# Assessment of the Landfill Barrier System through Numerical Analysis: Rehabilitation and Expansion of Belgrade Landfill Case Study

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## Abstract

**:**

## 1. Introduction

#### 1.1. Vinča Landfill Rehabilitation and Expansion Plans

#### 1.2. Geotechnical Aspects of the New Vinča Landfill Project

## 2. Geological and Geotechnical Conditions on the Site

#### 2.1. Natural Soil Description

#### 2.2. Hydrogeological Conditions at the Site

## 3. Numerical Calculation Assumptions

_{inter}on the results was also studied. The composite liner was approximated by a geogrid type of finite element representing the geomembrane in the models. The reduction factor R

_{inter}reduces the shear strength parameters of the linear elastic—perfectly plastic material model of the contact element. If relative movement occurs between the soil and geosynthetic layer (or between two geosynthetic layers), the shear strength in the soil–geosynthetic (geosynthetic–geosynthetic) interface is mobilized. In the cases of geomembranes and geotextiles, the interaction mechanism mobilized on the interface is the skin friction. When the shear strength of the interface is exceeded, the failure occurs by direct shear. The effective strength parameters of the interface elements (c

_{i}, tan φ

_{i}) are given by Equations (1) and (2), where c

_{i}and tan φ

_{soil}are the effective strength parameters of the soil surrounding the interface element. The same principle is applied when the soil strength is defined by the undrained shear strength s

_{u,soil}(Equation (3)).

_{inter}factor also influences the interface stiffness, and consequently, the displacements parallel to the interface (u

_{t}) and perpendicular to the interface (u

_{n}):

_{n}are the current shear and normal stress, respectively; G

_{i}is the shear modulus of the interface; E

_{oed,i}is the one-dimensional compression modulus of the interface; t

_{i}is the virtual thickness of the interface; and ν

_{i}is the Poisson ratio of the interface.

#### 3.1. Material Models Used in Simulation

- The linear elastic—perfectly plastic Mohr–Coulomb MC model (MC);
- The Hardening Soil Model (HS)—an elastoplastic model with shear and volumetric hardening [68].

_{50}is the secant stiffness in the standard drained triaxial test, E

_{ur}is the unloading/reloading stiffness, and E

_{oed}is the tangent stiffness for the primary oedometer loading. All stiffness modules are stress-dependent; thus, their values for the reference stress level p

_{ref}present inputs for the material model.

_{oed}is important in the displacement analysis of large embankments, and therefore, the adopted stress–stiffness formulation is stated below. The friction angle $\mathsf{\phi}$ and cohesion c are the shear strength parameters, m is the power for the stress-level dependence of stiffness, and K

_{0}

^{nc}is the K

_{0}value for normal consolidation (K

_{0}

^{nc}= 1 – $\mathrm{sin}\mathsf{\phi}$):

_{n}is the nodal excess pore pressure vector, f

_{n}is the incremental load vector, and q

_{n}is the vector due to the prescribed flow at the boundary.

_{1}= 309 kN/m and the characteristic tensile strength N

_{p,1k}= 34 kN/m were determined according to [72]. The characteristic value was decreased by a reduction coefficient R

_{FCR}= 1.5, which considers the creep behavior of the material. The design value of the tensile strength after this adjustment is N

_{p,1d}= 22.6 kN/m.

#### 3.2. Input Values of Soil and Waste Material Parameters

^{3}were considered in the present case according to the relationship based on the critical review of published field research data [76]. It is possible to find the results of shear box tests [6] in the literature aimed at determining the shear parameters of waste [6], e.g., [79,80]. Although MSW is an inherently variable substance, the published values of the shear strength parameters appear to be relatively consistent. Values between 0 to 30 kN/m

^{2}for cohesion and the range of 20 to 35 degrees for a friction angle can be considered reasonable for design purposes according to [6]. The values of effective strength parameters of the MSW determined according to the results of the undrained full-scale shear test published in [81] were considered in the presented analysis and are summarized in Table 4. Determining the filtration coefficient of MSW also poses a major challenge, as it is largely dependent on pore structure, which is directly affected by compression stress and degradation [82,83,84,85]. Based on the published results of an extensive review of the characteristics of landfilled MSW in several countries [86], the values of the permeability coefficient range from k = 3.5 × 10

^{−4}to 5.0 × 10

^{−10}m/s, which is also consistent with the results of other researchers [87,88]. The value of the permeability coefficient k = 1.0 × 10

^{−5}m/s was considered in the presented analyses, which is in accordance with the above referenced studies. In addition to MSW, the disposal of flue gas residues, namely, solidified fly ash (FGT), is also planned in an area of the newly constructed landfill. The mechanical and hydraulic parameters of solidified fly ash FGT used in the presented paper were taken from [89]. The values of strength, hydraulic and index parameters of materials used in analyses are summarized in Table 4.

## 4. Results

_{inter}= 0.5 caused the shear strength of that interface to be reached in the section between 170 and 250 m from the start of the model. This was reflected in the occurrence of unrealistic axial force oscillations during the consolidation stage (Figure 8).

_{tot}= 4.52 m in the case of the model of longitudinal section A–A′ and u

_{tot}= 2.73 m in the case of the cross-sectional model B–B′ were calculated at the time after the minimum excess pore pressure 1 kPa was reached.

## 5. Discussion

_{p,1d}= 22.6 kN/m of the geomembrane planned to be incorporated into the composite liner. A significant increase in the axial force can be observed where the liner transitions from the area of the current landfill to the area of the extended landfill (see, e.g., the section between 175 and 250 m from the start in the mathematical model B–B′ in Figure 8). In other words, the peak values in the axial force are observed in the sections where the subsurface properties change abruptly. The increases in axial forces in the geomembrane are also due to non-uniform layering of MSW given by the filling plan prescribed by the landfill operator.

_{inter}on the results was also evaluated. Without the strength reduction (R

_{inter}= 1.0), the maximum axial force 7.2 kN/m was calculated in the model of longitudinal section A–A′. Reducing the shear strength of the geomembrane-soil interface caused the shear strength to be reached in the section between 170 and 250 m in the mathematical model of cross-section A–A′. This was reflected in the occurrence of unrealistic axial force oscillations during the consolidation stage of calculation. The actual R

_{inter}value selection considers the weakest interface in the geomembrane–geotextile–drainage layer system. From these three interfaces, the geomembrane–geotextile contact is usually the weakest one. As the final choice of the composition of the sealing layer was not made in the initial phase of the project, it was not possible to perform an analysis with a particular value of R

_{inter}. Since the value of R

_{inter}affects the stresses induced in the geomembrane, further research regarding the modeling of this detail is still required.

_{tot}= 2.7 m to u

_{tot}= 4.5 m in the cross-sections presented). Most studies are concerned with the settlement of the MSW layer itself, but not with the settlement of a subgrade. As the results of the analyses conducted show, subgrade settlement can be a non-negligible component of total settlement. The settlement of only subgrade u

_{y}= 3.75 m in the case of longitudinal section A–A′ represents 83% of the total settlement u

_{tot}= 4.52 m, including the settlement of a 47 m thick MSW layer. This value is dependent on the constitutive model used for the description of the MSW behavior within the analysis. If the settlement of the MSW layer to the order of 25% to 50% of the initial thickness was theoretically considered, as reported by the results of referenced studies [49,50,51,52,53], the settlement of the originally 47 m thick layer would be u

_{MSW}= 11.75 m or u

_{MSW}= 23.5 m, respectively. Still, the total settlement of subgrade u

_{y}= 3.75 m would represent 32% of theoretical total settlement or 16%, respectively. Moreover, the settlement distribution is highly non-uniform along the cross-sections, due to the non-evenly deposited MSW layers.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**An engineering geological map of the quaternary deposits with indications of the main geotechnical types of soil and with the position of the analyzed cross-section B–B′ and longitudinal section A–A′.

**Figure 3.**Mathematical models with material description and FEM mesh: (

**a**) model of longitudinal section A–A′; (

**b**) model of cross-section B–B′.

**Figure 6.**Calibrated and measured dependence between effective stress σ

_{1}′ and ${\mathrm{E}}_{\mathrm{oed}}^{\mathrm{ref}}$ for soils PRGd (

**left**), Gj (

**middle**), GLj (

**right**).

**Figure 7.**Distribution of axial forces along the longitudinal section A–A′ for the individual phase of calculation—full contact in the geomembrane and adjacent layer (R

_{inter}= 1.0).

**Figure 8.**Distribution of axial forces along the longitudinal section A–A′ for the individual phase of calculation—reduced contact in the geomembrane and adjacent layer (R

_{inter}= 0.5).

**Figure 9.**Distribution of settlement of the new landfill subgrade along the longitudinal section A–A′.

**Figure 10.**Distribution of axial forces along the cross-section B–B′ for the individual phase of calculation.

FE Model | Model Width [m] | Model Height [m] | Number of Finite Elements [-] | Number of Nodes [-] |
---|---|---|---|---|

Longitudinal section A–A′ | 1580 | 258 | 5081 | 41,143 |

Cross Section B–B′ | 920 | 202 | 3081 | 24,987 |

No. | Description | Type of Calculation |
---|---|---|

01 | Calculation of the original stress state before the current landfill began operation. | Gravity loading |

02 | Loading of the original valley by the weight of the waste deposited up to the moment before the landfill reconstruction. | Plastic |

03 | Ground zone of new landfill modification. | Plastic |

04 | Activation of geogrid finite elements simulating the installation of the liner system | Plastic |

05 | “Waste 2. ETA”—waste storage in the new landfill between the 2nd and 4th year of operation | Consolidation 2 years |

06 | “Waste 4 ETA”—waste storage in the new landfill between the 6th and 9th year of operation | Consolidation 3 years |

07 | “Waste 5. ETA”—waste storage in the new landfill between the 9th and 14th year of operation | Consolidation 5 years |

08 | “Waste 7. ETA”—waste storage in the new landfill between the 18th and 19th year of operation | Consolidation 1 year |

09 | “Waste 8. ETA”—waste storage in the new landfill between the 19th and 23rd year of operation | Consolidation 4 years |

10 | “Waste 9. ETA”—waste storage in the new landfill between the 23rd and 26th year of operation | Consolidation 3 years |

11 | “Waste 9. ETA”—waste storage in the new landfill between the 26th and 28th year of operation | Consolidation 2 years |

12 | Simulation of the consolidation process until the dissipation of pore pressures | Consolidation |

No. | Description | Type of Calculation |
---|---|---|

01 | Calculation of the original stress state before the current landfill began operation. | Gravity loading |

02 | Loading of the original valley by the weight of the waste deposited up to the moment before the landfill reconstruction. | Plastic |

03 | Ground zone of new landfill modification. | Plastic |

04 | Activation of geogrid finite elements simulating the installation of the liner system | Plastic |

05 | “Waste FGT Ash”—deposition of solidified FGT fly ash | Plastic |

06 | “Waste 01. ETA”—storage of waste in the new landfill between the 1st and 2nd year of operation | Consolidation 2 years |

07 | “Waste 10. ETA”—waste storage in the new landfill between the 26th and 28th year of operation | Consolidation 2 years |

08 | Simulation of the consolidation process until the dissipation of pore pressures | Consolidation |

Material | Mass Unit Weight | Cohesion/Angle of Internal Friction | Hydraulic Conductivity Coefficient | ||
---|---|---|---|---|---|

γ_{unsat}[kN/m ^{3}] | γ_{sat}[kN/m ^{3}] | C′ [kPa] | φ′ [°] | k_{x,y sat}[m/day] | |

Modified terrain | 11.0 | 12.0 | 13.5 | 33.0 | 0.864 |

MSW | 11.0 | 12.0 | 13.5 | 33.0 | 0.864 |

FGT Ash | 15.0 | 15.0 | 34.0 | 29.0 | 0.864 |

Clay; Gj | 19.4 | 21.0 | 24.3 | 21.6 | 1.36 × 10^{−6} |

Marly clay; GLj | 19.6 | 21.0 | 26.0 | 20.5 | 1.36 × 10^{−6} |

Loess (silty clay); PRGd | 19.75 | 21.0 | 25.0 | 21.0 | 1.36 × 10^{−6} |

Material | MC | HS | ||||
---|---|---|---|---|---|---|

E′ [MPa] | ν′ [-] | E_{oed,ref}[MPa] | E_{50,ref}[MPa] | E_{ur,ref}[MPa] | m [-] | |

Modified terrain | 10.0 | 0.35 | ||||

MSW | 10.0 | 0.35 | ||||

FGT Ash | 15.0 | 0.35 | ||||

Clay; Gj | 10.0 | 10.0 | 30.0 | 0.55 | ||

Marly clay; GLj | 12.0 | 12.0 | 36.0 | 0.50 | ||

Loess (silty clay); PRGd | 7.0 | 7.0 | 21.0 | 0.65 |

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## Share and Cite

**MDPI and ACS Style**

Štefaňák, J.; Chalmovský, J.
Assessment of the Landfill Barrier System through Numerical Analysis: Rehabilitation and Expansion of Belgrade Landfill Case Study. *Sustainability* **2022**, *14*, 7647.
https://doi.org/10.3390/su14137647

**AMA Style**

Štefaňák J, Chalmovský J.
Assessment of the Landfill Barrier System through Numerical Analysis: Rehabilitation and Expansion of Belgrade Landfill Case Study. *Sustainability*. 2022; 14(13):7647.
https://doi.org/10.3390/su14137647

**Chicago/Turabian Style**

Štefaňák, Jan, and Juraj Chalmovský.
2022. "Assessment of the Landfill Barrier System through Numerical Analysis: Rehabilitation and Expansion of Belgrade Landfill Case Study" *Sustainability* 14, no. 13: 7647.
https://doi.org/10.3390/su14137647