TriaxialTest

Triaxial Test

Yade includes tools to simulate triaxial loadings on dense samples. The pre-processor TriaxialTest (and a few variants) do the following :

• generate random loose packings and compress them under isotropic confining stress, either squeezing the packing between moving rigid boxes or expanding the particles while boxes are fixed (depending on flag "InternalCompaction").
• simulate all sorts of triaxial loading path (there is however a default loading path corresponding to constant lateral stress in 2 directions and constant strain rate on the third direction - this loading path is used when the flag AutoCompressionActivation = true, otherwise the simulation stops after isotropic compression)

Essential engines :

1. The TrixialCompressionEngine is used for controlling the state of the sample and simulating loading paths. TrixialCompressionEngine inherits from TriaxialStressController, which can compute stress- strain-like quantities in the packing and maintain a constant level of stress at each boundary. TriaxialCompressionEngine has few more members in order to impose constant strain rate and control the transition between isotropic compression and triaxial test.
2. The class TriaxialStateRecorder is used to write to a file the history of stresses and strains.
3. TriaxialTest is currently using GlobalStiffnessTimeStepper to compute an appropriate dt for the numerical scheme. The TriaxialTest is the only preprocessor using these classes in Yade because they have been developped AFTER most of preprocessor examples, BUT they can be used in principle in any situation and they have nothing specifically related to the triaxial test.

NOTE : TriaxialStressController::ComputeUnbalancedForce(...) returns a value that can be usefull for evaluating the stability of the packing. It is defined as (mean force on particles)/(mean contact force), so that it tends to 0 in a stable packing. This parameter is checked by TriaxialCompressionEngine to switch from one stage of the simulation to the next one (e.g. stop isotropic confinment and start axial loading)

Frequently asked questions :

"How is generated the packing? How to change particles sizes distribution? Why do I have a message "Exceeded 3000 tries to insert non-overlapping sphere"?"

The initial positioning of spheres is done by generating random (x,y,z) in a box and checking if a sphere of radius R (R also randomly generated with respect to a uniform distribution between mean*(1-std_dev) and mean*(1+std_dev) can be inserted at this location without overlaping with others.

If the sphere overlaps, new (x,y,z)'s are generated until you a suitable place for the new sphere is found. This explains the message you have : after 3000 trial-and-error, the sphere couldn't be placed, so the algorithm stops.

You get the message above if you try to generate an initialy dense packing, which is not possible with this method. You should keep the default value of porosity (~0.7). The dense state will be obtained in the second step (compaction, see below).

"How is the compaction done, what are the parameters maxWallVelocity and finalMaxMultiplier?"

Compaction is done (1) by moving rigid boxes or (2) by increasing the sizes of the particles (decided using the option "internalCompaction" : true => size increase). Both algorithm needs numerical parameters to prevent instabilities. For instance, with method (1) maxWallVelocity is the maximum wall velocity, with method (2) finalMaxMultiplier is the max value of the multiplier applied on sizes at each iteration (always something like 1.00001).

"During the simulation of triaxial compression test, the wall in one direction moves with an increment of strain while the stresses in other two directions are adjusted to sigmaiso. How the stresses in other directions are maintained constant to sigmaiso? What is the mechanism? Where is it implemented in Yade?"

The control of stress on a boundary is based on the total stiffness K of all contacts between the packing and this boundary. In short, at each step, displacement=stress_error/K. This algorithm is implemented in TriaxialStressController, and the control itself is in TriaxialStressController::ControlExternalStress(...). The control can be turned off independantly for each boundary, using the flags wall_XXX_activated, with XXX = top, bottom, left, right, back, front. The imposed sress is a unique value (sigma_iso) for all directions if TriaxialStressController::isAxisymmetric, or 3 independant values sigma1,2,3.

"Which value of friction angle do you use during the compaction phase of the Triaxial Test?"

The friction during the compaction (whether you are using the expansion method or the compression one for the specimen generation) can be anything between 0 and the final value used during the Triaxial phase. Note that higher friction than the final one would result in volumetric collapse at the beginning of the test. The purpose of using a different value of friction during this phase is related to the fact that the final porosity you get at the end of the sample generation essentially depends on it as well as on the assumed Particle Size Distribution. Changing the initial value of friction will get to a different value of the final porosity.

"Which is the aim of the bool isRadiuControlIteration?"

This parameter allows to perform some cycle without expanding between two radius expansions. Cycling without expanding is just a way to speed up the simulation.

"How is it possible for the unbalanced force to reach a low value in order to satisfy the StabilityCriterion?"

The value of unbalanced force (dimensionless) is expected to reach low value, and so identifying a static-equilibrium condition for the specimen, only at the end of the compaction phase. It is not really a matter if the compaction is dynamic in between, since probably the interval growth is too small to let the sample stabilize.