## 3 Identification of Polymer Creep Properties Based on Macroscopic Creep Tests
### Hourly-Repeated Ultra-Short Creep Tests on Polymer-Modified Cement Pastes  
In order to characterize the creep behavior of polymer-modified cement pastes, hourly-repeated three-minute-long creep tests were carried out during the first week after production [9]. The raw materials used for the tests were a commercial Portland cement CEM I 42.5 N, distilled water and two chemically different polymers (in the form of aqueous polymer dispersions); see Table 1 for elasticity constants and [9] for more details on physical properties. A reference cement paste, without polymers, and two polymer-modified cement pastes (modified either by polymer P1 or P2) were produced, with a polymer-to-cement mass ratio amounting to \(p/c=0.10\). The water-to-cement ratio of all mixes amounted to \(w/c=0.40\) and accounts for both the distilled water and the water added via the polymer dispersion. The tests were carried out at a constant temperature of 20 \({}^{\circ}\)C.  
Creep testing followed the protocol of [PERSON] et al. [19]. Cylindrical specimens with a diameter of 70 mm and a height of 300 mm were produced and subjected, once every hour, to three-minute-long uniaxial compressive creep tests. The test series was started 21 h after production and finished seven days later. Thus, each specimen was subjected to 168 short-term creep tests. The compressive tests were carried out inside a temperature-controlled chamber at 20 \({}^{\circ}\)C. A universal testing machine of type ZwickRoell Z050 was used. Two metal cylinders at the top and the bottom of the specimens ensured uniaxial load introduction; see [9; 19; 56] for experimental details. In order to characterize the linear creep behavior, and in order to avoid damage of the specimens, the load levels were chosen to be considerably smaller than the compressive strength at the time instant of testing. As for the plain cement paste reference, the load levels were chosen to be smaller than or equal to 15 % of the compressive strength, whereby the strength was quantified based on the validated multiscale model described in [30]; see Figure 2a. As for the polymer-modified cement pastes, no predictive strength model is available. However, most polymer-modified concretes exhibit a smaller compressive strength than their unmodified counterparts, particularly for \(p/c\)-ratios larger than 0.05 [57; 58]. Therefore, the load levels were chosen to be smaller than or equal to 7.5% of the compressive strength of the plain cement paste, reached at the same hydration degree; see Figure 2.  
From the total deformations, measured by means of five inductive displacement transducers (LVDTs), the evolution of the viscous creep strains was quantified, considering that significant creep strains develop already during the very short loading phase, i.e., before reaching the load plateau; see [19] for details. The obtained viscous creep strains of the polymer-modified cement pastes are up to four-times larger than that of the plain paste; see Figure 3. With the increasing degree of hydration, which was measured by means of quasi-isothermal calorimetry [9], the differences between the two modified pastes, on the one hand, and the unmodified paste, on the other hand, decrease. Notably,  
Figure 2: Compressive loading prescribed during the ultra-short creep tests: (**a**) prescribed maximum forces applied to the plain and polymer-modified cement pastes; and (**b**) load history applied to the plain cement paste at an age of 35 h, including a holding plateau with a duration of 180 s.  
the macroscopic viscous creep strains of the cement paste samples can be perfectly fitted by means of power-law-type creep functions [9], defined as:  
\[J_{v,cp}^{\text{exp}}(t-\tau)=\frac{1}{E_{c,cp}^{\text{exp}}}\left(\frac{t-\tau} {t_{\text{ref}}}\right)^{\beta_{cp}^{\text{exp}}}. \tag{16}\]  
where \(E_{c,cp}^{\text{exp}}\) and \(\beta_{cp}^{\text{exp}}\) denote the cement paste-related creep modulus and the power-law exponent.