Project Results Cont.
Stress
The state of stress and the orientation of the principle stress axes changes with time in this experiment. Three general states of stress can be approximated: Pre-collision, Collision and Post-collision.
Pre-Collision Stress
The pre-collision stress conditions are outlined on the figure below.
Stress within the wedge in this situation can be explained by the critical wedge theory, which states that the entire wedge is on the verge of failure and that the active deformation occurs along a basal decollement fault with an angle of b.
In this situation, the stress can be described by the following equations:

sz = rgh cos a (1)

sx = rgh sin a (2)

Where:

sx = stress in the x direction

sz = stress in the z direction

r = density of the sand

g = gravitational acceleration constant

h = thickness of the sand

a = angle between horizontal and the surface of the wedge

In the critical wedge, the x-direction is parallel to the surface of the wedge and the z-direction is perpendicular to x. In front of the wedge, x is parallel with the surface and z is vertical.

It can be seen immediately that sz in the terrane is much larger than sz in the flat sand because h is larger. If we set the thickness of the sand to be 0.5 and the thickness of the terrane to by 2 (which are the boundary conditions set in the model), solving for equation (1), we see that:

sz (sand) = 0.5(rg)

sz (terrane) = 2(rg)

Since the material is the same in both locations, the factor that governs the strength of the body (sz) outside the critical wedge is its thickness (h).
Collisional Stress
The state of stress during collison is outlined on the diagram below.
In this setting, the wedge is overriding the terrane. Deformation is still concentrated along a basal fault, although the angle along that fault (b) has increased as the surface slope increases (a).
In this setting, the wedge is no longer critical because it is not at failure throughout like in the pre-collisional time period. We can see this visually because thrust faults develop in the wedge during the collision, indicating a localization of deformation. Also note that the x and z axes are rotating as the surface slope of the wedge changes.

Deformation starts to occur in the terrane when sx > sz(terrane) and the basal fault starts to cut down into the terrane. Thrusting in the terrane occurs first where it is thin because sz is smaller.
Post-Collisional Stress
The diagram below illustrates the situation after the terrane has accreted.
At this stage, the terrane is fully accreted to the overriding wedge and the two are moving together. The whole body is not behaving like a critical wedge because it is not at failure, but the behaviour at the toe of the orogen can be modelled as a critical wedge.
At this stage, a basal fault has stabilized at the toe of the terrane and material is being accreted in this area. This region can be governed by critical wedge physics, but the orogen as a whole cannot because it has not reached an equilibrium surface slope. The surface of the new wedge has a more gentle slope than the original wedge. This is to satisfy the criteria for the angle between the basal fault and the wedge surface be equal to a + b. If b is greater in this case, a must be smaller.
Stress