2.1.5. Prestress Loss Due to Crack Reduction and Closure, σ*l*<sup>4</sup>

In our experiment, due to the restraining effect of the prestressed steel strand, the cracks of the concrete core were reduced to some extent, or even closed. The reduction of the circumference of the pipe led to the prestress loss of the strands. Therefore, the change in the maximum width of the visible cracks in the concrete core can be utilized to estimate the prestress loss caused by crack reduction and closure.

The change in the maximum width of the cracks corresponds to the change in the length of the prestressed steel strands (Figure 6). The prestressed steel strand is in the elastic phase, and the stress is proportional to its strain. Therefore, the prestress loss, σ*l*4, caused by the crack reduction and closure, can calculated according to the following equation.

$$l\_i = \frac{r\_{st}}{D/2} w\_i \tag{18}$$

$$\frac{\sigma\_0}{\omega\_{0-\sigma\_{l4}}} = \frac{2\pi r\_{st} + l\_1}{2\pi r\_{st} + l\_2} \tag{19}$$

where *wi* is the maximum width of the visible cracks in the concrete core (m), *i* = 1, 2 for the condition before and after the reinforcement, *li* is the length of prestressed strands corresponding to the maximum width of the cracks in the concrete core before and after the reinforcement (m), and *D* is the outer diameter of the concrete core (*m*).

**Figure 6.** Correspondence between crack width and strand length.

Therefore, the prestress loss due to the crack reduction and closure, σ*l*4, can be defined as Equation (20):

$$
\sigma\_{l4} = \frac{\sigma\_0 (w\_1 - w\_2)}{\pi D + w\_1} \tag{20}
$$
