Joints

There are six built-in models available to represnt the material behavior of discontinuties. This section provides an overview of them and makes recommendations concerning their appropriate application. The Constitutive Models section presents background information on the model formulations.

The built-in joint material models in 3DEC are shown in the following table:

Table 1: 3DEC Joint Constitutive Models

Model	Description	Example Application
Elastic	elastic deformation in normal and shear directions; no slip or tensile failure	construction joints
Mohr-Coulomb	slip occurs when shear strength is exceeded; may be brittle or perfectly plastic	general rock mechanics; should be used in most applications
Bilinear Mohr-Coulomb	Mohr-Coulomb joint with different failure envelopes above and below a given normal stress	rock masses with a large range of normal stresses; joints that show evidence of changing friction angles at high compressive stresses.
Softening-Healing Mohr Coulomb	Mohr-Coulomb joint with gradual weakening; recovery of peak strength after slip stops	simulation of seismicity where the rate of energy release and stick-slip behaviors are important
Power Law Creep	time-dependent visco-plastic behavior in the shear direction	simulations of creeping material; when long-term shear displacements are important
Continuously Yielding	continuous weakening behavior as a function of accumulated plastic-shear displacement	cyclic loading and load reversal with predominant hysteretic loop; dynamic analysis

The joint models are assigned to one or more contacts by using the block contact jmodel assign command. Joint model properties are then assigned with the block contact property command.

The joint constitutive models are designed to be representative of the physical response of rock joints. The Mohr-Coulomb slip model provides a linear representation of joint stiffness and yield limit, and is based upon elastic stiffness, frictional, cohesive and tensile strength properties, and dilation characteristics common to rock joints. The model simulates displacement-weakening of the joint by loss of cohesive and tensile strength at the onset of shear or tensile failure (by default). It is possible to simulate perfectly plastic behavior by setting residual strength properties to be the same as the peak strength properties. The Coulomb slip model is most applicable for general engineering studies. Coulomb friction and cohesion properties are usually available more often than other joint properties. The Mohr-Coulomb model is the default material model when new contact or subcontacts are formed.

The Blinear model and the Softening-Healing model are variations on the basic Mohr-Coulomb model. The Blinear model allows the user to specify a different shear strength (cohesion and friction) above and below a threshold normal stress. The Softening-Healing model exhibits a gradual drop from peak to residual shear strength over some specified slip distance. This model also recovers its peak strength when slipping stops.

The Continuously Yielding joint model is a more complex model that simulates continuous weakening behavior as a function of accumulated plastic-shear displacement.

Selection of an Appropriate Model

A problem analysis should always start with simple zone and joint material models. In most cases, an elastic block model and a Mohr-Coulomb slip model should be used first. The Coulomb slip model requires six parameters: normal and shear stiffness, friction angle, cohesion, tensile strength and dilation angle. Estimates and references for these properties are given in Joint Properties section.

It is often helpful to run simple tests of the selected material model before using it to solve the fullscale boundary-value problem. This can provide insight into the expected response of the model compared to the known response of the physical material.

A simple example of a joint subjected to shear loading is presented in the decription of the Mohr-Coulomb joint model in the Theory and Background section..

In most cases, the Coulomb model parameters are relatively easy to estimate (see Joint Properties), and the simple modifications that are available with the Coulomb model may be sufficient to approximate the joint behavior.

For other joint models, such as the continuously yielding model, the determination of properties is more involved. In order to use the continuously yielding model, it is necessary to run a series of joint shear tests to best-fit the model properties to physical test results. It is recommended that simple shear tests always be performed, regardless of the joint model selected, to ensure that the joint behaves as expected under the anticipated problem conditions.

If it is necessary to simulate a complicated joint response, then a more complex joint model may be required. However, before going to a more complex model, it is usually helpful to apply a simple model first, to establish a basis for evaluating the influence of the more complicated joint behavior.