# [CIG-SHORT] Fault opening problem

Thu Oct 11 15:15:35 PDT 2007

```Marco-

The fault implementation uses cohesive cells. These zero volume cells
are inserted into the mesh causing a change to the topology. For a
kinematic fault rupture, we constrain the slip using Lagrange
multipliers. In creating the cohesive cells, we not only add a vertex
for each vertex that is already part of the fault, but we also add
another one between the vertices on each side of the fault (all three
have the same coordinates). This third vertex corresponds to the degrees
of freedom for the Lagrange multipliers. This is why 4 vertices are
added in the problem you created.

The symmetry of the solution depends on how the cohesive cell is
connected to the surrounding cells. The topology of connecting a
cohesive cell at the ends of the fault to the surrounding cells is an
ill-posed problem. In many cases there is a natural way to connect the
cohesive cell to its neighbors, but this is not straightforward to
implement. As a result, the precise topology of connecting a cohesive
cell to its neighbors at the end of a fault is mesh dependent. The
solution is to always set the slip on the last vertex of the fault to
zero (assuming the fault is not through-going). Fixing the end vertex of
the fault results in a well-posed problem and symmetric behavior. In
your case, you should add vertices 8 and 11 to the fault group and
adjust the spatial database file to have a 1-D variation in slip with
slip set to zero at the coordinates corresponding to vertices 8 and 11.

We will update the manual to explain this behavior before the next
significant release.

Marco Aloisi wrote:
> Dear CIG team
>
> we tried to simulate a fault opening in a 2D domain using a six quad
> mesh (see attached image). We chose the segment 9 - 10 as fault and a
> opening component of +0.01 m. We imposed no movements on the -x and +x
> edges.
>
> *1) Why do we observe a bigger movement on the left cell (vertices 4, 9,
> 10, 7) respect to the right one? Why isn't the movement symmetrical?*
>
> 2) Using the instruction "faultcohesivekin = 1", Pylith generated the
> vertices 12, 13, 14, 15 instead of 12 and 13 only....why?
>
>
>
>
> Thankyou very much
> Marco Aloisi
>       Istituto Nazionale di Geofisica e Vulcanologia
>       Sezione di Catania
>       Piazza Roma, 2
>       95123 Catania - Italy
>
>
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>
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```