GGU-STABILITY: General notes on analysis with fibre cohesion

Wastes dissimilar to soil such as untreated residual waste, for example, exhibit shear behaviour considerably different to that of soil and soil-like wastes (excavated soils, sieved MBT fractions (Mechanical Biological Treatment). In their GDA recommendations (GDA - Geotechnik der Deponien und Altlasten - Geotechnical Aspects of Landfill and Brownfield Sites), the German Geotechnical Society (Deutsche Gesellschaft für Geotechnik) recommends different analysis methods to suit these classifications. Using common installation techniques, waste dissimilar to soil leads to stratified, anisotropic landfill masses. Stability analyses for anisotropic landfill masses are dealt with in GDA recommendation R 2-29.

From a waste mechanics perspective, waste dissimilar to soil is regarded as a composite material, consisting of an underlying matrix and a fibre matrix, based on the principles of fibre-reinforced soils. Based on the model describing the interactions of tensile and friction forces in a composite material, superimposing the two shear strength components generally produces a non-linear failure condition. Such failure conditions are known from reinforced soil masses (EBGEO - Empfehlungen für Bewehrungen aus Geokunststoffen - Recommendations for Geosynthetic Reinforcements). The cause of the non-linearity is the limited dependence of the normal stress on the reinforcing effect.

The magnitude of the allowable tensile forces depends on the fibre properties and the grain matrix, as well as the surcharge load. The strength characteristics of the fibre matrix are described by two material parameters:

• The fibre-specific tensile strength z_max

• The angle ζ

A surcharge-independent component of the tensile strength (z₀), which cannot be differentiated from any cohesion c of the underlying matrix, may also occur. The angle ζ describes how the normal stress is a function of the reinforcing effect. The transfer of tensile forces by the fibres is limited by the fibre-specific tensile strength z_max. When the fibre-specific tensile strength is reached the fibres tear, the load-bearing effect of the fibre matrix fails.

The shear strength components of the underlying and the fibre matrix are determined in order to determine the shear strength of the anisotropic waste mass. The two components are then superimposed in the analysis. The so-called fibre cohesion (z) is calculated from the tensile forces in the fibres. One peculiarity of waste dissimilar to soil containing fibres and films is that the material is pressed flat by the compactor and horizontally stratified when installed in thin layers. This produces the anisotropic strength behaviour. Activation of the fibre cohesion (z) depends on the angle between the fibre layer and the shear joint.

Stability analyses can be performed using the material parameters differentiated for the underlying matrix and the fibre matrix . By using this separate approach, it is possible on the one hand to take the anisotropy of the fibre matrix into consideration numerically, and on the other to employ surcharge-independent material parameters despite the non-linear failure condition. The basis for slope failure analysis is the method of slices (DIN 4084:2002-11). The equation for analysis of the slice base shear resistance is extended by a term for the fibre cohesion as a function of the angle The slice base shear resistance T is given by:

Whereby the following condition is adhered to:

It must be taken into consideration when adopting the cohesion c_GM that surcharge-independent shear strength components resulting from the surcharge-independent tensile stresses may occur in both the underlying matrix (cohesion c_GM) and the fibre matrix (surcharge-independent fibre cohesion (z₀). Because these surcharge-independent shear strength components cannot be exactly differentiated, they may not be simultaneously adopted for analyses.

With the exception of the equation extension for analysis of the slice base shear resistance, no further changes have been made to the program's underlying analysis methods. The description given in the "General information on Janbu and Bishop" section applies.

Input of soil properties is described using an example for conventional analysis without fibre cohesion in "Worked example 2: Data input via editor/Step 2: Enter system parameters (Ex. 2)/Soil properties". As described above, further parameters are required for analysis with fibre cohesion; they are entered in the corresponding input screen.

Table 2 Soil properties input screen (examples from GDA recommendation R 2-35
and Collins et al., 1997)

The degree of activation parameter describes the bonding behaviour when the tensile forces are converted to fibre cohesion. Fibre redistribution and similar effects are taken into consideration globally, beside the bonding effect. With good bonding (homogeneous mixing of underlying matrix and fibre matrix, high-friction underlying matrix, etc.) the degree of activation may be 1. Because knowledge of the bonding behaviour is limited, a conservative degree of activation of 0.7 is recommended (Kölsch, 1996). In the analysis, the degree of activation acts as an additional partial safety factor on the fibre cohesion.