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Primary Consolidation Settlements under Landfill Lining Systems - Design Calculator

 

Problem Statement
When landfill liners are constructed on saturated inorganic clayey or silty foundation, primary consolidation settlements take place in these layers due to additional stresses imposed by the waste weight.

The uneven distribution of these stresses (different waste thickness), creates a differential settlement between different points along the landfill cross section. The potential impact of these settlements on the performance of the leachate collection system and liner system must be evaluated.

Problem Approach

  1. Evaluate vertical subgrade stresses due to the waste weight at two points of consideration, point 1 and point 2. The stresses need to be evaluated at the worst case loading scenario, as shown in Figure 1.
  2. Define compressibility of subgrade at the two points, using laboratory test data on the representative clay sample of the subgrade.
  3. Calculate total and differential settlements between points 1 and 2.
  4. Examine impact on leachate collection system slope.
Below is an example of a cross section in a landfill showing the required geometrical and material input variables.


Figure 1. Landfill Consolidation Calculation - Geometry and Parameters

The primary consolidation settlement is evaluated using the following equation:

where:

Symbol

 Description

Unit
SC primary consolidation settlement m
n number of clay sublayers m
Cr recompression index (as shown in Figure 2) -
Hi thickness of clay sublayer # i m
eo initial void ratio -
OCR overconsolidation ratio -
σ'voi effective normal stress (evaluated at the middle of the sublayer # i) kPa
Cc compression index (as shown in Figure 2) -
Δσvi additional normal stress (at the middle of the sublayer # i) kPa


Figure 2. Settlement Calculations for Overconsolidated Soils

Additional stresses imposed by the waste weight is calculated underneath the two selected points: Point 1, and Point 2 as follows (see Figure 3):


Figure 3. Additional Stresses Underneath Point 1 and Point 2

where:

Symbol

 Formula
Po = γWASTE * h1
P1 = γWASTE * h2
a = h1/S1
X = h2/S2
β = π * [90 + tan-1(X/Z)]/180

Finally, the average slope resulted form the differential settlement between Points 1 and 2 is calculated as follows (see Figure 4):


Figure 4. Average Slope Resulted From Differential Settlement

 

Input Values

1) Landfill Waste / Geometry

h1 Height of waste above ground surface (m)
h2 Depth of waste below ground surface (m)
s1 Slope of waste above ground surface (-)
s2 Slope of waste below ground surface (-)
L Distance between the two selected points (m)

2) Landfill Waste / Material Properties

γwaste Unit weight of waste (kN/m3)

3) Clay Layer / Geometry

Ho Thickness of clay layer (m)
Hw Groundwater table (m)
 

4)  Clay Layer / Material Properties

γSAT Saturated unit weight of clay (kN/m3)
eo Initial void ratio (-)
Cr Recompression Index (-)*
Cc Compression Index (-)*
OCR Overconsolidation Ratio*
* Determined from Consolidation Test. OCR shall be equal to 1.0 (for normally consolidated soils) or large than 1.0 (for overconsolidated soils) .

 
References

"Designing with Geosynthetics". R.M. Koerner, Prentice Hall Publishing Co., Englewood Cliffs, NJ, 1998.

"Geosynthetic Design Guidance for Hazardous Waste Landfill Cells and Surface Impoundments", G. N. Richardson and R. M. Koerner, 1987.

"Soil Mechanics & Foundations", Muni Budhu, John Wiley & Sons, NY, 2000.

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