## Appendix C Model B3  
In 1995, RILEM TC-107-GCS recommended the B3 model which is based on the statistical analysis of creep and shrinkage data in a computerized data bank involving about 15,000 data points and about 100 test series. The model is an improved version of the earlier models namely BP model and BP-KX model [46; 47]. The prediction of material parameters of B3 model is restricted to the Portland cement concretes, having a 28-day mean cylinder compressive strength varying from 17 to 70 MPa, w/c ratio 0.30-0.85, a/c ratio 2.5-13.5 and cement content 160-720 kg/m\({}^{3}\). For this model  
\[E_{c}(t)=4.734\sqrt{f_{cm}}\sqrt{\frac{t}{4+0.85t}} \tag{105}\]  
The mean shrinkage strain in the cross section  
\[\epsilon_{sh}(t,t_{c})=-\kappa_{h}S(t)\epsilon_{sh\infty} \tag{106}\]  
\[\epsilon_{sh\infty}=\epsilon_{\infty}\frac{E_{c}(607)}{E_{c}(t_{c}+\tau_{sh})}\] with \[\epsilon_{s\infty}=\alpha_{1}\alpha_{2}(0.019w^{2.1}f_{cm}^{-0.28}+270) \tag{107}\]  
\[S(t)=\tanh\sqrt{\frac{t-t_{c}}{\tau_{sh}}} \tag{108}\]\[\tau_{sh}=k_{t}(k_{s}D)^{2}\qquad\text{and}\qquad k_{t}=0.085t_{c}^{-0.08}f_{cm}^{-0.25} \tag{10}\]  
where \(D=2v/s=\) effective cross-section thickness (v/s = volume to surface ratio of the concrete member), \(\alpha_{1}=1\) for type I cement, =0.85 for type II cement, =1.1 for type III cement, \(\alpha_{2}=0.75\) for steam-curing, =1.2 for for sealed or normal curing in air with initial protection against drying, =1.0 for for curing in water or at 100% relative humidity. \(k_{t}\) is a factor given by  
\[k_{t}=8.5t_{c}^{-0.08}f_{cm}^{-1/4} \tag{11}\]  
and \(k_{s}\) is the cross-section shape factor as  
\[k_{s}=\begin{cases}1.0&\text{for \ an infinite slab},\\ 1.15&\text{for \ an infinite cylinder},\\ 1.25&\text{for \ an infinite square prism},\\ 1.30&\text{for \ a sphere},\\ 1.55&\text{for \ a cube}.\end{cases} \tag{12}\]  
The average compliance function is expressed as  
\[J(t,t_{0})=q_{1}+C_{0}(t,t_{0})+C_{d}(t,t_{0},t_{1}) \tag{13}\]  
in which \(q_{1}=\) instantaneous strain due to unit stress, \(C_{0}(t,t_{0})=\) compliance function for basic creep, and \(C_{d}(t,t_{0},t_{1})=\) additional compliance function due to simultaneous drying.  
\[C_{0}(t,t_{0})=q_{2}Q(t,t_{0})+q_{3}\text{ln}[1+(t-t_{0})^{0.1}]+q_{4}\text{ln }\frac{t}{t_{0}} \tag{14}\]  
\[Q(t,t_{0})=\frac{\left[1+\left(\frac{\left(0.086(t_{0})^{2/9}+1.21(t_{0})^{4/9 }\right)^{-1}}{(t_{0})^{-1/2}\text{ln}[1+(t-t_{0})^{0.1}]}\right)^{1/7(t_{0}) ^{0.12}+8}\right]^{\frac{-1}{1/7(t_{0})^{0.12}+8}}}{0.086(t_{0})^{2/9}+1.21(t_{ 0})^{4/9}} \tag{15}\]  
\[C_{d}(t,t^{\prime},t_{0})=q_{5}[e^{-8(1-(1-h)S(t))}-e^{-8(1-(1-h)S(t^{\prime} _{0}))}]^{1/2} \tag{16}\]  
where \(t^{\prime}_{0}=\text{max}(t^{\prime},t_{0})\) if \(t\geq t^{\prime}_{0}\), otherwise \(C_{d}(t,t^{\prime},t_{0})=0\); \(t^{\prime}_{0}\) is the time at which drying and loading first act simultaneously.  
The creep coefficient is calculated by the following expression:  
\[\phi(t,t_{0})=E_{c}(t_{0})J(t,t_{0})-1 \tag{17}\]  
The model parameters can be estimated from the concrete strength and composition according to the following formulae  
\[q_{1}=\frac{0.6\ \times\ 10^{-6}}{4734\sqrt{f_{cm}}},\qquad q_{2}=18 5.4c^{0.5}f_{cm}^{-0.9},\qquad\ q_{3}=0.29(w/c)^{4}q_{2}\] \[q_{4}=20.3(a/c)^{-0.7},\qquad q_{5}=7.57\ \times\ 10^{5}f_{cm}^{-1}|e_{ sh\infty}|^{-0.6} \tag{18}\]