## 4 Results
### Simulation Results
#### 4.2.3 Analysis of the Simulation Results  
The difference between the measured and simulated results can depend on material properties, simplifications in the model, insufficient depth of samples and the assumption of the that the temperature in the material is following the boundary temperature.  
Looking at the expected material dependence, from Equation (28) it was obtained:  
\[m_{A}=\frac{\left(\varphi_{b,\max}-\varphi_{b,\min}\right)/2}{2\sqrt{\pi}} \xi\cdot\sqrt{\tau_{p}}\cdot f_{A}\propto\xi\cdot\sqrt{\frac{\delta_{v}^{0}}{ \xi}}\sqrt{\int_{0}^{t_{p}}v_{s}(T(t))\,dt}\cdot f_{A} \tag{37}\]  
\[=\sqrt{\delta_{v}^{0}\xi}\sqrt{\int_{0}^{t_{p}}v_{s}(T(t))\,dt}\cdot f_{A} \tag{38}\]  
\[=b_{v}\sqrt{t_{p}}\sqrt{\overline{v}_{s}}\cdot f_{A}\qquad b_{v}=\sqrt{ \delta_{v}^{0}\xi} \tag{39}\]  
Here, \(b_{v}=\sqrt{\delta_{v}^{0}\xi}\) is the moisture vapour effusivity.  
The formula shows that the slope of the sorption curve and the diffusion coefficient play an equal role for the moisture uptake. The factor \(f_{A}\) calculated previously for all cases is not significant, as it appears to depend weakly on the RH boundary function. The same consideration applies to the square root of the integrated humidity at saturation over the time period. The previous calculation for gypsum showed that the measured value would fit if either of the parameters are increased by 66%. Considering the expression for the effusivity, it also means that a good fit happens when both material properties are increased by \(\sqrt{1.66}=1.29\) i.e., 29% increase. Figure 11 shows the comparison between the experimental _Triangular 12/12h_ case, when this increase of the material properties is applied in the simulation.  
The error estimates in relation to effusivity value gives a maximum of 13.5% higher value, not fully support a 29% higher simulation value required for a good fit. By increasing the effusivity by 66% the peak value of the experimental moisture uptake was still higher than the simulated one. The measurement uncertainty is estimated to be less than 3% which would not explain the differences  
Figure 10: Comparison between measured (blue) and simulated (red) moisture uptake for Gypsum and triangular 12 h/12 h cycles.  
between the measurement and simulations. Another potential uncertainty lies in the surface resistance value. The surface resistance value is especially important for the diurnal variations since the equivalent surface resistance thickness and the periodic penetration depth is closer in magnitude. For gypsum it is round 0.5 mm. The previous calculation shows that for a zero surface resistance, the moisture buffering effect increases by 8%.  
The only material specific part of Equation (39) that gives the amplitude of the moisture uptake is the vapour effusivity \(b_{v}\). By applying the same environmental variations to clay and gypsum by doubling \(b_{v}\), the moisture uptake doubled. On fact, it can be observed that the ratio between the case of gypsum and clay is constant for the same load profile, following the ratio of the effusivity. The measurement give the ratio 0.45 to 0.53 while the simulations 0.48-0.49 for all cases. The variations in the simulation values are due to the small variations in \(f_{A}\).  
In Equation (39) the term that contains the humidity at saturation depends only on the temperature variation. For a certain load profile (Tri or Sine) and time schedule (12/12 h and 72/72 h) this is constant. The ratio basically only depends on the square roots of the time period. Consequently, it can be expected \(\sqrt{6}=2.4494\) times greater moisture buffering effect for the 72/72 h period compared to the 12/12 h variation. The experimental ratio of the moisture uptake between the six days variations and 12/12 h was 2.38-2.92 while simulations gave 2.50-2.56. The variations in the simulation values is due to the small variations in \(f_{A}\).