# Learning from the Past: Parametric Analysis of Cob Walls
## 2 Materials and Methods
### Linear Elastic FEM Analysis  
Linear elastic FEM analyses were performed using ANSYS [34]. It was decided to study the response of the walls subjected to both in-plane as well as out-of-plane behavior due to the multidirectional nature of dynamic actions. For either case, a free-standing cob wall fixed (translational degrees of freedom constrained) at its bottom was simulated. This assumption is justified by the fact that most earthen vernacular buildings in Ireland do not have rigid diaphragm roofs (lack of bond beam, root trusses directly placed on top of cob wall). Thus, cob walls do not present a _\"box-like\"_ behavior and most of the time act individually to support the actions imposed upon them. Moreover, vertical cracks are quite common, especially at the corners (see Figure 3), which would cause the detachment of perpendicular wall connections easing their out-of-plane overturning under horizontal loads. These assumptions were adopted to simulate a general _\"worst-case scenario\"_ in which a cob wall, part of a surviving cob building in Ireland, may be found. When dealing with existing structures that have cultural heritage value, a detailed study of the structure is desirable to avoid the design of over conservative interventions which may endanger the historic fabric [35]. Therefore, the assumptions adopted for specific case studies must be based on the results provided by a structural integrity inspection after which the following may be found:  
* wall interconnectivity (perpendicular walls providing out-of-plane support);
* top restraint at roof level;
* _\"box-like\"_ behavior (provided by a strengthening/retrofitting intervention). Any of these factors would improve the structural response of the building and if they are neglected, the design of the intervention may be too invasive. On the other hand, wall voids and the presence of damage or decay would diminish the structure's capacity. The walls were subjected to their weight, to an external force at their top, simulated as a concentrated mass representing the loads transferred by the roof, and finally, to a horizontal acceleration representing the effects of dynamic loads on the wall. The point  
Figure 3: Vertical cracks in a cob building located in County Kildare, Ireland (pay special attention to the cracks at the corners running all along the wall’s height). mass at the top of the wall was assumed to be that of a thath root with a thickness of 305 mm (including battens) and a self-weight of 450 N/m\({}^{2}\)[36], with a tributary span of 3 m giving a value of 137.6 kg/m for every meter of wall length. The setup of the in-plane and of the out-of-plane models are shown in Figure 4a,b, respectively. The finite element used was the SOLID186 [37] and the constitutive material model adopted was a simple linear elastic model. The response of the structure was monitored with the help of a Mohr-Coulomb stress safety tool. This tool is based on the Mohr-Coulomb theory for brittle materials and uses the principle stress values to determine the occurrence of failure. The yielding safety factor capacity of the material, \(F_{ys}\), is computed with Equation (1) [38]. \[F_{ys}=(\sigma_{1}/S_{yt}+\sigma_{3}/S_{yc})^{-1}, \tag{1}\]  
where \(\sigma_{1}\) and \(\sigma_{3}\) are the maximum and minimum principal stresses, and \(S_{yt}\) and \(S_{yc}\) are the material yielding tensile and compressive strengths. Strictly speaking, the tool provides a distribution of safety factors throughout the model as it bases its calculations on the independent distributions of maximum and minimum stresses and not on the absolute principal stresses, developed most likely at two different locations in the model. Therefore, the minimum value of such a distribution is reported as the minimum factor of safety. The compressive strength of common brittle materials is usually much greater than their tensile strength. In this analysis, this assumption is considered to be valid for cob as well.