Approximate J estimates for combined primary and secondary stresses with large elastic follow-up

• This paper proposes a method for J estimates under combined primary and secondary stresses.
• The method is given in terms of the V-factor within the failure assessment diagram approach.
• The elastic follow-up is characterized and quantified by three parameters.
• An approximate expression for the V-factor is proposed, showing good agreement with finite element solutions.

This paper proposes the V-factor for approximate J estimates under combined primary and secondary stresses with large elastic follow-up within the failure assessment diagram approach. The elastic follow-up is characterized by three parameters. The first two are the relative magnitudes of the primary load and of the secondary stress, β. The third parameter is the initial slope of the Vo–β curve where Vo is the value of V for zero primary load. Elastic follow-up effects are more pronounced for contained yielding, smaller β and a larger initial slope of the Vo–β curve. An approximate expression for V/Vo is proposed, showing good agreements with finite element solutions.