Thesis DESARROLLO DE UN CÓDIGO DE ELEMENTOS FINITOS PARA MODELAR LA RESPUESTA SÍSMICA DE SUELOS
Date
2016
Authors
KUNCAR GARCÍA, FELIPE ANDRÉS
Journal Title
Journal ISSN
Volume Title
Publisher
Abstract
En las últimas décadas los análisis unidimensionales en el dominio de la frecuencia han sido utilizados ampliamente en el estudio de la respuesta sísmica de suelos. Sin embargo, las múltiples limitaciones que presenta este tipo de análisis ha resultado en que este enfoque ha sido desplazado por los análisis en el dominio del tiempo basados en métodos numéricos (como el método de elementos finitos) y modelos constitutivos formulados en base a la teoría de plasticidad. Este enfoque se encuentra en constante desarrollo debido a la complejidad de la respuesta no lineal del suelo bajo sismos de mediana y alta intensidad. En este sentido, el desarrollo de nuevos modelos constitutivos para suelos de distintas características es un tópico de investigación recurrente en ingeniería geotécnica. En la actualidad, existe una serie de programas computacionales disponibles en el mercado para realizar este tipo de modelación, sin embargo, estos ofrecen posibilidades acotadas de análisis y un tratamiento simplificado de la interacción suelo-fluido en los poros durante la respuesta sísmica. En este contexto, este trabajo de tesis pretende iniciar el desarrollo de un código computacional que posibilite una nueva línea de investigación en el Departamento de Obras Civiles, cuya orientación sea el mejoramiento de las técnicas de modelación numérica de la respuesta sísmica de suelos saturados en el contexto geológico y sísmico nacional.En esta primera etapa de investigación se incorpora, en primer lugar, una relación constitutiva lineal elástica para la modelación del suelo. En segundo lugar, y con el propósito de considerar el comportamiento no lineal de este, se implementa el modelo constitutivo Mohr-Coulomb, basado en la teoría de plasticidad. La implementación de este modelo se lleva a cabo a través del esquema de retorno propuesto por Clausenet al. (2007) que incorpora la superficie de fluencia y el potencial plástico del modelo de manera exacta. La resolución del problema no lineal se lleva a cabo a trav´es del método de Newton-Raphson de rigidez inicial. En el caso del an´alisis est´atico, se implementaadem´as el procedimiento de correcci´on autom´atica del tama˜no del paso decarga propuesto por Van Langen & Vermeer (1990).Para realizar la integraci´on en el tiempo, en el caso del an´alisis din´amico, se implementa el m´etodo de Newmark. Este ofrece la posibilidad de utilizar esquemas de integraci´onincondicionalmente estables e incluir amortiguamiento num´erico en la soluci´on. Por otrolado, y con el prop´osito de incorporar una condici´on de borde artificial que permitatruncar lateralmente el modelo de elementos finitos, se implementa la condici´on deborde viscoso est´andar, propuesta por Lysmer & Kuhlmeyer (1969), que consiste enla inclusi´on de amortiguadores viscosos en los bordes del modelo. Con respecto a laincorporaci´on del registro s´ismico, esta se lleva a cabo a trav´es de la imposici´on deldesplazamiento del sismo en los grados de libertad horizontales de la base del modelo,utilizando para esto el m´etodo de penalizaci´on.Finalmente, el c´odigo permite la modelaci´on de suelos saturados en condici´on no drenada,condici´on que es especialmente relevante en el caso del an´alisis s´ismico. Paraesto se considera el caso completamente no drenado, en donde la formulaci´on u-p, quedescribe la interacci´on entre el esqueleto s´olido del suelo y el fluido en los poros, puede desacoplarse bajo ciertos supuestos. De esta manera, el an´alisis es separado en uno detensiones efectivas y otro de generaci´on de presiones de poros.La validaci´on del c´odigo es llevada a cabo a trav´es de diferentes ejemplos num´ericos,que involucran todas las posibilidades de an´alisis del programa. Para esto, las respuestas obtenidas mediante el c´odigo son comparadas con soluciones anal´iticas y con las respuestas obtenidas mediante un programa comercial de elementos finitos, de ampliouso, llamado Plaxis. Los resultados validan la implementaci´on desarrollada y evidencian que el c´odigo entrega resultados confiables.Como ejemplo de aplicaci´on se desarrolla la modelaci´on de la respuesta de sitio de un dep´osito de suelo ubicado en el centro de Vi˜na del Mar, sometido al terremoto del Maule del 2010, utilizando el c´odigo desarrollado. La caracterizaci´on del suelo se realiza a partir de ensayos de mec´anica de suelos y ensayos geof´isicos disponibles. A trav´es de este ejemplo se muestra que es indispensable la correcta calibraci´on de la mallade elementos finitos, as´i como de los par´ametros que definen el amortiguamiento deRayleigh. Para la modelaci´on del suelo se utiliza tanto el modelo lineal el´astico como elmodelo Mohr-Coulomb y los resultados obtenidos son comparados con los del m´etodo lineal equivalente, as´i como con el espectro de la norma de dise˜no s´ismico de edificios para el caso en estudio.El c´odigo desarrollado representa solo una primera etapa, ya que se espera que este siga evolucionando en trabajos futuros. Teniendo esto en cuenta, y en base al estudio realizado, se proponen futuras lineas de investigaci´on y desarrollo que permitan superarlas limitaciones identificadas y extender las capacidades del programa.
In the last decades, one-dimensional analyzes in the frequency domain have beenwidely used in the study of the seismic response of soils. However, the multiple limitationsof this type of analysis have resulted in the fact that this approach has beendisplaced by time domain analyzes based on numerical methods (such as the finiteelement method) and constitutive models formulated on the basis of theory of plasticity.This approach is in constant development due to the complexity of the nonlinearresponse of the soil under medium and high intensity earthquakes. In this sense, thedevelopment of new constitutive models for soils of different characteristics is a recurrentresearch topic in geotechnical engineering. Currently, there are a number ofcomputer programs available in the market to perform this type of modeling, however,these offer limited possibilities of analysis and a simplified treatment of the soil-porefluid interaction during the seismic response. In this context, this thesis aims to initiatethe development of a computational code that will enable a new line of research in theDepartment of Civil Engineering, whose orientation will be the improvement of numericalmodeling techniques of the seismic response of saturated soils in the geologicaland seismic national context.In this first stage of research an elastic linear constitutive relationship is incorporated,firstly, for the soil modeling. Secondly, and for the purpose of considering the nonlinearbehavior, the Mohr-Coulomb constitutive model, based on the theory of plasticity, isalso implemented. The implementation of this model is performed through the returnscheme proposed by Clausen et al. (2007), which incorporates exactly the yield surfaceand the plastic potential of the model. The resolution of the nonlinear problem iscarried out by the initial stiffness method. For the static analysis case, the automaticstep size correction procedure proposed by Van Langen & Vermeer (1990) is in additionimplemented.In order to integrate in time, in the dynamic analysis case, the Newmark methodis implemented. This offers the possibility to use unconditionally stable integrationschemes and to include numerical damping in the solution. On the other hand, and in order to incorporate an artificial boundary condition that allows truncate laterally thefinite element model, the standard viscous boundary, proposed by Lysmer & Kuhlmeyer(1969), is implemented. This involves the inclusion of viscous dampers at the boundariesof the model. Regarding the incorporation of the seismic record, this is carried outthrough the imposition of the displacement of the earthquake on the horizontal degreesof freedom in the bottom of the model, using for this the penalty method.Finally, the code allows the modeling of saturated soils under undrained condition,a condition that is specially relevant in the case of seismic analysis. For this it isconsidered the completely undrained case, wherein the u-p formulation, which describesthe interaction between the solid skeleton of the soil an the pore fluid, can be decoupledunder certain assumptions. In this way, the analysis is separated into one of effectivestresses and another of pore pressure generation.The code validation is carried out through different numerical examples, involvingall the analysis possibilities of the program. For this, the responses obtained by thecode are compared with analytical solutions and with the responses obtained by acommercial finite element program, of extensive use, called Plaxis. The results validatethe developed implementation and show that the results provided by the code arereliable.As an example of application, the site response of a soil deposit located in the centerof Vi˜na del Mar, subject to the 2010 Maule Earthquake, is modeled using the codedeveloped. The soil characterization is done from soil mechanics and geophysical testavailable. Through this example it shows that it is essential the correct calibration ofboth the finite element mesh and the parameters defining the Rayleigh damping. Forthe soil modeling, both the linear elastic and the Mohr-Coulomb model are used andthe obtained results are compared with those of the equivalent linear method, as wellas with the spectrum of the seismic design code for building, for the case of study.The developed code represents only a first step, as it is expected that it continue evolvingin future works. With this in mind, and based on the study conducted, futureresearches and developments are proposed in order to overcome the identified limitationsand to extend the capabilities of the program.
In the last decades, one-dimensional analyzes in the frequency domain have beenwidely used in the study of the seismic response of soils. However, the multiple limitationsof this type of analysis have resulted in the fact that this approach has beendisplaced by time domain analyzes based on numerical methods (such as the finiteelement method) and constitutive models formulated on the basis of theory of plasticity.This approach is in constant development due to the complexity of the nonlinearresponse of the soil under medium and high intensity earthquakes. In this sense, thedevelopment of new constitutive models for soils of different characteristics is a recurrentresearch topic in geotechnical engineering. Currently, there are a number ofcomputer programs available in the market to perform this type of modeling, however,these offer limited possibilities of analysis and a simplified treatment of the soil-porefluid interaction during the seismic response. In this context, this thesis aims to initiatethe development of a computational code that will enable a new line of research in theDepartment of Civil Engineering, whose orientation will be the improvement of numericalmodeling techniques of the seismic response of saturated soils in the geologicaland seismic national context.In this first stage of research an elastic linear constitutive relationship is incorporated,firstly, for the soil modeling. Secondly, and for the purpose of considering the nonlinearbehavior, the Mohr-Coulomb constitutive model, based on the theory of plasticity, isalso implemented. The implementation of this model is performed through the returnscheme proposed by Clausen et al. (2007), which incorporates exactly the yield surfaceand the plastic potential of the model. The resolution of the nonlinear problem iscarried out by the initial stiffness method. For the static analysis case, the automaticstep size correction procedure proposed by Van Langen & Vermeer (1990) is in additionimplemented.In order to integrate in time, in the dynamic analysis case, the Newmark methodis implemented. This offers the possibility to use unconditionally stable integrationschemes and to include numerical damping in the solution. On the other hand, and in order to incorporate an artificial boundary condition that allows truncate laterally thefinite element model, the standard viscous boundary, proposed by Lysmer & Kuhlmeyer(1969), is implemented. This involves the inclusion of viscous dampers at the boundariesof the model. Regarding the incorporation of the seismic record, this is carried outthrough the imposition of the displacement of the earthquake on the horizontal degreesof freedom in the bottom of the model, using for this the penalty method.Finally, the code allows the modeling of saturated soils under undrained condition,a condition that is specially relevant in the case of seismic analysis. For this it isconsidered the completely undrained case, wherein the u-p formulation, which describesthe interaction between the solid skeleton of the soil an the pore fluid, can be decoupledunder certain assumptions. In this way, the analysis is separated into one of effectivestresses and another of pore pressure generation.The code validation is carried out through different numerical examples, involvingall the analysis possibilities of the program. For this, the responses obtained by thecode are compared with analytical solutions and with the responses obtained by acommercial finite element program, of extensive use, called Plaxis. The results validatethe developed implementation and show that the results provided by the code arereliable.As an example of application, the site response of a soil deposit located in the centerof Vi˜na del Mar, subject to the 2010 Maule Earthquake, is modeled using the codedeveloped. The soil characterization is done from soil mechanics and geophysical testavailable. Through this example it shows that it is essential the correct calibration ofboth the finite element mesh and the parameters defining the Rayleigh damping. Forthe soil modeling, both the linear elastic and the Mohr-Coulomb model are used andthe obtained results are compared with those of the equivalent linear method, as wellas with the spectrum of the seismic design code for building, for the case of study.The developed code represents only a first step, as it is expected that it continue evolvingin future works. With this in mind, and based on the study conducted, futureresearches and developments are proposed in order to overcome the identified limitationsand to extend the capabilities of the program.
Description
Catalogado desde la version PDF de la tesis.
Keywords
ELEMENTOS FINITOS , MODELOS CONSTITUTIVOS , RESPUESTA SISMICA DE SUELOS
