Soil Model according to Mohr-Coulomb

Ground and slope failure

Soil stratification and deformations
Animation of a slope failure

In order to evaluate the load-bearing capacity of soils and possible failure scenarios such as the formation of slip surfaces, the Mohr-Coulomb plasticity model is available in InfoCAD. The model can be used for base failure analyses as well as for estimating the stability of slopes (Phi-C reduction). The analysis can be carried out either with associative or non-associative flow rules, whereby the respective model approach is activated by specifying a corresponding dilatancy angle.

Ground failure

The verification of the numerical results is carried out on the basis of the problem described above (Zienkiewicz et al., 1975). Two limiting cases are investigated, a rigid and a flexible foundation. Numerically, this is implemented by a displacement-controlled (rigid) or load-controlled (flexible) analysis, where the load is applied directly to the weightless soil.

Example ground failure: dimensions, boundary conditions and material parameters

The settlement that occurs when the load is increased and the lateral upward displacement of the floor (bulging) can be clearly understood with the deformation figure shown below.

Deformation of the soil layer (flexible foundation / load-controlled calculation)
Deformation of the soil layer (flexible foundation / load-controlled calculation)

The mechanism of the bearing capacity failure of foundation (active wedge, radial shear zone, passive wedge) becomes clear using the equivalent plastic strains. The shape of the slip surface becomes obvious.

Equivalent plastic strain (maximum values form slip surface)
Equivalent plastic strain (maximum values form slip surface)

In addition to the fracture figures, the ultimate load of the soil (max. soil pressure) can also be predicted. The analyses performed with the arc length method are in very good agreement with the reference solutions.

Load-deformation curve (associative flow rule: ϕ = ψ = 20°)
Load-deformation curve (associative flow rule: ϕ = ψ = 20°)

Slope failure

To calculate the factor of safety (FoS) of an embankment, the method according to Fellenius (1927) [Phi-C reduction] is used in InfoCAD. In this method, the soil parameters (friction angle and cohesion) are successively reduced until the failure of the soil occurs, characterized by the sliding of the sliding body on a sliding joint (slope failure).

Verification of the numerical results is now carried out using the problem illustrated below, taken from the publication by Griffiths & Lane (1999).

Example slope failure: dimensions, boundary conditions and material parameters

In order to show the respective influence on the calculation of the factor of safety (FoS), the analysis was performed with different calculation methods and discretizations (tetrahedral elements). The factors determined are included in Table 1.

Elements Newton Arc Length Method
1822 1,35 1,325
18922 1,35 1,325
55085 1,35 1,325

Influence of discretization and calculation method

Newton and the arc length method result in a safety factor of 1.35 and 1.325, respectively, which is independent of the discretization. The values agree very well with the numerical reference solution of Griffiths & Lane (1999) [FoS = 1.35 (last convergent state)] and the analytical solution of Bishop & Morgenstern (1960) [FoS = 1.38].

In the same way as in the ground failure analysis, the sliding surface occurring within the soil can also be clearly seen here with the aid of the equivalent plastic strains.

Equivalent plastic strain (maximum values form slip surface)