in their leachate samples, evaluating Cd, Pb, Cu, Cr, Fe, Hg, Ni and Zn, for example. Souto (2007) presented the range of values for metals, and other parameters, found in Brazilian leachate. Naveen et al. (2017) commented that heavy metals found in landfill leachate are major pollutants and toxic to the environment and human health. The parameters presented in the charts, and discussed below, can be seen in Table 1, in maximum and minimum values, compared to the literature mentioned.
Table 1. CRVR raw leachate monitoring compared to the studied literature
As commented by Lange and Amaral (2009), the characteristics of the waste directly influence the composition of the leachate. The authors also mention that the leachate's polluting potential is inversely proportional to the waste landfill time, despite having found that in landfills in operation this characteristic is not so evident.
Application of existing mathematical models (Gomes and Caetano, 2010)
After analyzing the leachate monitoring data from the CRVR/SL landfill, it was possible to apply them to the mathematical model developed by Gomes and Caetano (2010). The model has the variables: Time (days), Total Phosphorus (mg.L-1), Leachate Recirculation (L), Total Nitrogen/Total Phosphorus (mg.L-1) and pH. Exactly these parameters were applied, considering that the leachate recirculation is not monitored by CRVR, therefore, this parameter was considered as zero on all dates. The nitrogen and phosphorus parameters were monitored only on four dates, throughout the analyzed period, as a result, to apply the model, only the dates that had monitoring of all parameters were considered.
To compare the settlements with the model, only the SL 12 was used, as it had settlement monitoring for every day of leachate analysis. In a few months, the leachate collection was not carried out on the same date as the settlement monitoring, therefore, data with an approximate date were selected.
Equation 1 presents the model developed by Gomes and Caetano (2010), which was applied with available data, from CRVR/SL.
S = -0.1359486 + 0.0002756A + 0.0000310B + 0.0173660C + 0.0005716D+ 0.0220027E
Eq. (1)
Where: S = Settlement; A = time (days); B = Phosphorus (mg.L-1); C = Leachate Recirculation; D = total nitrogen (mg.L-1)/Phosphorus (mg.L-1); E = pH.
Table 2 presents the results of applying the Gomes and Caetano (2010) model.
Table 2. Application of the model of Gomes and Caetano (2010)
The application of the Gomes and Caetano (2010) model showed average adherence to the superficial landmark, with a relative error in the range of 3.3% to 60.2%. Some parameters used in the model were not monitored in the landfill on some dates (nitrogen and phosphorus, leachate recirculation), and were not applied to the model in these situations, one of the likely reasons for the error percentages may be the low amount of data, considering that the more data, the greater the analysis confidence of the model.
It is also considered that the Gomes and Caetano (2010) model may not be exactly suitable for the study of settlements in another landfill, as it has already been proven by the authors themselves in the application of data from another landfill with similar characteristics. In the situation pointed out in the authors' study, the error in applying the model to another landfill was 356%.
Therefore, it is considered that each situation must be analyzed separately, given the fact that even landfills with similar characteristics, but which are in different regions, may have different settlement behavior depending on the climate of the region and differences in the operation of the landfill. Therefore, it is necessary to develop a specific model for each landfill, reducing the probability of errors in the prediction model in relation to the actual settlement.
Monitoring of settlements
The monitoring of CRVR settlements, of the installed superficial landmarks, took place from October 2014. For this study, monitoring data from the Superficial Landmark number 11, 12, 15, 16, 20, 21, 23, 24, 25 were used, as shown in the methodology, in Figure 1.
So far, all the completed phases of the landfill have had surface landmarks installed. For this study, the milestones of phases 1, 2, 3 and 4 were monitored, which began with the disposal of waste in 2011 and ended in 2015.
Figure 6 shows the settlements that have taken place since the installation of the studied landmarks.
It is possible to verify that the superficial landmark where the highest settlement occurred was No. 11, installed in Phase 1, with a total monitoring of 1134 days, presenting 2.32 m of total settlement, at an average deformation rate of 3.5 mm/day, in the first six months; followed by SL 15, installed in Phase 2, with a total settlement of 0.81 m, in 1001 days, considering that the strain rate was higher after 800 days, with an average of 2.1 mm/day. The other landmarks ranged from 0.02 m to 0.58 m of vertical settlement, with a displacement rate in the range of 0.2 to 0.8 mm/day.
Development of the mathematical model for prediction of settlements
Correlation
As mentioned in the methodology and verified in tests, it was not possible to run the statistical analysis with all the leachate parameters that were analyzed in the previous subchapters, as there were several variables that had zero or missing values and this negatively influences a statistical analysis, since the greater the number of complete observations for each variable, the more reliable the analysis.
It was then decided to run the analysis only with the independent variables that had all the observations. The following were chosen: Time, Total Alkalinity, Chlorides, Conductivity, Total Chromium, BOD, COD, BOD/COD Ratio, Nickel, Dissolved Oxygen, pH, Sulfate, Temperature. The dependent variable was Settlement.
Significant correlations were observed at the 0.01 level and others at the 0.05 level. Variables with a significance level of 0.01 have a correlation coefficient above 0.355, positive or negative (which directly or indirectly influence the relationship of two variables). Variables with a significance level of 0.05 have a weaker correlation, up to 0.355.
Assessing the correlation of the data, it was noticed a strong correlation between some variables, for example: Chloride and total alkalinity; COD and chlorides; BOD and BOD/DQO ratio; among others, presented in Table 1, in summary.
Exemplifying these correlations, with coefficients above 0.3, according to Hair et al. (2009), the use of factor analysis was justified in order to proceed with multiple linear regression. Otherwise, some variables could have "masked" the result, not showing the real significance of each parameter, which is a characteristic of the multicollinearity of the data, where three or more independent variables are correlated with each other, and this correlation can interfere in the construction of the model, which is the case of this study, where several variables had moderate (0.3 - 0.7) to strong (0.7 - 1.0) correlation between them, causing a "confusion" in the interpretation of data by the statistics software, as observed in the development of the study.
In the same way as in this study, Miloca and Conejo (2009), after verifying the multicollinearity of the variables, through the correlation matrix, applied the orthogonal factor model to the data using the principal components method via Varimax Rotation, in the factor analysis performed and then adjusted a multiple linear regression model. The Varimax type method is a criterion that maximizes the values presented in the factorial matrix, being considered the least variable method and the most successful in the analytical approach of a factor analysis. For this reason, it was the chosen method, aiming to obtain the best possible treatment of the data in the statistical analysis.
In Table 3 it is possible to verify only the correlations with a significance level of 0.01, considering moderate correlation values (0.3 - 0.7), in light color, to strong (0.7 - 1.0), in dark color .
Table 3 Summary of the highest-level correlations
It is possible to see in Table 3 that there are more moderate correlations (0.3 – 0.7) than strong (0.7 – 1.0). Even so, there are correlations between several parameters, which indicates the phenomenon of multicollinearity, where more than three variables are correlated. For example, total Chromium has a strong correlation with time, nickel and pH, in the range of 0.701 to 0.779; which can be considered a problem in linear regression. Among other parameters, total alkalinity, for example, is related to eight other parameters (Chlorides, Conductivity, Total Chromium, Nickel, Dissolved Oxygen, pH, Time and COD), one of which has a strong correlation (chlorides) and the others of moderate correlation. These and other correlations show multicollinearity, which indicates the need to use the factor analysis method.
Factor Analysis
For the factor analysis, the method of principal components by Varimax rotation was applied. Table 4 presents the commonalities of the factor analysis, which are the amounts of correlations for each variable, explained by the factors. This analysis considers the commonalities after the extraction, which vary between 0 and 1. When the common factors explain little or no variance in the variable, the value is closer to zero; when common factors explain all or most of the variance, the value is closer to one, which is the expected result when using factors to explain the mathematical model.
Table 4 Factor analysis commonalities
Analyzing Table 4, it can be seen that the variables BOD, Sulfate, Total Chromium, BOD/COD, COD, Chlorides and total alkalinity, Nickel and pH are the variables that most explain the total variance, as they have a strong correlation with the retained factors . The other variables have a moderate correlation, but still explain a part of the total variance.
Table 5 shows the total explained variance which, based on the Kaiser criterion, chooses the number of factors to be retained, depending on the number of eigenvalues above 1. It is interesting to know the percentage of retained factors that can explain the variance of the data in the original form.
Table 5. Total explained variance - factor analysis
In Table 5, the components presented in the first column represent the groups of variables that were created in the factor analysis. In the “Total” column of the rotating sums of squared loads, it is verified that four factors with eigenvalues greater than one were retained, and that these are able to explain 79.665% of the variance of the original data, as shown in the column of the cumulative percentage.
In Table 6, it is possible to verify the rotating component matrix, which presents the load of each parameter of the leachate in relation to each created factor (components). When generating the matrix, it was opted to suppress values smaller than 0.5, due to the prioritization of factors with a higher load.
Table 6 Rotating component matrix - factor analysis
Then, the relationship of components is verified as follows: Component 1 – COD, Chlorides, Total Alkalinity, Conductivity, Dissolved Oxygen and Nickel; Component 2 – Total alkalinity, total chromium, pH and time; Component 3 – BOD and BOD/COD Ratio; Component 4 – Sulfate and temperature.
As a conclusion of the factor analysis, it can be said that the first component is measuring the more general parameters of the leachate quality, and as seen in the correlation matrix, the strongest correlation levels are between: COD – chlorides; total alkalinity – chlorides; conductivity – chlorides; and nickel - chlorides; nickel – dissolved oxygen (inversely proportional). It is observed that most parameters are more strongly related to the variable chlorides, which confirms the multicollinearity of the data, since more than three independent variables are related to each other, according to Hair et al. (2009).
In the second component, the parameters with higher levels of correlation are: Total alkalinity – Total chromium; Total chromium – time; pH – time, being more related to the degradability of the leachate and, indirectly, the pH influences the precipitation of toxic chemical elements, such as heavy metals (Ex: chromium). (OLIVEIRA; CUNHA, 2014).
In the third component there are only two variables, which are BOD and BOD/DQO ratio, which have a strong correlation, justifying the occurrence of biodegradability, previously presented in the leachate graphs and confirmed by authors such as Abreu; Vilar (2017), Naveen et al. (2017), Barlaz et al. (2010) and Kjeldsen et al. (2002).
And in the fourth and last component, the variables are Sulfate and temperature. These being influenced by each other inversely, that is, when the temperature increases, the sulfate variable decreases, and vice versa. This relationship can be explained by the fact that temperature influences the solubility of sulfate ions, as reported by Brady; Russell; Holum (2000) and Aucélio; Teixeira (2010).
Multiple linear regression
After the factor analysis, it was possible to perform the Multiple Linear Regression with the four components that were created. Regression was performed using the “insert” method, and considered Settlement as a dependent variable, and the four components, with the respective leachate parameters mentioned above, were the independent variables.
Table 7 shows the model summary, where R (or multiple R) corresponds to the correlation coefficient between Settlement and the independent variables (four components); the R² corresponds to the predictive power of the model; and adjusted R² is a modified measure of R², which considers the number of independent variables included in the regression equation and the sample size. The standard error of the estimation is a measure of the variation in predicted values and is similar to the standard deviation of a variable around its mean. (HAIR et al., 2009; RAUPP, 2013).
Table 7. Summary of Multiple Linear Regression model (Regression 1)
Analyzing Table 7, using the concepts of Raupp (2013), it appears that the multiple R presented (0.778) indicates that there is a direct and strong correlation between Settlement and the selected independent variables. The R², coefficient of determination or explanation, which informs the power of the predictive model, shows that 60.6% of Settlement is explained by the regression model. The adjusted R², undergoing an adjustment as a function of the number of independent variables that were placed in the model, shows that 57.0% of the settlement is explained by the model.
Table 8 presents the Analysis of Variance (ANOVA) of the regression model.
Table 8. ANOVA of the regression model (Regression 1)
The ANOVA method, shown in Table 8, is used to test the significance of the adjusted model. As the p-value presented in the significance column is below 0.05, it can be said that the adjusted model of this study is significant at the 5% level, which indicates that Settlement can be significantly explained from the set of independent variables used, according to concepts studied by Raupp (2013).
Table 9 presents the model coefficients, considering the significance of each variable.
Table 9. Model coefficients (Regression 1)
In Table 9, of model coefficients, it is observed that only the constant and components 2 and 3 are significant, therefore, they are part of the model equation. In the column identified by B, in the non-standardized coefficients, the coefficients for writing the regression equation are presented.
With the equation generated by the first regression model, the standard error of the model was considered high for this study, although this model approximates 60.6% of the real data, according to R², further analyzes were performed to propose a prediction more accurate. Then, the attempt to perform the linear regression of each significant component generated in the factor analysis was considered, aiming to obtain coefficients closer to the reality of the independent variables and, thus, adding them to the first equation. It was decided to carry out the new regression only with the components that were significant in the first attempt, component 2 and 3. These regressions serve to explain the composition of the components based on their variables.
In the linear regression performed for Component 2, the component itself was the dependent variable, and the parameters that made it up were the independent variables (total alkalinity, total chromium, pH, time). The value of R² showed that 95.2% of the Settlement was explained by the Component 2 regression model. The ANOVA showed that the adjusted model is significant at the 5% level, which indicates that it can significantly explain the settlement from the set of independent variables used in Component 2. The coefficients state that all the variables contained in Component 2 are significant, at the 5% level of significance, therefore, all of them must be used in the model equation, with the coefficients found.
In the linear regression performed for Component 3, the component itself was the dependent variable, and the parameters that made it up were the independent variables (BOD and BOD/COD ratio). The value of R² showed that 92.6% of the Settlement was explained by the Component 3 regression model. The ANOVA showed that the adjusted model is significant at the 5% level, which indicates that it can significantly explain the settlement from the set of independent variables used in Component 3. The coefficients state that all the variables in Component 3 are significant, at the 5% level of significance, therefore, all of them must be used in the model equation, with the coefficients found.
Mathematical model
According to the coefficients found, the model equation was written, based on the regression analysis performed for all components and with components 2 and 3 (Equation 2). In detailing the equation, the parameters that make up each component are presented (Equation 3).
As can be seen in Eq. 3, the components were replaced by the variables that represent them, and each variable was multiplied by the coefficient corresponding to the regression performed with the components.
After writing the equation, the parameter values were applied to its variables and the similarity to the model was verified. An average error of 20% (range 0.3% - 54.9%) of the actual settlement compared to the developed model was verified.
The errors can be attributed to several factors, but the main ones that can be mentioned are the replication of the variables (necessary to obtain a larger number of observations), and the choice only of the variables that had all the complete data, in the analyzed period, to develop the statistical analysis. It would have been more interesting, if possible, to carry out the analysis with all, or almost all, of the leachate parameters that CRVR monitors, but due to the large number of gaps in monitoring, these variables only served as an obstacle to model generation, because this, were removed from the analysis.
Analyzing this study, it was observed that the general model, generated in the first regression, explained only 60.6% of the occurrence of repression. And after the regression analysis for components 2 and 3, the most significant of the sum of these results to generate the model equation, and its application, it was verified 80% of average adherence of the developed model, compared to the real data of settlements, measured by CRVR.
The estimation of settlements in landfills, through mathematical models, has already proved to be complex in several studies carried out, due to the heterogeneity of the MSW, factors that influence the operation characteristics, climate, and particularities of each area, in addition to the measurement of data that varies in each area studied.
In this study, it was possible to verify that the application of the model by Gomes and Caetano (2010) showed good adherence to real settlement data, with an average error of 27.9%, but with a coefficient of variation of 49.5%. This model considered data from physical-chemical monitoring of the leachate, where CRVR data were applied, and this type of model can demonstrate the issue of biodegradability of MSW, as analyzed.
The model generated through the multiple linear regression statistical analysis in this study proved to be 80% adequate, on average, for the CRVR landfill, considering the leachate parameters included in the analysis. The model generation through a statistical analysis was useful for the prediction of settlements that cannot be estimated in the field before its occurrence and consequent monitoring in the field.
The use of settlement prediction models is suitable for estimating the useful life of landfills, provided that some adjustments in data monitoring are considered, considering the possibility of biweekly or monthly monitoring for all parameters, as it was evidenced a large part of the percentage of errors due to lack of data.
It is interesting to note that there is no single mathematical model for all landfills, as each one has intrinsic characteristics that cannot simply be replicated to another area, without proper studies.
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. (Data sheets and statistical calculations developed from data provided by CRVR).
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Denardin, G. P. (2013). Estudo dos recalques do aterro sanitário da Central de Resíduos do Recreio – Minas do Leão/RS [Study of settlement at the Recreio Waste Center sanitary landfill – Minas do Leão/RS]. [In Portuguese]. Santa Maria: Universidade Federal de Santa Maria (UFSM).
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Gomes, L. P.; Caetano, M. O. (2010). “Municipal Solid Waste Sanitary Landfill Compressibility Study with Linear Regression Application Study with Linear Regression Application”. Soils and Rocks, 33 (3), 145–157.
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Kjeldsen, P.; Barlaz, M. A.; Rooker, A. P.; Baun, A.; Ledin, A.; Christensen, T. H. (2002). “Present and Long-Term Composition of MSW Landfill Leachate: A Review”. Critical Reviews in Environmental Science and Technology, 32 (4), 297–336. https://doi.org/10.1080/10643380290813462
Lange, L. C.; Amaral, M. C. S. (2009). Geração e Características do Lixiviado. In: GOMES, L. P. (Coord.). Resíduos Sólidos: Estudos de Caracterização e Tratabilidade de Lixiviados de Aterros Sanitários para as Condições Brasileiras. [Solid Waste: Characterization and Treatability Studies of Landfill Leachate for Brazilian Conditions]. [In Portiguese]. Rio de Janeiro: ABES (Associação Brasileira de Engenharia Sanitária e Ambiental), 26–59.
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Souto, G. D. B.; Povinelli, J. (2007). “Características do Lixiviado de Aterros Sanitários no Brasil”. In Proc., 24th Congresso Brasileiro de Engenharia Sanitária e Ambiental. Belo Horizonte: ABES.
Table 1. CRVR raw leachate monitoring compared to the studied literature
Subtitles: a L3 landfill values, b T1 landfill values; c G Landfill (original cell); d Standard deviation
|
Parameter |
Unit |
Present study |
Naveen et al. (2017)a |
Gomes and Caetano (2010)b |
Barlaz et al. (2010)c |
Souto and Povinelli (2007) |
||||
|
Minimum value |
Maximum value |
Minimum value |
Maximum value |
Minimum value |
Maximum value |
Minimum value |
Maximum value |
|||
|
Landfill type, location |
Large landfill , São Leopoldo – RS, Brazil (7 years) |
Large landfill (L3), Mavallipura, Bangalore, India (23 years) |
Small landfill (T1), Presidente Lucena – RS, Brazil (2 years) |
Large Landfill (G) Pennsylvania, USA (10 years) |
Variation in the composition of leachate generated in Brazilian landfills |
|||||
|
Total Alkalinity |
mg.L-1 CaCO3 |
6,78 |
16,69 |
11,000 |
- |
- |
- |
- |
750 |
11,400 |
|
pH |
- |
7.30 |
8.65 |
7.50 |
6.10 |
7.40 |
5.60 |
8.10 |
5.70 |
8.60 |
|
BDO |
mgO2/L |
620 |
3.16 |
3,000 |
- |
- |
- |
- |
<20 |
30,000 |
|
COD |
mgO2/L |
4.02 |
9.09 |
10,800 |
152 |
5,700 |
- |
- |
190 |
80,000 |
|
BOD/COD |
- |
0.15 |
0.35 |
0.28 |
- |
- |
0.5 (0.28)d |
- |
- |
|
|
Aluminum |
mg.L-1 |
0.38 |
1.84 |
- |
- |
- |
- |
- |
- |
- |
|
Arsenic |
mg.L-1 |
0.01 |
0.04 |
- |
- |
- |
- |
- |
- |
- |
|
Barium |
mg.L-1 |
0.08 |
0.19 |
- |
- |
- |
- |
- |
- |
- |
|
Boron |
mg.L-1 |
1.68 |
2.52 |
- |
- |
- |
- |
- |
- |
- |
|
Cadmium |
mg.L-1 |
0 |
0.07 |
0.02 |
0 |
0.9 |
- |
- |
0 |
0.03 |
|
Lead |
mg.L-1 |
0 |
0.10 |
0.22 |
0.1 |
0.9 |
0 |
0.01 |
0.01 |
2.8 |
|
Copper |
mg.L-1 |
0.01 |
0.05 |
0.00 |
- |
- |
0 |
0.21 |
0.01 |
0.6 |
|
Total Chromium |
mg.L-1 |
0.28 |
1.40 |
0.01 |
0.1 |
0.4 |
0.02 |
0.42 |
0 |
0.8 |
|
Iron |
mg.L-1 |
2.45 |
17.80 |
11.25 |
32.1 |
78.9 |
- |
- |
0.01 |
260 |
|
Manganese |
mg.L-1 |
0.12 |
1.55 |
- |
- |
- |
- |
- |
0.04 |
2.6 |
|
Mercury |
mg.L-1 |
0 |
0 |
- |
- |
- |
0 |
0 |
- |
- |
|
Nickel |
mg.L-1 |
0 |
0.64 |
0.68 |
- |
- |
- |
- |
0.03 |
1.1 |
|
Zinc |
mg.L-1 |
0.67 |
8.03 |
2.40 |
0.1 |
1.9 |
0.05 |
10.6 |
0.01 |
8.0 |
Table 2. Application of the model of Gomes and Caetano (2010)
|
Days (settlement) |
S (Model) |
SL 12 (m) |
Error (m) |
Error % |
|
0 |
- |
- |
- |
- |
|
164 |
0.074 |
0.186 |
0.112 |
60.2% |
|
314 |
0.166 |
0.263 |
0.097 |
37.0% |
|
1312 |
0.528 |
0.546 |
0.018 |
3.3% |
|
1404 |
0.504 |
0.567 |
0.064 |
11.2% |
|
Mean |
0.318 |
0.391 |
0.073 |
27.9% |
|
Standard deviation |
0.232 |
0.195 |
0.036 |
25.9% |
|
Coefficient of variation |
0.730 |
0.498 |
0.495 |
- |
Table 3 Summary of the highest-level correlations
|
|
Time |
Total Alkalinity |
Chlorides |
Conductivity |
Total Chromium |
BOD |
COD |
BOD/COD |
Nickel |
Dissolved oxygen |
pH |
Sulfate |
Temperature |
Settlement |
|
Time |
0.611 |
|
|
0.779 |
|
|
|
|
|
0.440 |
|
|
0.853 |
|
|
Alkalinity |
0.611 |
|
0.836 |
0.370 |
0.690 |
|
0.642 |
|
0.528 |
-0.618 |
0.480 |
|
|
0.574 |
|
Chlorides |
|
0.836 |
|
0.456 |
0.584 |
|
0.831 |
|
0.635 |
-0.564 |
0.369 |
|
|
|
|
Conductivity |
|
0.370 |
0.456 |
|
|
|
0.479 |
|
0,369 |
-0.371 |
|
|
|
|
|
Total Chromium |
0.779 |
0.690 |
0.584 |
|
|
|
|
|
0.701 |
-0.415 |
0.724 |
|
|
0.694 |
|
BOD |
|
|
|
|
|
|
|
0.844 |
|
|
|
|
|
|
|
COD |
|
0.642 |
0.831 |
0.479 |
|
|
|
|
0.594 |
-0.557 |
|
|
|
|
|
BOD/COD |
|
|
|
|
|
0.844 |
|
|
-0.479 |
|
|
|
|
|
|
Nickel |
|
0.528 |
0.635 |
0.369 |
0.701 |
|
0.594 |
-0.479 |
|
|
0.434 |
|
0.472 |
0.375 |
|
Dissolved oxygen |
|
-0.618 |
-0.564 |
-0.371 |
-0.415 |
|
-0.557 |
|
|
|
|
|
|
|
|
pH |
0.440 |
0.480 |
0.369 |
|
0.724 |
|
|
|
0.434 |
|
|
|
0.382 |
0.406 |
|
Sulfate |
|
|
|
|
|
|
|
|
|
|
|
|
-0.412 |
|
|
Temperature |
|
|
|
|
|
|
|
|
0.472 |
|
0.382 |
-0.412 |
|
|
|
Settlement |
0.853 |
0.574 |
|
|
0.694 |
|
|
|
0.375 |
|
0.406 |
|
|
|
Caption:
|
|
Moderated Correlation |
|
Strong correlation |
Table 4 Factor analysis commonalities
|
Variables |
Extraction |
|
BOD (mg.L-1) |
0.939 |
|
Sulfate (mg.L-1) |
0.927 |
|
Total Chromium (mg.L-1) |
0.925 |
|
BOD/COD |
0.913 |
|
COD (mg.L-1) |
0.905 |
|
Chlorides (mg.L-1) |
0.879 |
|
Total alkalinity (mgCaCo3.L-1) |
0.828 |
|
Nickel (mg.L-1) |
0.770 |
|
pH |
0.716 |
|
Time (days) |
0.698 |
|
Temperature (ᵒC) |
0.640 |
|
Dissolved Oxygen (mg.L-1) |
0.637 |
|
Conductivity |
0.581 |
|
Extraction Method: Principal Component Analysis |
|
Table 5 Total explained variance - factor analysis
|
Component |
Initial eigenvalues |
Sums of squared load extraction |
Rotating sums of squared loads |
||||||
|
Total |
% of variance |
% cumulative |
Total |
% of variance |
% cumulative |
Total |
% of variance |
% cumulative |
|
|
1 |
5.125 |
39.423 |
39.423 |
5.125 |
39.423 |
39.423 |
3.599 |
27.682 |
27.682 |
|
2 |
2.170 |
16.695 |
56.118 |
2.170 |
16.695 |
56.118 |
3.027 |
23.286 |
50.968 |
|
3 |
1.749 |
13.456 |
69.574 |
1.749 |
13.456 |
69.574 |
2.241 |
17.237 |
68.205 |
|
4 |
1.312 |
10.091 |
79.665 |
1.312 |
10.091 |
79.665 |
1.490 |
11.460 |
79.665 |
|
5 |
0.971 |
7.467 |
87.132 |
|
|
|
|
|
|
|
6 |
0.602 |
4.633 |
91.764 |
|
|
|
|
|
|
|
7 |
0.426 |
3.273 |
95.037 |
|
|
|
|
|
|
|
8 |
0312 |
2.403 |
97.440 |
|
|
|
|
|
|
|
9 |
0.154 |
1.182 |
98.622 |
|
|
|
|
|
|
|
10 |
0.119 |
0.915 |
99.537 |
|
|
|
|
|
|
|
11 |
0.056 |
0.430 |
99.967 |
|
|
|
|
|
|
|
12 |
0.004 |
0.030 |
99.997 |
|
|
|
|
|
|
|
13 |
0.000 |
0.003 |
100.000 |
|
|
|
|
|
|
|
Extraction Method: Principal Component Analysis |
|||||||||
Table 6. Rotating component matrix - factor analysis
|
|
Components |
|||
|
1 |
2 |
3 |
4 |
|
|
COD (mg.L-1) |
0.944 |
|
|
|
|
Chlorides (mg.L-1) |
0.871 |
|
|
|
|
Total alkalinity (mgCaCo3.L-1) |
0.668 |
0.592 |
|
|
|
Conductivity |
0.666 |
|
|
|
|
Dissolved oxygen (mg.L-1) |
-0.657 |
|
|
|
|
Nickel (mg.L-1) |
0.583 |
|
|
|
|
Total Chromium (mg.L-1) |
|
0.900 |
|
|
|
pH |
|
0.829 |
|
|
|
Time (days) |
|
0.814 |
|
|
|
BOD (mg.L-1) |
|
|
-0.934 |
|
|
BOD/COD |
|
|
-0.912 |
|
|
Sulfate (mg.L-1) |
|
|
|
0.933 |
|
Temperature (ᵒC) |
|
|
|
-0.642 |
|
Extraction Method: Principal Component Analysis Rotation Method: Varimax with Kaiser Normalization a |
||||
|
a. Rotation converged in 6 iterations |
||||
Table 7. Summary of Multiple Linear Regression model (Regression 1)
|
Model |
R |
R2 |
Adjusted R2 |
Standard error of estimation |
|
1 |
0.778a |
0.606 |
0.570 |
0.089396 |
|
a. Predictors: (Constant), REGR component 4, REGR component 3, REGR component 2, REG component 1 |
||||
Table 8. ANOVA of the regression model (Regression 1)
|
Model |
Sum of Squares |
Degrees of freedom |
Medium square |
Test statistics |
Sig. |
|
|
Regression |
0.540 |
4 |
0.135 |
16.901 |
0.000b |
|
|
Residue |
0.352 |
44 |
0.008 |
|
|
|
|
Total |
0.892 |
48 |
|
|
|
|
|
a. Dependent variable: Settlement |
|
|||||
|
b. Predictors: (Constant), REGR component 4, REGR component 3, REGR component 2, REG component 1 |
|
|||||
Table 9. Model coefficients (Regression 1)
|
Model |
Non-standardized coefficients |
Standardized coefficients |
t |
Sig. |
||
|
B |
Standard Error |
Beta |
||||
|
1 |
(Constant) |
0.334 |
0.013 |
|
26.182 |
0.000 |
|
REGR component 1 |
0.003 |
0.013 |
0.019 |
0.201 |
0.842 |
|
|
REGR component 2 |
0.099 |
0.013 |
0.729 |
7.697 |
0.000 |
|
|
REGR component 3 |
0.037 |
0.013 |
0.273 |
2.883 |
0.006 |
|
|
REGR component 4 |
0.001 |
0.013 |
0.009 |
0.095 |
0.925 |
|
|
a. Dependent variable: Settlement |
||||||
No competing interests reported.