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I am trying to relate the degree of corrosion with the pressure exerted in surrounding concrete. My common sense tells me that higher the degree of corrosion, higher should be the pressure exerted, but my equation tells me it is constant. Obviously, I am making a calculation mistake but could not figure it out. What mistake am I making (figure attached)? Consider unit length along the rebar:

enter image description here

Area after corrosion is $A_1=A_0(1-p)$, where $p$ is the percentage of corrosion.

The volume occupied by rust if there was sufficient space is given by converting the volume of steel to equivalent volume or rust: $A_2=A_1+pA_0\dfrac{\rho_s}{\rho_c}$.

  • Initial volume: $V_1=A_2-A_1$
  • Final volume: $V_2=A_0-A_1$
  • Change in volume: $\Delta V=V_1-V_2$
  • strain: $\epsilon=\dfrac{\Delta V}{V_1}$

Solving, we get $\epsilon=\dfrac{-\rho_c + \rho_s}{\rho_s}$. There is no $p$.

What am I doing wrong?

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  • $\begingroup$ Or you could coat the steel rebar with epoxy and/or zinc like the real world , as wet bare steel just keeps corroding and expanding. $\endgroup$ Apr 15 '19 at 18:32
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I'd say the mistake is assuming infinite stiffness for concrete and steel so only the rust has a strain. In reality, rust is probably the stiffest material involved, and you will get a better approximation by assuming infinite stiffness for rust and steel and calculating the strain and stress in concrete.

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  • $\begingroup$ For now we can assume the boundary is rigid. $\endgroup$ Feb 2 '19 at 14:30
  • $\begingroup$ But assuming a rigid boundary between rust and concrete will not give useful results — just immediate failure. Try calculating the interface stress, if you're still in doubt. $\endgroup$
    – ingenørd
    Feb 4 '19 at 14:21
  • $\begingroup$ Common.. just dont comment for the sake of commenting. Its an engineering question. You need to review the details before commenting or providing your suggestions. And provide your answer in equations will be much better than wordly sentences. $\endgroup$ Feb 6 '19 at 1:13
  • $\begingroup$ Steel expands from 100% to 650% when it rusts and rust has an elasticity modulus of around 300GPa, so your calculation principle assumes a concrete capacity of $1.00 \times 300GPa = 300,000MPa$ or greater. $\endgroup$
    – ingenørd
    Feb 6 '19 at 7:45
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I found the error.

The strain in concrete should be $\dfrac{A_2-A_0}{A_0}$ which will result in strain equal to $p\left(\dfrac{\rho_s - \rho_c}{\rho_c}\right)$.

The strain calculated previously would only account for strain in corrosion particles.

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