# Stabilization Methodology in Foundation Soils by ERT-3D Application in Estepona, South Spain
## 3 Case Study
### Damaged Building Analysis
This phenomenon caused the building to swing forward, which caused serious damage to its structure, as can be seen in Figure 4. The foundation of wall A also suffered a small movement in its seat (S1) (Figure 4). Figure 2: (**a**) Structural scheme of the damaged building, formed by three load-bearing walls, A, B, and C, and forged of semi-resistant joists, 24 cm thick. Building foundation scheme formed by three parallel, longitudinal shallow foundations (A, B, C), where the load-bearing walls rest and transmit the structure’s weight. (**b**) Floor plan of the distribution of the damaged building in the slope. Due to the type of movement and structural typology, displacement occurred as shown in Figure 4. When load-bearing walls deform, they collapse, and destruction of the building becomes a major threat. To determine the building deformation as a function of the angular distortion, it was calculated as the differential settlement, defined as the settlement difference between foundations A and C, which were the extreme foundations affected by the settlements,  
Figure 4: Cross-section scheme, presenting the likely behavior of the building’s foundation and structure. There was a differential settlement of the S1 and S2 foundations due to a possible settlement-removal of the soil and the lack of bearing capacity of the resistant subsoil. Displacement occurred through the variable \(\Phi\) = 95 mm, which is the depth B and C have descended, with respect to A. The seat of the foundation for wall A (S1) has lowered a depth of 25 mm, remaining within the admissible limit according to the Spanish Building Technical Code (CTE). Figure 3: The building’s state of conservation in April 2012, after the movement of the subsoil and its shallow foundation. (C—see Figure 2 for reference) Structure of load pilasters and semi-circular arches, a structure that has suffered a decrease in its foundation with respect to the foundations of the load-bearing walls (B) and (A) on Figure 2. This has caused the building to deform and rotate forward. applying the following equation. Knowing that in this case, it was the same height that has descended B and C with respect to A:  
\[\delta_{AC}=S_{A}-S_{C} \tag{4}\]  
where \(\delta_{AC}=\) foundation vertical differential displacement between points A and C; \(S_{A}=\) suffered differential settlement at point A; \(S_{C}=\) suffered differential settlement at point C.  
The equation of angular distortion is also applied [3; 70; 71; 72]:  
\[\beta=\frac{\delta_{AC}}{L_{AC}} \tag{5}\]  
where: \(\beta=\) angular distortion; \(L_{AC}=\) distance between foundation points A and C.  
The Spanish Building Technical Code (2006), also known as CTE, establishes limitations on \(\beta\) movements, according to building structure typology. Studies regarding \(\beta\) began in the 1940s [73] and continue today [74; 75; 76]. The CTE limitation for the \(\beta\) value, for building damages, must be >L/300 for load-bearing walls. In this case, the differential settlement between foundations A and C was \(\delta_{AC}=\) 95 mm and \(\beta=\) 0.0086, which are above the admissible limit established by the CTE, indicating imminent building collapse. Authors also link angular distortion \(\beta\) values with damages suffered in enclosures (shell and internal partitions) and structural elements. The present case exceeded the limit values established by these authors, where the dimensions of cracks in enclosures must be >25 mm to be considered a serious structural risk, according to a programmed damage classification [77]. As shown in Figure 4, this building had serious damage, due to cracks in enclosures and structural elements (load-bearing walls), which were measured at greater than 50 mm. Therefore, according to this classification, the building was close to collapse. Due to the type of structure, foundation, and damages suffered, the methodology proposed in this research seems appropriate for the case.