The Mohr-Coulomb model is defined by an elasto-plastic behavior as shown in the figure below. This behavioral assumption shows reliable results for general nonlinear analysis of the ground and is widely used in simulating most terrain.

<Material behavior of Mohr-Coulomb model>

The Mohr-Coulomb yield criterion has 2 flaws when using geo-materials. First, the intermediate principal stress does not affect yield, which is a contradictory assumption to real soil test results. Second, the Meridian and Failure envelope of the Mohr-Circle is linear; so the Strength parameter (angle of friction) does not change with the Confining pressure (or Hydrostatic pressure). This criterion is accurate within a limited range of confining pressure but as the range difference increases, the accuracy decreases. However, this criterion is often used because it is easy to use and displays considerably accurate results within the general confining pressure range.

The major nonlinear parameters used to define the Coulomb yield criterion are as follows.

[Cohesion (C) , Friction angle (Φ)]

Soils have different cohesion and friction angle depending on their type and these values are applied to the shear strength equation. Soils, unlike other construction materials, have very little resistance to tension and in most cases shear failure occurs. When an external force or self weight is applied, shear stress occurs in the ground. The strain increases with stress increase and as this progresses, it works along a plane causing what is known as shear failure. The shear stress induces shear resistance and the shear resistance limit is called shear strength. The shear resistance of soil is made up of 2 comp1nts: cohesion and friction angle.

According to Coulomb, the shear strength of soil can be expressed in the following linear equation.

τ= c + σtanφ(c: Cohesion, σ: Normal stress, φ: Interior friction angle)

Cohesion is the shear strength when the interior friction angle is '0(zero)' according to the yield criterion. It can be defined as an undrained shear strength of cohesive soils. Sandy soils with no cohesion can be defined as c=0, but to avoid errors in analysis, it is recommended that a value of at least 0.2 (kN/m2) be entered.

Defining the cohesion automatically sets the tensile strength by that amount. However, because tensile resistance is generally ignored for geo-materials, the Tension-Cutoff is set to prevent unrealistic resistance behavior to tension.

<Mohr-Coulomb Failure envelope (Drained/Undrained)>

[Increment of Cohesion Reference Height]

In general, the strength properties of the soil change with the depth and confining pressure; even within a ground layer composed of the same material. For example, defining a soil layer several meters deep as a ‘strength parameter’ may be a limitation in the detailed simulation of a ground behavior. The ground layer can be further subdivided and modeled, but this characteristic can be replaced by changing cohesion according to height. If the cohesion increases according to the height being '0(zero)', the cohesion has a constant value and if it is not '0(zero)', the cohesion is calculated with reference to a standard height (reference height based on the Global Coordinates) using the following equation.

    :  Input cohesion value

    :  Incremental amount depending on cohesion depth

    :  Depth of measurement

<Conceptual diagram of cohesion increment>

The in the equation represent the integral point positions of an element where the finite element method calculation occurs. If the integral point position is higher than , the cohesion can be less than 0 in some places. To avoid this, use the  value instead of further decreasing the cohesion value.

Dilatancy Angle

The dilatancy angle can be viewed as the volume increase rate according to shear strain. It is a type of strength parameter for roughness and is generally defined as dilatancy angle = interior friction angle-30˚. Hence, if the interior friction angle is less than 30˚, the dilatancy angle is close to '0(zero)'. In real tests, a negative dilatancy angle can be defined for vey loose sandy soil but numerically, the dilatancy angle has a value between 0 and the interior friction angle.

For undrained analysis, the dilatancy angle must be set as '0(zero)' when the interior friction angle is '0(zero)'. The important thing is that the dilatancy angle is a parameter considered in analysis after changes have been made to the constitutive equation. If the effects of the dilatancy angle are not considered, the same value must be entered for the dilatancy angle and interior friction angle. In other words, not checking the ‘Consider dilatancy angle’ option automatically performs the analysis with the dilatancy angle equal to the interior friction angle.

Tensile Strength (Tension-CutOff)

Input the allowable tensile strength of the geo-material. In many cases, tension cracks can be observed on the natural ground surface rather than shear failure. Input the allowable tensile strength to assign tensile resistance to the geo-material. The tensile resistance of geo-materials are generally ignored and so the default setting is '0(zero)'. Not checking the tensile strength option uses a tensile stress, automatically calculated from cohesion and the interior friction angle, into the analysis.