# Learning from the Past: Parametric Analysis of Cob Walls
## 3 Results and Discussions
### Macro-Element In-Plane Analysis Taking into Account the Compressive Strength of the Material  
As it was observed in the parametric analysis of the previous sub-section that the thickness of the wall does not influence its in-plane response (the results of that parametric analysis confirmed the expected behavior based on the plane stress assumption), it was decided to ignore that parameter for the macro-element in-plane analysis taking into account the compressive strength of the materials. The compressive strength of the material was introduced as a categorical parameter with two levels representing both the yield and the ultimate compressive strength of cob (see Table 1). Therefore, the DOE using a CCD with two continuous factors (height and length) and one categorical factor (compressive strength) consisted of eight cube points, ten center cube points, and eight axial points. It used a value for the distance of the axial points equal to 1.41421 to ensure rotatability, and generated 26 design points.  
The minimum value computed for \(\alpha\) is equal to 0.31. This value was obtained for a wall with 2.43 m height, 1.76 m length (a length of 1.76 m is outside the range of values adopted, it is automatically generated by using the specified axial spacing value), and a compressive strength of 0.48 MPa. A mass seismic multiplier of 0.31 corresponds to a lateral acceleration of 3.041 m/s\({}^{2}\) or to a PGA of 0.31 g. This level of acceleration corresponds to the lower range of values for high-seismic-hazard areas. As the higher the compressive strength of the material, the smaller the value of \(t\), it was expected that the response would also be influenced by this parameter. Effectively, a directly proportional relationship exists between cob's compressive strength and \(\alpha\).  
The full quadratic model was refined by removing those non-significant terms. Thus, the expression shown in Equation (14) was obtained for a compressive strength of 0.48 MPa and the expression shown in Equation (15) was obtained for a compressive strength of 1.59 MPa.  
\[\alpha_{0.48}=1.328+0.414L_{small}-1.169H_{small}+0.237H_{small}^{2}-0.091L_{ small}H_{small}, \tag{14}\]  
Figure 11: Response surface for the in-plane mechanism assuming infinite compressive strength.  
\[\alpha_{1.59}=1.468+0.414L_{small}-1.169H_{small}+0.237H_{small}^{2}-0.091L_{small}H _{small}, \tag{15}\]  
If Equations (14) and (15) are evaluated for a wall height of 3.05 m and a length of 3.00 m, then, \(\alpha_{0.48}=0.377\) and \(\alpha_{1.59}=0.516\). This indicates that under the most adverse combination of values for the geometric parameters explored, and based on the assumptions adopted, a cob wall would have to be subjected to an acceleration of 4.00 m/s\({}^{2}\) or 0.408 g to generate the out-of-plane mechanism if the yield compressive strength value is taken into account, and would have to be subjected to an acceleration of 4.69 m/s\({}^{2}\) or 0.478 g to generate the out-of-plane mechanism if the ultimate compressive strength value is taken into account. As these levels of acceleration correspond to the upper range values for a high-seismic-hazard area, and since Ireland is located in a low-seismic-hazard area, it can be concluded that the in-plane mechanism analyzed would not form in Irish surviving cob walls.  
Equations (14) and (15) were also used to create the response surfaces shown in Figure 12 for values of compressive strength of 0.48 MPa and 1.59 MPa. The response surfaces show information regarding the effect of two input parameters, wall height and length, on the response, \(\alpha\). These response surfaces reflect the quadratic effect the input parameters have on the response.