5.1. SEISMICITY

The seismic activity in Peru has its origin in the friction generated by the subduction process of the Nazca plate under the South American plate and in the internal deformation of both plates (intraplate earthquakes), the latter being the ones with the greatest incidence or danger about the Ayacucho city. Silgado²¹, made an important ordered description of the seismic history of Peru for the period between 1513 to 1974. From it, it has been shown that many of the earthquakes that occurred in Peru were generated outside the Ayacucho city, but due to its destructive nature with magnitudes of up to 8.4 Ms, its waves came to shake the city of Ayacucho, reaching an intensity of IV to V MM. Peru is one of the countries that has little information on the earthquakes that occurred between the 16th century and the 19th century, where the records that are available are usually not representative, since important earthquakes may have occurred in remote regions that were not recorded. It is from 1980 onwards that more information began to be obtained on a large number of seismic records that occurred in Ayacucho, reaching intensities of up to VII on the MSK scale. The areas of the districts of San José de Ticllas, San Pedro de Cachi, Vinchos and Santo Tomas de Pata (very close to the district of Ayacucho) have suffered continuous and high seismic activity, due to the presence of faults and folding of several kilometers in length that have an alignment SE - NW.

A total of twenty-nine seismogenic sources have been used in the present research. Twenty of these were subduction, in which interface mechanisms have been differentiated (F1, F2, F3, F4, F5 and F6), superficial intraplate (F7, F8, F9, F10, F11, F12, F13, F14, F15 and F16) and intermediate (F17, F18, F19 and F20). Similarly, nine continental seismic sources have been used (F21, F22, F23, F24, F25, F26, F27, F28 and F29). Both geometries of these sources are consistent with the subduction model proposed by²².

The geometry of each of these sources (Fig.3) was entered into the program, always keeping the Source is living option selected. Besides, the Software contemplates various types of seismic sources through the Source Type option and for the present study the area type sources were used. Together with the geometry of the source, the size of the rupture area that generates the seismic movement can be defined through the parameters K1 and K2; in the present research, for the definition of these parameters, the model of Singh et al.²³ in all seismogenic sources. In the same way, a single integral part of the source is considered with a thickness equal to zero since they are working with area-type sources.

The seismic recurrence analysis was performed considering the Gutenberg and Richter model²⁴. TABLE I shows seismological recurrence parameters of the twenty-nine seismogenic sources used. Each of these seismological parameters were integrated into R-CRISIS software, additionally, the coefficient of variation β was introduced due to the uncertainty that this parameter may have. In the same way, no standard deviation or uncertainty range of the maximum magnitude is considered (M_max).

In order to determine the seismic response of the ground in a given place produced by a seismic event in a specific source, the attenuation laws are used. In Peru, several attenuation laws have been used, prepared with seismic records from Peru and other countries; a large number of these were analyzed by²⁵ who concluded that, among all the attenuation laws analyzed, they are those of Youngs et al.²⁶ and Sadigh et al.²⁷ which yielded average results of acceleration values and that these are consistent with tectonics and seismotectonics in Peru. Therefore, in order to determine the seismic response in Ayacucho city, the attenuation laws of Youngs et al. for subduction earthquakes and those of Sadigh et al. for continental earthquakes are used.

5.2 SEISMIC MICROZONATION

The study area at the regional level corresponds to the geomorphological unit called Penillanura Disectada. On the other hand, at the local level, the geomorphology of the Ayacucho city is made up of units of ravines and slopes which have given rise to a cover of alluvial deposits that are overlying the sedimentary deposits of the Ayacucho formation. The local geology of Ayacucho city is composed of rocks of sedimentary and volcanic origin whose ages range between the upper Tertiary and the recent Quaternary. Specifically, in study area, the sedimentary deposits of the Ayacucho formation and the alluvial deposits are found in a greater proportion, and in a lesser proportion there are volcanic deposits of the Molinoyocc formation that overlie deposits of the Ayacucho formation.

In order to characterize the soil in Ayacucho city, a large database of soil studies prepared by²⁸ and²⁹ was taken into account. It was possible to collect information on classification, exploration and sampling of soils and rocks, as well as values of soil bearing capacities and some seismic refraction tests. In order to achieve a seismic geotechnical zoning in Ayacucho city, geophysical tests MASW (Multichannel Analysis of Surface Waves) were carried out and allowed to soil characterize from shear wave velocities. Fig. 4 depicts a map of the distribution of seismic refraction probing, as part of the information collected, as well as the MASW probing of the present study.

The MASW method or Multichannel Analysis of Surface Waves allows to determine the stratigraphy of the subsoil under a point indirectly, based on the change in the dynamic properties of the materials that make it up” [³⁰, p. 35]. Each of these tests were carried out at various points in study area, distributed in such a way that the results could be interpolated in order to generate seismic zoning maps. In addition, to achieve this end, the optimal field parameters of a MASW survey established by³¹ were taken into account.

Once the field work was completed, data processing continued. This process consisted of obtaining dispersion curves (a curve that relates phase velocity versus frequency) (Fig. 6) from the seismic wave record obtained in each field scan line (Fig. 5). Then, through an iterative process (inversion method), shear wave velocity profiles (Vs) were obtained using the different modules of the SeisImager/SW program (Fig. 7).

The soil, geological, geotechnical and geophysical studies have made possible to describe the mechanical soil characteristics and its seismic response. With these results, a seismic geotechnical zoning map of Ayacucho city is obtained, as can be shown in Fig. 8. This map presents 3 zones, where the first two are subdivided into A and B. Zone IA differs from zone IB by the type of material and by bearing soil capacity. Zone IIA differs from zone IIB due to the bearing soil capacity and the land slope, where zone IIA presents lower soil resistance and greater slopes. A better description of each zone is shown in TABLE II. This table shows values such as the bearing capacity of the soil obtained from the Meyerhof formula, for which the geomechanical properties of the geological units and direct shear tests were taken into account as part of the information collected. On the other hand, the seismic amplification of the soil obtained from the one-dimensional propagation theory of shear waves in soil deposits is also described, using three recorded input earthquakes as excitation force through the SHAKE program.

5.3 EVALUATION OF THE SEISMIC HAZARD

The seismic hazard curves are determined under the probability theorem: the probability that the intensity I is greater than or equal to a specific value i, is calculated for a possible earthquake at a possible location within the source and then multiplied by the probability that specific magnitude can occur at that location. Then, the process is repeated for all possible magnitudes and locations, to finally add all of them. The calculation of the seismic hazard for a specific place of interest is influenced by the magnitude (m) and the distance (r), being defined by equation (1).

Where P[I≥i/(m,r)] is the probability that the intensity I exceeds a specific value i for a possible earthquake located within the source, and it is obtained through the attenuation relationship. Also, f_M(m) and f_R(r) are the probability density functions for magnitude and distance.

Equation (1) summarizes the theory developed by Cornell³² to analyze seismic hazard. The evaluation of this integral is given by the R-CRISIS software, which was developed by Ordaz et al.³³ in calculating the seismic hazard.

As part of the results of the probabilistic evaluation of seismic hazard, the R-CRISIS program allowed knowing the maximum acceleration of the ground at any point within the study area. For a better representation, in Fig. 9 a map of isoaccelerations of Ayacucho city is presented for a return period of 475 years (design earthquake, according to the E.030 Peruvian Norm). In addition, in TABLE III, the results of the maximum ground accelerations for the different seismic scenarios analyzed are presented.

Another of the results obtained from the use of the R-CRISIS program are the seismic hazard curves, also known as hazard curves, which represent the interrelation between a range of ground motion levels and the probability of exceedance for a given period determined exposure. These seismic hazard curves will be very useful in the seismic risk assessment process when the damage level of buildings is knowing for any other seismic scenario that has not been described in TABLE III. Furthermore, the hazard curves are presented in Fig. 10 for each structural period considering an exposure period of 50 years.

In the same way as the seismic hazard curves, the uniform hazard spectra were obtained, which help the interpretation of the seismic hazard as well as the construction of design spectra. The results of the uniform hazard spectra for each seismic scenario analyzed in this research are shown in Fig. 11. Besides, a spectrum of its own design for Ayacucho city according to Standard Code E.030 can be obtained from the uniform red hazard spectrum (Fig. 11), whose spectral values have the same probability of exceedance (10%) in all structural periods for an exposure period of 50 years.

6.1 VULNERABILITY INDEX

The vulnerability index for confined and adobe masonry structures is calculated as the weighted sum of the numerical values of the factor K_i by the weight factor W_i, of each of the parameters that are considered to characterize the seismic behavior of the structure, as shown in equation (2).

During field data collection, each parameter is assigned to the four A, B, C, D classes, depending on the condition of analyzed parameter, which ranges from A (Optimal) to D (Unfavorable). Where each of these classes corresponds to a numerical value K_i that varies between 0 and 45, this can be seen in TABLE IV. In addition, it can be seen that each parameter is affected by a weight factor W_i, which, according to [³⁵, p. 39], reflects the importance of each of the parameters within the resistant system of the structure.

The evaluation of the vulnerability index for reinforced concrete structures is carried out in a similar way for masonry structures, but in this case only three ratings are assigned (A, B, C), where each assigned class corresponds to a numerical value K_i that varies between -1 and 3, it can be seen in TABLE V. Finally, the vulnerability index is obtained from a weighted sum of the weight factors W_i and K_i considering equation (3).

Finally, the level of vulnerability for both masonry and reinforced concrete is classified according to TABLE VI.

6.2 DATA COLLECTION

In the Ayacucho city it is common to see confined masonry buildings with poor structuring, adobe buildings in poor condition, very old colonial buildings and among many other conditions that show their precariousness, as can be seen in Fig. 13. In this sense, in order to characterize the degree of seismic vulnerability of the building, previously, the data collection of the eleven parameters that encompasses the methodology proposed by³⁴ is carried out, after that, the vulnerability index is calculated from the use of expressions (2) and (3). To achieve this goal, it was necessary to label each block in a cadastral map with a respective number that allows data to be collected in an orderly manner.

Then, the data collection of eleven parameters is carried out using a field evaluation form that allows collecting the information to characterize the vulnerability index. This evaluation form was previously validated by the opinion of experts, who previously carried out research work related to seismic vulnerability and seismic risk. The use of this instrument requires prior knowledge for a correct assignment of classes A, B, C and D that encompasses each of eleven proposed parameters. The evaluation criteria were considered taking into account the recommendations given by³⁶ and³⁷ for masonry buildings, and by¹² for reinforced concrete buildings.

The data of the most representative building in each block was collected taking into account the structural system and the type of material to be evaluated. For each block, three representative buildings were evaluated: one made of adobe, one of confined masonry, and one of reinforced concrete. It was carried out in order to take into account all the types of buildings present in Ayacucho city and that are better classified.

All the information collected in study area was emptied into a database taking into account each structural typology. Likewise, the vulnerability index was calculated in an automated manner and this entire database was stored in a Geographic Information System (ArcGIS) to generate the seismic vulnerability maps.

6.3 EVALUATION OF THE SEISMIC VULNERABILITY

Once the vulnerability index of the buildings had been evaluated, the degree of vulnerability was classified according to structural typology (TABLE VII). These results are shown graphically in Fig. 14, where 80.98% of the adobe buildings have medium vulnerability, being the most prevalent level of vulnerability in the study area. In addition, buildings with high and low vulnerability represent 9.77% and 9.25% respectively. In the case of confined masonry buildings, there is a slight advantage of buildings with medium vulnerability (53.53%) over those with low vulnerability (44.90%) and a minimum percentage of buildings with high vulnerability (1.58%). On the other hand, 100% of the reinforced concrete buildings showed low vulnerability. The general results of TABLE VII show that of the 2078 buildings evaluated: 29.40% have a low vulnerability; 65.26%, medium vulnerability; and 5.34%, high vulnerability.

Additionally, for a better graphical representation of the results, a seismic vulnerability map was obtained at the block level, as shown in Fig. 15. The preponderance of the average vulnerability of the buildings is represented with the color yellow. The blank spaces correspond to markets whose structural system was not analyzed, likewise the cream and light green spaces represent stadiums and parks respectively, where a level of vulnerability was not evaluated due to the fact that there are no buildings.

From Fig. 15, it can be seen that in the central area of Ayacucho city, located around Sucre Park, the buildings have a high and medium vulnerability level for the most part, this as a consequence of the large number of colonial buildings in poor condition and with adobe materials that have cracks due to some seismic movements produced in the city. Likewise, it can be noted that in the peripheral areas located to the west of the city, the buildings also present a high and mostly medium level of vulnerability, and this as a consequence of the disorderly growth of the city whose buildings are self-constructed on land with steep slopes without no slope stability analysis.

7.1 DAMAGE INDEX

There are a variety of methodologies for assessing seismic risk. For instance, it is possible to estimate the level of damage as a function of the maximum structural distortion, where the latter is estimated using the methodology presented in³⁸ and³⁹, supported by⁴⁰. In the present research, the damage level of buildings is estimated using the vulnerability functions, which relate the normalized vulnerability index (I_v) with the damage index (I_D) conditioned by the maximum soil acceleration. The vulnerability functions proposed by Grimaz⁴¹ are used here for adobe buildings (Fig. 16); and those of Quispe¹², for confined masonry and reinforced concrete buildings (Fig. 17).

Once the damage index of each building has been determined, it is necessary to characterize the level of damage to them, for this, TABLE VIII, recommended by the Earthquake Engineering Research Institute of California was used. In this case, the damage index data was obtained in the previous step as a result of vulnerability functions, besides, the structural damage level is considered as: None, Light, moderate, considerable, strong, severe or collapse.

Likewise, a brief definition of structural damage and non-structural elements that each level of damage implies is made, including the repairing structural cost. This allows giving a better idea of the consequences that an eventual earthquake of a certain magnitude can bring.

7.2 EVALUATION OF SEISMIC RISK IN AYACUCHO CITY

In this section, the level of damage is evaluated for four seismic scenarios: frequent, occasional, rare and very rare earthquakes. TABLE IX shows the results of the quantity and percentage of buildings that suffer a certain damage level, depending on the intensity of earthquake. Likewise, the statistical results are presented in Fig. 18.

The results show that when a frequent earthquake is presented (0.14g), it is estimated that 39.7% of total buildings would not suffer any damage; 10.5% of buildings would suffer slight damage, affecting non-structural elements in a general way; 3.0% of buildings would suffer moderate damage, causing significant damage to non-structural elements and affecting structural behavior to a lesser extent. The 11.4% of buildings would suffer considerable damage, where the structural elements would suffer significant damage requiring major repairs; 35.3% of the buildings would suffer a strong damage that implies that the structural elements have very important damages, putting the stability of the structure at risk and where the cost of repair can represent a high percentage of structural cost. Finally, the 0.1% of buildings would suffer severe damage, causing the stability of the structure to be precarious due to great damage in structural elements.

Analogously to the previous considerations, for an occasional earthquake (0.17g), it is estimated that 20.8% of buildings would not suffer any damage; 11.5% would suffer light damage; 15.9%, moderate damage; 5.2%, considerable damage; 45.2%, strong damage; 1.3%, severe damage; and the rest of the buildings would collapse.

Similarly, for a rare or design earthquake (0.31g), it is estimated that 20.1% of the buildings would suffer considerable damage; 30.0%, strong damage; 31.0%, severe damage; and the rest may collapse.

For a very rare earthquake (0.37g), it is estimated that 0.1% of the buildings would suffer considerable damage; 36.1%, strong damage; 18.4%, severe damage; and the rest may collapse.

On the other hand, the highest percentage of buildings would have a strong or severe damage for a design earthquake (0.31g). This can compromise the stability of the structure. In this way, the great risk posed by most of the buildings in Ayacucho city is shown, which would be heavily damaged after an earthquake whose return period is 475 years. In addition, if it is a very rare earthquake, whose return period is 970 years, almost all the buildings would have a damage greater than the strong one, which implies that most of them would be unusable or uninhabitable.

Finally, Fig. 19 plots the seismic risk maps for different seismic scenarios analyzed. From which, it can be seen that the degree of damage is greater each time the seismic intensity (PGA) increases.

From Fig. 19, in accordance with the results of seismic vulnerability, it can be seen that the buildings located in the downtown area of the city are the ones that would suffer the greatest damage due to a seismic movement, these results are more noticeable for the scenarios seismic rare (PGA=0.31g) and very rare (PGA=0.37g) in which it is clearly distinguished that, like the central part of the city, the buildings located in the peripheral areas of urban expansion present the highest levels of damage. From the above precision it can be concluded that the buildings of Ayacucho city with a medium vulnerability level are exposed to strong and severe damage after the occurrence of a rare earthquake and even collapse for a very rare earthquake; Similarly, buildings with a high level of vulnerability are very likely to collapse after the occurrence of an earthquake whose maximum ground acceleration exceeds 0.31g.