Bounding Cam Clay Model

[STKO Team]

Assume you have 2 stages, where you first add the first soil layer, you analyze it and then you add another layer on top of the first one.

The objective of the initial state analysis is to reset the displacements to zero so that the second layer will not have stresses due to the initial displacements of the first layer (constructed on the deformed configuration), and at the same time keep the stress values in the first layer (so that the reset of the displacement will not reset its stress as well)

Instead of using the initialStateAnalysis concept to reset the displacements of the first layer before adding the second one, you can simply model the 2 layer separately and link them with equalDOFs.

Then your analysis will look like this:
Add first layer
Analyze
Add second layer + equalDOFs with the first layer
Analyze
(Note you have to use the latest version of OpenSees (>= 3.7.0) for it to work)

From OpenSees v 3.7.0, the Constraints are incremental: If you add an equalDOF to a second stage, where one (from first stage) node has an initial displacement and another node (from second stage) has a zero displacement, the EqualDOF will constraint the displacement increment to be equal, not the total displacement.
In this way it will keep the gap between the two layers constant, so the first layer will have it's own stress and displacements, while the second layer will not be affected by the initial displacements of the first layer.

[Lei Lei]

I think I understand your point.
However, if the soil in the second stage is replaced by a shield tunnel, can this approach achieve the same results as the initial analysis? Since the tunnel and the soil share a common boundary, it's important to consider that after the first stage of analysis, the soil has already undergone some deformation, causing the common boundary to no longer be circular. At the start of the second stage, the tunnel remains undeformed and retains its original shape. I am concerned that this disparity in the common boundary may lead to inaccuracies in the subsequent calculations.

[STKO Team]

This is not a major problem. If the tunnel is build onto the deformed configuration of the soil, in this configuration the tunnel will be stress-free anyway.
It's only a problem if the deformed shape of the soil is so large that the shape is completely different from what you modeled. In that case you need to do some survey and draw the tunnel with it's real configuration (but I don't think this is the case)

[Lei Lei]

During the tunnel construction process, the excavation area is initially larger than the tunnel itself. Before formal construction, this excavation area undergoes continuous deformation. To accommodate this, the gap between the constructed tunnel and the deformed excavation face is filled by grouting. After grouting, the soil and tunnel deform together. In this situation, although the shapes of the excavation face and tunnel are not identical, assuming infinite stiffness after grouting solidification, equal degrees of freedom (equalDOF) can approximate the interaction between the soil and structure, substituting for the grouting layer. This, however, is a significant simplification of actual conditions.

If the initialStateAnalysis command is applied, the excavation face of the soil typically matches the tunnel's outer boundary. Following soil excavation, a gradually decreasing support force is applied to the excavation surface, causing it to deform with the decreasing force. Once the support force reduces to a critical level, turn initialStateAnalysis command off, allowing for tunnel construction. At this stage, the sizes and shapes of the tunnel’s outer surface and the excavation face remain aligned. During the process of releasing any residual support force to zero, the soil and tunnel deform together. If the initialStateAnalysis command isn't applied, the deformed excavation face will intersect slightly with the tunnel’s outer boundary upon tunnel construction. This deformation is minor, with radial movement of the excavation face about 1% of the original diameter. If equaldof is used for this situation, what is the impact?

[STKO Team]

If the initialStateAnalysis command isn't applied, the deformed excavation face will intersect slightly with the tunnel’s outer boundary upon tunnel construction. This deformation is minor, with radial movement of the excavation face about 1% of the original diameter. If equaldof is used for this situation, what is the impact?

This is true. The nodes of the soil will have at this stage (call it "0") a non-zero displacement, while the newly added nodes of the tunnel will have (obviously) a zero displacement.
However, from OpenSees' version 3.7.0, MultiPoint Constraints such as EqualDOF take into account any initial displacement at the master and slave nodes, and they will apply the constraint only on the extra displacement experienced after the condition is applied.

Immagine this scenario

Using InitialStage:

• SoilNode added: Usoil_t0 = 0
• First analysis: Usoil_t1 = A
• Reset with InitialStage -> Usoil_t1 = 0 (keep stresses due to Usoil_t1 = A)
• TunnelNode added: Utun_t1 = 0
• apply equalDOF
• Second analysis -> Usoil_t2 = Usoil_t1 + B= 0 + B = B
  EqualDOF -> (Utun_t2-Utun_t1) = (Usoil_t2-Usoil_t1) -> (Utun_t2-0) = (B - 0) -> Utun_t2 = B

Without InitialStage (with the incremental version of MP constraints v >= 3.7.0):

• SoilNode added: Usoil_t0 = 0
• First analysis: Usoil_t1 = A
• TunnelNode added: Utun_t1 = 0
• apply equalDOF
• Second analysis -> Usoil_t2 = Usoil_t1 + B = A+ B
  EqualDOF -> (Utun_t2-Utun_t1) = (Usoil_t2-Usoil_t1) -> (Utun_t2-0) = (A+B - A) -> Utun_t2 = B

As you can see the displacement increment in the second stage is the same.
Do a test by yourself, even if you see different displacement (due to initialState or not) what is important is the state of stress.
Check that it is the same

[Lei Lei]

Thanks for your explanation!
I will make a comparison with the effect of whether there is initial displacement.

[STKO Team]

You're welcome