Metodología numérica automatizada para la evaluación de la respuesta dinámica de construcciones prehispánicas de piedra de junta seca en el Perú
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2024-05-28
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Pontificia Universidad Católica del Perú
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El estudio y la conservación del patrimonio de estructuras de piedra es una preocupación mundial, sobre todo,
si estas construcciones están ubicadas en zonas sísmicas. En el Perú -debido a su gran variedad cultural e
histórica- existe un gran número de construcciones de piedra en diferentes sitios arqueológicos, abarcando
varias tipologías constructivas. Lamentablemente, gran parte de estas construcciones aún no han sido
evaluadas estructuralmente, por lo que se desconoce su comportamiento estructural. También, no se cuenta
con una taxonomía de tipologías estructurales y, por ende, diversas características de las construcciones
existentes son desconocidas. Una forma de evaluar el comportamiento dinámico no lineal de estas estructuras
es usando una rigurosa -pero rápida- metodología numérica que reproduzca adecuadamente los diferentes
mecanismos de fallo, basada en la dinámica de cuerpos rígidos bajo el enfoque del método de elementos
finitos.
Como una primera contribución, en este proyecto se presenta una clasificación taxonómica de construcciones
prehispánicas de piedra en el Perú a partir de un estudio de campo. A partir de esta taxonomía, se clasificaron
diversos sitios arqueológicos de las regiones de Puno y Cusco, y se identificaron las tipologías más recurrentes
de estas regiones.
Por otro lado, se elaboraron novedosos códigos en Python, para la obtención del modelo geométrico de
estructuras de junta seca, a partir de las imágenes tomadas por un cámara, o de una fotografía existente
(incluyendo la identificación de las piedras y las juntas por medio de la segmentación de imágenes). Estas
rutinas permiten crear el modelo 3D de cada bloque (piedra), ensamblarlos y exportarlos a un programa de
análisis numérico para evaluaciones posteriores.
Para el desarrollo de la metodología numérica, se propone la dinámica de los cuerpos rígidos bajo el enfoque
del método de los elementos finitos. Cada bloque de piedra se considera como un cuerpo rígido interconectado
con otros bloques mediante interfaces no lineales. Esta metodología es validada usando Abaqus, basado en
los resultados de ensayos experimentales en esta tesis. En la campaña experimental se construyeron tres muros
con bloques de concreto simulando la geometría de estructuras Inca. Los muros fueron construidos sobre una
mesa inclinable y fueron ensayados por volteo fuera de su plano. Luego, se elaboraron modelos numéricos
de estos ensayos, en los cuales se calibraron las propiedades de contacto con tal que simulen correctamente
el comportamiento experimental. Los resultados numéricos del peso, el ángulo de colapso, los
desplazamientos relativos en distintos puntos de la estructura y los mecanismos de colapso fueron muy
similares a los registrados experimentalmente.
Como caso de estudio, se evaluó numéricamente la sección de un muro de contención Inca de Sacsayhuamán,
Cusco, frente a diversas acciones sísmicas. El modelo geométrico completo del muro de piedra se obtuvo
mediante las rutinas de Python. El terreno contenido detrás del muro se representó por partículas de elementos
discretos. Las propiedades del modelo numérico fueron tomadas de la campaña experimental y de calibración,
y las frecuencias predominantes de la estructura se obtuvieron por medio del enfoque de vibraciones. Se
verificó que la estructura puede soportar adecuadamente estos registros sísmicos escalados hasta una
aceleración pico de 0.1 g; sin embargo, la estructura sufre desplazamientos remanentes considerables para
registros escalados superiores o iguales a 0.2g.
Se concluye que la metodología planteada permite evaluar las estructuras piedra de junta seca de una manera
rigurosa, y así conocer si la estructura debe ser intervenida para asegurar su funcionalidad. Se espera que los
resultados de esta tesis doctoral puedan contribuir al estudio de las construcciones patrimoniales de piedra, y
abrir posibilidades de mejora de la metodología ante diversas configuraciones estructurales.
The study and the conservation of stone heritage is a global concern, mainly when these constructions are in seismic zones. Due to its great cultural and historical diversity, Peru has many stone constructions in different archaeological sites, covering different construction typologies. Unfortunately, many of these constructions have not yet been structurally evaluated, so their structural behaviour is unknown. In addition, there is no classification of the stone structural typologies (taxonomy), so the different characteristics of existing constructions are unknown. One way to study the nonlinear dynamic behaviour of these stone structures is to use a rigorous -but fast- numerical methodology to adequately reproduce the different failure mechanisms based on the dynamics of rigid bodies within the finite element method. Then, this work presents a taxonomic classification of prehispanic stone constructions in Peru, derived from a field study, as the first contribution. Based on this taxonomy, several archaeological sites in Puno and Cusco were classified, and the most common typologies of these regions were identified. The research also proposes novel algorithms developed in Python to obtain the geometric model of dry-joint stone structures using images taken by a camera, a mobile phone, or an existing photograph (including identification of stones and joints, named image segmentation). These routines allow the creation of a 3D model of each block (stone), assembling them, and exporting them to a finite element program for further evaluation. Regarding developing a numerical methodology, the dynamic of rigid bodies within the finite element method is proposed here. Each stone block is considered a rigid body interconnected with other blocks through nonlinear interfaces. This methodology was validated using Abaqus, based on the results of experimental tests developed in this thesis. The experimental campaign was carried out on three walls built with concrete blocks, simulating the geometry of the Inca structures. The walls were built on a tilting table and tested by rotating them out of the plane of the wall. Then, numerical models of the tests were developed by considering each stone as a rigid body and calibrating the contact properties to simulate the experimental behaviour correctly. The numerical results in weight, collapse angle, relative displacements at different points of the structure and collapse mechanisms were very similar to those obtained in the experimental campaign. As a case study, a section of an Inca stone wall from Sacsayhuaman, Cusco, was numerically evaluated using various seismic records. The complete geometric model of the stone wall was automatically obtained using the Python routines. Furthermore, discrete element particles represented the soil behind the wall. The properties of the numerical model were obtained from the experimental campaign, and the predominant frequencies of the structure were obtained using the vibration approach. As a result, the structure can adequately support these seismic records scaled up to a peak acceleration of 0.1g. However, it suffers significant residual displacements for scaled records greater than 0.2 g. The proposed numerical methodology allows the rigorous evaluation of dry-jointed stone structures, knowing if the structure should be intervened to ensure its functionality. Therefore, it is expected that the results of this research will be used to study other stone constructions, opening possibilities for improving the methodology for different structural configurations.
The study and the conservation of stone heritage is a global concern, mainly when these constructions are in seismic zones. Due to its great cultural and historical diversity, Peru has many stone constructions in different archaeological sites, covering different construction typologies. Unfortunately, many of these constructions have not yet been structurally evaluated, so their structural behaviour is unknown. In addition, there is no classification of the stone structural typologies (taxonomy), so the different characteristics of existing constructions are unknown. One way to study the nonlinear dynamic behaviour of these stone structures is to use a rigorous -but fast- numerical methodology to adequately reproduce the different failure mechanisms based on the dynamics of rigid bodies within the finite element method. Then, this work presents a taxonomic classification of prehispanic stone constructions in Peru, derived from a field study, as the first contribution. Based on this taxonomy, several archaeological sites in Puno and Cusco were classified, and the most common typologies of these regions were identified. The research also proposes novel algorithms developed in Python to obtain the geometric model of dry-joint stone structures using images taken by a camera, a mobile phone, or an existing photograph (including identification of stones and joints, named image segmentation). These routines allow the creation of a 3D model of each block (stone), assembling them, and exporting them to a finite element program for further evaluation. Regarding developing a numerical methodology, the dynamic of rigid bodies within the finite element method is proposed here. Each stone block is considered a rigid body interconnected with other blocks through nonlinear interfaces. This methodology was validated using Abaqus, based on the results of experimental tests developed in this thesis. The experimental campaign was carried out on three walls built with concrete blocks, simulating the geometry of the Inca structures. The walls were built on a tilting table and tested by rotating them out of the plane of the wall. Then, numerical models of the tests were developed by considering each stone as a rigid body and calibrating the contact properties to simulate the experimental behaviour correctly. The numerical results in weight, collapse angle, relative displacements at different points of the structure and collapse mechanisms were very similar to those obtained in the experimental campaign. As a case study, a section of an Inca stone wall from Sacsayhuaman, Cusco, was numerically evaluated using various seismic records. The complete geometric model of the stone wall was automatically obtained using the Python routines. Furthermore, discrete element particles represented the soil behind the wall. The properties of the numerical model were obtained from the experimental campaign, and the predominant frequencies of the structure were obtained using the vibration approach. As a result, the structure can adequately support these seismic records scaled up to a peak acceleration of 0.1g. However, it suffers significant residual displacements for scaled records greater than 0.2 g. The proposed numerical methodology allows the rigorous evaluation of dry-jointed stone structures, knowing if the structure should be intervened to ensure its functionality. Therefore, it is expected that the results of this research will be used to study other stone constructions, opening possibilities for improving the methodology for different structural configurations.
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Análisis numérico, Análisis estructural (Ingeniería), Construcciones de piedra--Evaluación
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