2.1.3. Prestress Loss Caused by Anchorage Deformation, σ*l*<sup>2</sup>

The prestress loss caused by deformation at the end of the anchorage should be taken into consideration. This refers to the prestress loss caused by the deformation of the anchor and the retraction of the clip due to the concentrated stress. A slip at the anchorage depends on the particular prestressing system adopted and is not a function of time. This loss can be written as per Equation (16):

$$
\sigma\_{l2} = E\_{\rm st} \frac{\Delta l\_{\rm tr}}{2\pi r\_{\rm st}}.\tag{16}
$$

### 2.1.4. Prestress Loss Caused by the Elastic Compression of Concrete During Batch Tensioning, σ*l*<sup>3</sup>

The prestress loss can be adjusted using certain construction technologies, including ultra-tensioning and repeated tensioning. For example, the tensioning can be started from the middle of the pipeline and gradually pulled symmetrically to both sides when batch tensioning is adopted. The steel strands that would later be tensioned would cause elastic compression deformation of the concrete, which would contribute to the prestress loss of the previously anchored strands. This prestress loss can be simplified by the following formula [21]:

$$
\sigma\_{l3} = \frac{m-1}{2m} n\_{\bar{y}} \sigma\_{h1} \tag{17}
$$

where *m* is the total number of batches and σ*h*<sup>1</sup> is the normal stress of the concrete produced by the combined force of the steel strands at the action point (the center of gravity of all steel strands), which is equal to the sum of the normal stresses of the concrete produced by the batch of steel strands, which is Δσ*h*1. That is, σ*h*<sup>1</sup> = Δσ*h*<sup>1</sup> = *m*Δσ*h*1. *ny* is the combined force of all of the steel strands. Δσ*h*<sup>1</sup> is the normal stress of the concrete generated by the subsequent batch of steel strands at the center of gravity of the first tensioned steel strand, as calculated by the following formula: Δσ*h*<sup>1</sup> = *<sup>n</sup> m* 1 *Aj* <sup>+</sup> *ey*·*yi Ij* .

During engineering, ultra-tensioning or repeated tensioning technologies can be utilized in the first several batches of strands, so that the actual effective prestress of the pipe is substantially equal to the design level. After ultra-tensioning or repeated tensioning, the prestress loss caused by the elastic compression of the concrete during batch tensioning, σ*l*3, is considered to be approximately zero.
