# Bouc Wen Hysteretic Rule

## Bouc Wen Hysteretic Rule

Bouc Wen hysteretic rule is often used in literature to model soil nonlinear response in case of dynamic Winkler foundation.

The formulation is usually presented as uy*dz/dy=1+-(beta+-gamma)*zeta^n, where beta is the parameter related to loading and gamma to unloading. In Ruaumoko IHYST=23 requires parameters A1-A5, of which A3,4,5 are mentioned to be often equal to 1. Performing calculation for both formulations I conclude A1=beta and A2=gamma.

Firstly, is this right?

Secondly, where and how parameters D3-D4-D5, which account for strength-loop-stiffness degradation in Ruaumoko, are incorporated in the calculations? At least in the manual they do nor appear in the model's equations?

The formulation is usually presented as uy*dz/dy=1+-(beta+-gamma)*zeta^n, where beta is the parameter related to loading and gamma to unloading. In Ruaumoko IHYST=23 requires parameters A1-A5, of which A3,4,5 are mentioned to be often equal to 1. Performing calculation for both formulations I conclude A1=beta and A2=gamma.

Firstly, is this right?

Secondly, where and how parameters D3-D4-D5, which account for strength-loop-stiffness degradation in Ruaumoko, are incorporated in the calculations? At least in the manual they do nor appear in the model's equations?

**costas**- Posts : 22

Join date : 2010-01-12

Location : ROSE School, Pavia, Italy

## Re: Bouc Wen Hysteretic Rule

Skipping the first part of the question about A parameters, which I have clarified, I would like to bring up the second part of the question:

Parameters D3,D4,D5 related to strength, loop and stiffness degradation are not mentioned in the formulation of the loop, neither in Ruaumoko, or in other literature I ahve searched. How do they influence the cyclic response?

Parameters D3,D4,D5 related to strength, loop and stiffness degradation are not mentioned in the formulation of the loop, neither in Ruaumoko, or in other literature I ahve searched. How do they influence the cyclic response?

**costas**- Posts : 22

Join date : 2010-01-12

Location : ROSE School, Pavia, Italy

## Bouc Wen hysteresis

I think they are covered in the original ASCE paper of the mid 1970s but I would have to search through many boxes of papers to find the original, and that will not be just now.

**Athol Carr**- Posts : 115

Join date : 2009-12-09

Location : Christchurch, New Zealand

## Re: Bouc Wen Hysteretic Rule

Thanks for the answer.

Could you figure out why in hyst=23 during initial loading an elastoplastic loop is followed and not the proper backbone curve? When first unloading starts and afterwards, the loop "behaves" as expected.

Could you figure out why in hyst=23 during initial loading an elastoplastic loop is followed and not the proper backbone curve? When first unloading starts and afterwards, the loop "behaves" as expected.

**costas**- Posts : 22

Join date : 2010-01-12

Location : ROSE School, Pavia, Italy

## Loops for cyclic soil response

Extending from the issue of Bouc-Wen loop (23), I have noticed that other loops, used for soil response, like the hyperbolic (34) or Ramberg-Osgood and its modifications (3,40,41) exceed the maximum strength of the spring specified in the first general line of input for the element. More "classic" loops like EP conform perfectly to the yield force. Is that a problem of the loops or a problem of my modeling? I would appreciate any help, I am quite stuck on that :-(

**costas**- Posts : 22

Join date : 2010-01-12

Location : ROSE School, Pavia, Italy

## Bouc Wen

In the Ramberg-Osgood and some other loops, like Hyperbolic, the 'so called' level is an indicator of strngth. In the Ramberg-Osgood, if one looks at the theory the yield action is reached when the deformation is twice the deformation of the linear elastic system with the same action. One need to carefully understand the basis of the hysteresis rules, Even the diagrams for Ramberg-Osgood show strength greater than the yieild strength. The original Ramberg-Osgood could, if reversal occurred during the unloading path between the initial reversal point and the yield level action end up on a new path where the actions coulf easily exceed twice yield. This is problem using mathematically defines rules (very elegant) but which have not been set up to actually follow observed characteristics.

**Athol Carr**- Posts : 115

Join date : 2009-12-09

Location : Christchurch, New Zealand

## Bouc Wen

I think I have identified adequately the meaning of modeling parameters in Bouc-Wen hysteretic loop. However, no matter what change I make, the result of the loop (force vs elongation) is something similar to an elastoplastic loop. Has it been verified that this loop works correctly? If yes, then I am making a mistake that can not find for days

**costas**- Posts : 22

Join date : 2010-01-12

Location : ROSE School, Pavia, Italy

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