**1. Introduction**

#### **1.1 The seismic vulnerability assessment**

The ability to assess the vulnerability of residential infrastructure to earthquake damage is undoubtedly one of the most important challenges facing structural engineers. Two methods are typically used to predict earthquake damage: nonlinear finite element analysis (FE) and seismic vulnerability curves. Nonlinear FE analysis is particularly applicable when a detailed damage estimate is required only for a small

number of structures. However, if an estimate is required for the many structures, the process becomes slow and inefficient. Seismic vulnerability curves provide a more efficient method for predicting damage to a class of similar structures. These curves often relate strong ground motion and structural properties to damage.

Vulnerability curves are generally constructed from statistical analyses of historical field data, as example Ref. [1], or analytically simulated data, as Ref. [2]. However, the number of parameters considered when creating vulnerability curves is usually very limited. Research on widespread methods of damage prediction has been scarce. Notable examples include Ref. [3, 4] who used discriminatory analysis to predict the damage to buildings in a classification of two or three damage degrees (DD). Vulnerability studies have recently been conducted using artificial neural networks [5], where the soil movement intensity parameter is correlated with the damage states of type structures, for large-scale risk analysis. In a vulnerability study [6], defined sets of single-degree freedom oscillators and a series of ground motion records using nonlinear time history analysis, and the resulting damage distributions were used to derive sets of fragility functions.

#### **1.2 The two catastrophic earthquakes of September 19: 1985 and 2017**

Many of the seriously damaged buildings during the September 19, 2017, Earthquake (M = 7.1) were medium-height buildings (4–10 stories), with natural periods ranging between 0.7 to 1.4 sec, located in the Lake-bed zone. **Figure 1a** shows the location of the buildings that suffered the greatest damage caused by the 2017

#### **Figure 1.**

*(a) Damaged buildings due to the September 19, 2017, Earthquake: Damage Degree 5 (DD5), Damage Degree 4 (DD4), Damage Degree 3(DD3). (b) Collapsed buildings during September 19, 1985, Earthquake.*

*Probabilistic Seismic Vulnerability and Loss Assessment of the Buildings in Mexico City DOI: http://dx.doi.org/10.5772/intechopen.109761*

earthquake (DD3, DD4, and DD5), while **Figure 1b** shows the location of the collapsed buildings (DD5) for the September 19, 1985, Michoacan Earthquake (M = 8.1); As can be seen, these damages occurred in the same area of the Valley of Mexico for both earthquakes. One of the most vulnerable typologies corresponds to buildings structured with columns of reinforced concrete without girders and supporting a waffle slab, which was built before the September 19, 1985, Earthquake. A complete information statistic of damaged buildings during September 19, 2017, Earthquake, could be founded for example in Ref. [7, 8]. Among the principal causes of buildings damaged were, a) lack of seismic strength; b) structural irregularities, in this case, most configuration problems were associated with the contribution of no-structural elements to the building response, especially in corner buildings; and c) tilting and foundation problems.

This study focuses on the vulnerability assessment of two groups of buildings, the first the structures built before 1985 when the 1976 Mexican Building Code [9] was applicable, and the second includes those built after that date.
