Modeling existing shear walls can be quite challenging. The first question to ask is how far we want to go – and how much we want to spend on- when it comes to modeling a wall structure. The modeling can be as simple as a beam-columns element, or as complex as a nonlinear 3D finite element model.

The design and detailing of reinforced concrete shear walls is a straight forward task using most modern design codes. Following the requirements of design codes – and seismic provisions – ensures the proper response of the wall at the time of design earthquake; however, this is not the case for deficient concrete shear walls.

Modeling existing shear walls can be quite challenging. Concrete material as well as steel reinforcement should be modeled properly. Certain deficiencies such as inadequate lap splice length can trigger premature brittle failure of the walls. Location of the lap splices, on the other hand, can change the response of the walls. As a result, identifying important failure modes will be the first step in developing behavioral models.

In this brief note, I will discuss the special case of flexural walls. The response of squat walls will be different and requires taking into account other factors.

## Modeling Existing Shear Walls (Flexural)

The general response of a flexural wall, as its name implies, is governed by flexure. This will be the case if we no other failure mode happens earlier. General deficiencies in older construction often prevents the walls from reaching their design capacity; even when the sections have enough to reach to the yield point, the lack of confinement around the corner bars (or boundary elements if we can call them) will significantly reduce the plastic response of these walls. This will eventually limit the effectiveness of the shear wall.

### Material Properties

Most behavioral models depend on the mechanical properties of materials. For example, one needs to know the approximate compressive strength of concrete, the crushing strain, the yield strength of steel, etc. The more information we have about the materials, the better we can predict their behavior in complex scenarios. For example, this information can be used to model the response of concrete material under reversed cyclic loading.

### Global response: Flexural or Shear

An appropriate model for existing shear wall should account for the global response of the wall, as well as potential local failure modes. For walls with high h/l ratio, the response is governed by flexure. The response of squat shear walls is governed by shear in most cases; and for majority of walls, as we can expect, there is a mix of both flexural and shear response. Why is this important? I will take a flexural wall for instance. The response of the wall, as I expect, should be governed by flexure. In order to model this response properly, I should have a good estimate of the potential plastic hinge location, and length, as these two parameter will eventually affect the maximum drift. A good behavioral model should account for the shear deformations as well. In this case, the interaction of flexure and shear should be taken into account.

### Lap splices

If we have lap splices, we should take their effect into account. Lap splices, if located at the plastic hinge location, can significantly limit the flexural response. They may even cause a premature failure is the length is inadequate (which is the case for most older construction.

### Bar slip

The effect of bar slip at the base of the wall should be taken into account. This can have a significant effect on the overall response of the wall.

## A modeling scenario

A displacement-based beam-column element with a fiber cross section can be used in order to model the shear wall components. The fiber displacement-based beam-column element was proposed by Taucer et al. (1991) and was based on a displacement formulation that allows for distributed plasticity modeling which would allow yielding to occur at any location along the element. The nonlinear response of the element is therefore derived from the nonlinear stress-strain relationships for each individual fiber (concrete and steel). In displacement-based approach section deformations are interpolated from an approximate displacement field.

It should be noted that since the formulation of the fiber displacement-based beam-column element is based on sectional analysis, it does not model bond slip effects and neglects the effect of shear deformations. Therefore, additional behavioral features should be included in the model to appropriately model these phenomena.

Fiber displacement-based beam column element can be used along with a translational shear spring to account for shear deformation. However, this does not model the interaction of flexure and shear. A rotational spring at the base of the wall can be used to model the bond-slip of the wall.

The following graph shows the response of a deficient wall that is modeled using previously described technique.

Reference: Seismic Retrofit of Deficient Reinforced Concrete Shear Walls, PhD Thesis