# Does the pressure due to corrosion in concrete depends on degree of corrosion?

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:

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?

• 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. Apr 15 '19 at 18:32

• 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. Feb 6 '19 at 7:45
The strain in concrete should be $$\dfrac{A_2-A_0}{A_0}$$ which will result in strain equal to $$p\left(\dfrac{\rho_s - \rho_c}{\rho_c}\right)$$.