OGS
[case] ReleaseNodalForce

Boundary condition for simulating excavation using the release nodal force approach.

This class implements a boundary condition that applies a time-dependent, released nodal force to nodes on an exposed surface for excavation simulations.

The initial state assumes a non-equilibrium stress \( \sigma_0 \). In the finite element method, the nodal force is given by:

\[ \mathbf{b} = \int \left( \text{B}^\top (\mathbf{\sigma} - \mathbf{\sigma}_0) + \mathbf{N}^\top (\mathbf{f} - \mathbf{f}_0) \right) \, \mathrm{d}\Omega + \int_{\Gamma_q} (\boldsymbol{\sigma}-\boldsymbol{\sigma}_0)\cdot \mathbf n \mathrm{d}\Gamma \]

where:

  • \( \text{B} \) is the strain-displacement matrix,
  • \( \mathbf{\sigma} \) is the current total stress,
  • \( \mathbf{\sigma}_0 \) is the initial total stress,
  • \( \mathbf{f} \) is the current body force,
  • \( \mathbf{f}_0 \) is the initial body force,
  • \(\int_{\Gamma_q}\) is the boundary where the traction condition is applied, and \( \mathbf n\) is the outward normal of the boundary,
  • \( \mathbf{N} \) is the shape function,
  • \( \Omega \) is the domain of integration.

After excavation, the stress and body force inside the excavated domain vanish, leaving non-zero nodal forces at the exposed surface nodes. These are computed as:

\[ \mathbf{b}_0 = -\int \left( \text{B}^\top \mathbf{\sigma}_0 + \mathbf{N}^\top \mathbf{f}_0 \right) \, \mathrm{d}\Omega - \int_{\Gamma_q} \boldsymbol{\sigma}_0 \cdot \mathbf n \mathrm{d}\Gamma \]

where \(\Omega\) is the remaining domain.

The elements of \( \mathbf{b}_0 \) corresponding to the exposed surface nodes define the released nodal force vector:

\[ \mathbf{f}_\text{r} := (\mathbf{b}_0)_i, \quad i \in \text{exposed surface nodes}. \]

\(\Omega\) can be the excavated domain, which leads to the negative \(\mathbf{f}_\text{r}\).

To simulate excavations under an assumption of gradual release of these forces, the boundary condition applies the released nodal force vector to the global right-hand side (RHS) vector b, scaled by a time- and position-dependent release parameter \( g(t, \mathbf{x}) \):

\[ \mathbf{b} = \mathbf{b} + \mathbf{f}_\text{r} \cdot g(t, \mathbf{x}) \]

The release parameter should be a monotonically decreasing function, representing the progressive removal of support over time, e.g., \( g(0, \mathbf{x}) = 1 \) and \( g(t_e, \mathbf{x}) = 0 \), where \( t_e \) is the end time of excavation, and \( \frac{\partial g}{\partial t} < 0 \).

This boundary condition is particularly useful for modeling staged excavations or similar processes where loads are released in a controlled manner over time.

Note
Setting compensate_non_equilibrium_initial_residuum to true in the process variable configuration is required when using this boundary condition to ensure that the initial non-equilibrium stress state is properly accounted for.

Child parameters, attributes and cases

Additional info

From ProcessLib/BoundaryConditionAndSourceTerm/CreateBoundaryCondition.cpp line 297

  • This is a required parameter.
  • Expanded tag path: process_variables.process_variable.boundary_conditions.boundary_condition.ReleaseNodalForce
  • Go to source code: → ogs/ogs/6.5.7

Used in the following test data files