## 2 Materials and Experimental Methods
### Microindentation for Creep Response Evaluation  
A Shimadzu DUH-211S dynamic micro-indentation machine (Figure 2) was used to evaluate the creep response of cementitious composites. The machine was equipped with a Berkovich indenter that has a conical angle of 115\({}^{\circ}\). Each sample was held under a constant loading rate of 20 mN/s until a maximum load of 1500 mN was achieved. Next, this force was kept constant for 600 s to replicate creep conditions. For each case, ten indentations were performed by varying the locations. Four replicate samples were tested for each case.  
Figure 1: Universal testing machine compression test setup.  
For indentation analysis, [PERSON] [42] has provided the load penetration depth equation for an axisymmetric probe. The contact stiffness can be determined by differentiating the Galin penetration equation as seen in Equation (1) [42; 58].  
\[S=\frac{dP}{dh}=\beta(\theta,\theta)\frac{2}{\sqrt{\pi}}E_{eff}\sqrt{A_{c}} \tag{1}\]  
where \(E_{eff}\) is the effective modulus (indentation modulus) and \(A_{c}\) is the area of contact. The correction factor, \(\beta(\theta,\theta)\), is 1.034 for a Berkovich indenter. This method originates from the Bulychev-Alekhin-Shorshoro (BASh) equation to determine Young's Modulus using nanoindentation [59]. The relationship between effective modulus (\(E_{eff}\)) and contact stiffness (\(S\)) as per [PERSON]'s Equation [41] is given as:  
\[E_{eff}=M=\frac{\sqrt{\pi}S}{\beta(\theta,\theta)\sqrt{A_{c}}} \tag{2}\]  
The slope of the unloading curve of the force-displacement graph represents the contact stiffness from the indentation test. The contact area of the microindenter is determined by:  
\[A_{c}=\pi(h_{c}tan\theta)^{2} \tag{3}\]  
where \(h_{c}\) is the contact depth along the vertical axis and \(\theta\) is the effective conical angle of the indenter. Equation (4) relates the effective modulus to the moduli of the material and indenter tip [41].  
\[\frac{1}{E_{eff}}=\frac{1-\theta_{in}^{2}}{E_{in}}+\frac{1-\theta^{2}}{E_{it}} \tag{4}\]  
where \(E_{in}\) and \(v_{in}\) are the elastic modulus and Poisson's Ratio of the rigid indenter tip, respectively. For the Shimadzu DUH-211S indenter \(E_{in}\) and \(v_{in}\) are given as 1140 GP and 0.07, respectively. \(E_{it}\) is [PERSON]'s modulus of the material of interest, and \(v\) is Poisson's Ratio of the cement paste. During dwell time the penetration depth of the indenter increases in relation to the creep response. Plasticity is induced at every stage of loading due to the sharp corners of the indenter. The contact creep compliance is given as a function \(L(t)\) seen in Equation (5) [60].  
\[L(t)-L(0)=\frac{2a_{c}\Delta h(t)}{P_{max}}\hskip 28.452756 ptL(0)=\frac{1}{M_{0}} \tag{5}\]  
Figure 2: Microindentation test setup.  
where \(a_{c}\) is contact radius, \(\Delta h(t)\) is time-dependent indentation depth, \(P_{max}\) is the maximum load, and \(M_{0}\) is indention modulus. Equation (6) describes the logarithmic function of \(\Delta h(t)\) that was introduced by [PERSON] during the holding phase [2; 61].  
\[\Delta h(t)=x_{1}\ln(x_{2}t+1) \tag{6}\]  
Substituting \(\Delta h(t)\) into Equation (5), the following expression is obtained:  
\[L(t)-\frac{1}{M_{0}}=\frac{2a_{c}x_{1}\ln(x_{2}t+1)}{P_{max}}=\ \frac{\ln(t/\tau+1)}{C} \tag{7}\]  
where \(C\) is the contact creep modulus and \(\tau\) is the time characteristic given by:  
\[C=\frac{P_{max}}{2a_{c}x_{1}}\ \ \ and\ \ \tau=\frac{1}{x_{1}} \tag{8}\]  
The time characteristic is a long-term creep dominator in the logarithmic model that was created by [PERSON] [2; 61].