Hierarchical Modeling and Simulation of Inelastic, Three...
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Hierarchical Modeling and Simulation of Inelastic, Three Dimensional (3D) Earthquake Soil Structure Interaction Behavior Boris Jeremi´ c and Yuan Feng et al. UCD and LBNL version: 22:32, 5. February, 2018 1
Transcript of Hierarchical Modeling and Simulation of Inelastic, Three...
Hierarchical Modeling and Simulation ofInelastic, Three Dimensional (3D)
Earthquake Soil Structure InteractionBehavior
Boris Jeremic and Yuan Feng et al.UCD and LBNL
version: 22:32, 5. February, 2018
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Contents
1 Introduction 3
2 Inelastic, Nonlinear, Hierarchical Analysis Steps 42.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Free Field 1D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Elastic Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6Elastoplastic Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.3 Free Field 3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Elastic Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9Elastic-Plastic Material. . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.4 Soil-Foundation Interaction 3D . . . . . . . . . . . . . . . . . . . . . . . . . . 12Elastic Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Inelastic Material Model, von-Mises Armstrong-Frederick or von-Mises
G/Gmax Material or Drucker-Prager Armstrong-Frederick or Drucker-Prager G/Gmax Material. . . . . . . . . . . . . . . . . . . . . 12
Contact Elements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Inelastic Soil Material Model and Inelastic Contact . . . . . . . . . . . . 13
2.5 Analysis of a Structure Alone . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5.1 Eigen Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.5.2 Imposed Motion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.6 3D Soil-Structure Interaction . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Elastic Material. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18Inelastic Soil and Inelastic Contact Model. . . . . . . . . . . . . . . . . 18Inelastic, Nonlinear Concrete Structure. . . . . . . . . . . . . . . . . . . 18Simulation using 1D motions. . . . . . . . . . . . . . . . . . . . . . . . 18Simulation using 3D motions. . . . . . . . . . . . . . . . . . . . . . . . 18
3 Summary 18
4 Acknowledgements 18
2
1 Introduction
Inelastic analysis of earthquake soil structure interaction (ESSI) behavior requires expertise in anumber of areas. For example, knowledge of soil and rock mechanics is necessary for propermodeling of dry, partially or fully saturated soil and rock domain under a structure. Interfacebetween structural foundations and the soil/rock beneath is modeled using (soft) contact ele-ments, that can also be dry or saturated. Modeling of structure, made of concrete and/or steel,requires knowledge of structural mechanics. Modeling of systems and components (SCs) withinstructure can also be done with tne same large scale modeling endeavor, although such SCs canalso be modeled separately, de-coupled as they might not contribute in any significant way toESSI of the system. Earthquake motion modeling, that are used for ESSI analysis, represents avery important component of overall modeling approach.
Equally important is the numerical simulation approach used to develop numerical results usingabove developed models. Different finite elements with a variety of mass, damping and stiffnessmatrices, different numerical algorithms for constitutive and global solution advancement, anddifferent finite element meshes will influence results.
Presented here is a step by step, hierarchical approach to modeling and simulation of earth-quake soil structure interaction (ESSI) for a generic concrete building. Approach is based onreliance on numerical modeling and simulation expertise as well as on sound engineering judg-ment.
Input files for all the examples from this section are available online at this LINK. All theexamples can run directly at the Amazon Web Services (AWS), using RealESSISimulator,through Real ESSI image that is available on AWS.
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2 Inelastic, Nonlinear, Hierarchical Analysis Steps
2.1 The Model
Chosen for this exercise is a simple concrete box structure with 3 levels and 2 bays. Structure israther tall, (3× 20m, including roof level) with two bays (2× 15m) and is made of walls/platesthat are 2m thick. Structure is founded on slab foundation that is 5m thick. Concrete foundationis embedded 5m so that top level of the foundation is flush with soil surface.
Beneath the structure is a uniform layer of soil. Interface of concrete foundation and the soilbeneath can slip in friction. Axial, normal contact between concrete and the soil beneath canopen a gap.
Figure 1 shows dimensions of the model. This figure also shows extent of the soil model,
30m
65m
5m3x
20m
2x15m
100m
Soil
DRM Layer
Damping Layers
Contact
5m 10m
45m5m10m
30m
Figure 1: Soil structure model to be analyzed. Full 3D motions, inelastic soil, inelastic contact,inelastic sgtsructure.
together with a layer of finite elements that is used to input earthquake motions into the finiteelement model using Domain Reduction Method (DRM) (Bielak et al., 2003, Yoshimura et al.,2003).
Earthquake motions are characterized by body waves that propagate from the source. Bodywaves interacting with the surface create surface waves. Both body and surface earthquake waveswill excite motions in the soil structure system.
All the models presented are available online. Models can be updated, materials changes, andmaterial parameters updated by the end users. All the models can be analyzed using the RealESSI Simulator (http://real-essi.us/) that is available on Amazon Web Services (https://aws.amazon.com/).
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Figure 2: Finite element mesh of the full model.
Figure 3: Soil structure model to be analyzed. Cut through the full model, showing finite elementmesh on a deformed model.
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2.2 Free Field 1D
First step in model development is the 1D wave propagation analysis. Figure 4 shows a 1Dmode wave propagation model. The model is made up with 3D brick finite elements, that areconstrained with boundary conditions so that only 1D shear waves, polarized in vertical plane,hence SV waves, can propagate. A presence of the DRM layer in the model shown in Figure 4,
Figure 4: 1D wave propagation simulation model.
as well as two layers of finite elements outside of the DRM layer, that are used to support themodel.
Seismic motions used for this 1D analysis are obtained from one component of a full 3Dseismic motions at the surface. Surface motions are then deconvoluted to the DRM layer, andare used to develop DRM forces.
Elastic Material. Analysis of 1D wave propagation using elastic material is first performed.Results obtained with linear elastic material using Real ESSI Simulator can be compared using
analytic 1D wave propagation solution for elastic material. Such analytic solutions are available inbooks (Kramer, 1996, Semblat & Pecker, 2009, Kausel, 2006, 2017), and are also implementedin a number of available programs, such as SHAKE (Idriss & Sun, 1992).
Input files for this models are available at this LINK, and can be directly simulated using RealESSI Simulator (http://real-essi.us/), that is available on Amazon Web Services (https://aws.amazon.com/).
Elastoplastic Material. Elastic plastic analysis of 1D wave propagation can be accomplished onthe very same 1D model, as described in a section above.
Figure 5 shows results at the top of 1D soil column.Response spectrum of motion is shown in Fig. 6.
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Figure 5: 1D, elastic-plastic results for the top of soil column.
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Figure 6: Simulation results: response spectrum at the top of soil.
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Deformed shape of a 1D wave propagating through the model, at particular time instance, isshown in Figure ??. It is noted that a DRM layer, single finite element in this case, is significantlydeformed, as that layer is used to input seismic motions into the model.
Figure 7: 2 Simulation model.
Input files for this models are available at this LINK, and can be directly simulated using RealESSI Simulator (http://real-essi.us/), that is available on Amazon Web Services (https://aws.amazon.com/).
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2.3 Free Field 3D
The very same seismic wave field that is used the previous 1D example, is used for input in thefull 3D finite element model, shown in Figure 8.
Figure 8: 3D simulation model for free field wave propagation modeling.
Although finite element model is full 3D, since the seismic wave field input is 1D, only 1Dwave is expected to propagate, and results should be very similar to the 1D model results.
Two sets of material parameters are used, linear elastic and elastic-plastic.
Elastic Material. Input files for this models are available at this LINK, and can be directlysimulated using Real ESSI Simulator (http://real-essi.us/), that is available on AmazonWeb Services (https://aws.amazon.com/).
Elastic-Plastic Material. Inelastic, nonlinear, elastic-plastic material parameters, are given forvon Mises material model with nonlinear kinematic hardening of Armstrong Frederic type, sameas material model used for the 1D model.
It is important to note that material models for 1D and 3D cases are exactly the same. Thedifference between 1D and 3D models is in model geometry and boundary conditions.
The time series of top surface accelerations and spectra displacements are are shown in Fig. 9.
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Figure 9: Simulation results: acceleration time series.
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The response spectra of top surface motion are shown in Fig. 10.
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Figure 10: Simulation results: response spectrum at soil top.
Deformed shape at a particular time step is shown Fig. 11.
Figure 11: 4 Simulation model.
Input files for this models are available at this LINK, and can be directly simulated using RealESSI Simulator (http://real-essi.us/), that is available on Amazon Web Services (https://aws.amazon.com/).
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2.4 Soil-Foundation Interaction 3D
After 1D annd 3D free field motions are developed, using first linear elastic and then inelasticmaterial models, next step is to add a foundation. The idea is that by adding just a foundationand not a complete foundation-structure system, model is not significantly changed from previousfree field model. Hence, response of the soil foundation system should be similar to the free fieldresponse.
Elastic Material. Initial analysis is using linear elastic model, for soil, for foundation, for thecontact zone, as well as for the structure. Analysis begins with very small motions, in 1D andthen extends to 3D motions, both of which are described later.
Input files for this models are available at this LINK, and can be directly simulated using RealESSI Simulator (http://real-essi.us/), that is available on Amazon Web Services (https://aws.amazon.com/).
Inelastic Material Model, von-Mises Armstrong-Frederick or von-Mises G/Gmax Material orDrucker-Prager Armstrong-Frederick or Drucker-Prager G/Gmax Material. Analysis using in-elastic, nonlinear soil material begins with very small motions. It is expected that such very smallmotions, will produce essentially linear elastic response that should be comparable and very closeto linear elastic response.
It should be noted that depending on complexity of soil behavior and on available test data,different material models can be used for modeling soil, as discussed in Chapter 3. For pressureinsensitive material behavior (total stress analysis for example, von Mises based material modelsare used. When mean stress (mean confining pressure/stress) is important, pressure sensitivemodels need to be used, that are based on versions of Drucker Prager yield surface.
Contact Elements. In addition to inelastic behavior of soil, modeled using elastic-plastic materialmodels for soil solids, contact zone, between foundations and adjacent soil/rock significantlycontributes to the inelastic/nonlinear behavior of the ESSI system.
Addition of contact elements to the ESSI model requires further model verification, as wasdone for addition of inelastic/elastic-plastic models. It is recommended that contact elements beinitially added to a model where all other components are linear elastic. ESSI model with contactelements is initially tested with using very small motions so that contact is not expected to opena gap or slip. Response with no slip can achieved by prescribing large friction angle, that is usedonly to prevent slop. No gap condition cannot be insured, even if the first loading stage if selfweight, since some gaps might open during self weight, however large or small friction angle isused. Another option for initial testing is to apply sticky condition to contact elements, whereplastic slip or gap opening is prevented by contact model implementation.
Once contact elements are verified for very small forces and motions, more realistic materialparameters should be used. For frictional behavior, elastic – perfectly plastic, or elastic – hardeningplastic or elastic – hardening-softening contact constitutive law should be chosen based on contactbehavior test data. Axial contact behavior for concrete and soil/rock is best modeled using softcontact, where axial stress-strain response is a nonlinear function, as described in chapter 7.
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Inelastic Soil Material Model and Inelastic Contact Once both inelastic, elastic-plastic modelingof soil (solids) and contact is verified separately, inelastic models for soil and contact can beintroduced into the finite element model. Again, very small motions or forces should be usedinitially, with expectation of an elastic. Increase in demand (forces or motions) should result inyielding of elastic-plastic soil and contacts. Inelastic response results in reduction of frequenciesand dynamic motions, with a potential increase in permanent deformation after shaking.
40m
5m
100m
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Contact
100m5m 10m
45m
5m10m
30m
Figure 12: 5 Simulation model.
Results of the simulation are shown in Fig. 22.
Figure 13: Soil foundation interaction results.
Input files for all the models in this section are available at this LINK, and can be directlysimulated using Real ESSI Simulator (http://real-essi.us/), that is available on AmazonWeb Services (https://aws.amazon.com/).
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2.5 Analysis of a Structure Alone
In order to verify structural model, it is useful to separate structural model from the soil andanalyze fixed based model.
2.5.1 Eigen Analysis
Eigen analysis of a fixed base structural model should provide a good check of the structuralmodel, natural (eigen) frequencies, and natural (eigen) modes.
30m
65m
5m3x
20m
2x15m
Figure 14: Structure on a fixed based simulation model.
For this particular example, eigen modes and frequencies are given in Figures 15 and 16
Figure 15: Eigen frequencies: f1 = 3.473873Hz f2 = 3.473873Hz f3 = 6.877667Hz (eigen mode1 to 3 from left to right).
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Figure 16: Eigen frequencies: f4 = 11.500571Hz f5 = 11.500571Hz f6 = 12.133523Hz (eigenmodes 4 to 6 from left to right).
Input files for eigen analysis of the fixed base structure are available at this LINK, and canbe directly simulated using Real ESSI Simulator (http://real-essi.us/), that is available onAmazon Web Services (https://aws.amazon.com/).
2.5.2 Imposed Motion
In addition to eigen analysis, fixed base structural model is used to test response of a fixed basestructure. This is important as it provides an opportunity to compare results between differentfinite element programs, some of which can only model dynamics of fixed base structures.l
Fixed based structural model is shown in Figure 17 while deformation during imposed motionsat the base, at one particular time instance, is shown in Figure 18.
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Figure 17: Fiexed base structural model with motions imposed at the base.
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Figure 18: Fixed base structural model, deformation shape during imposed motions at the base.
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Figure 19: Simulation Results: Acceleration Time Series with 1D imposed motion.
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The time series of simulation results is shown in Fig. 19.The response spectrum of motion is shown in Fig. 20.
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Figure 20: Simulation Results: Response Spectrum of Structure Top with 1D imposed motion.
Input files for eigen analysis of the fixed base structure are available at this LINK, and canbe directly simulated using Real ESSI Simulator (http://real-essi.us/), that is available onAmazon Web Services (https://aws.amazon.com/).
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2.6 3D Soil-Structure Interaction
Much like in the case of soil and the foundation alone, full earthquake soil structure interaction(ESSI), with complete model for soil, contacts, foundation and the structure, starts, with verysmall forcing and small motions, expecting essentially linear elastic response.
Elastic Material. Elastic material applies to all components of the system including the soil,contacts (no slip or gapping), foundation and the structure.
Inelastic Soil and Inelastic Contact Model. Inelastic soil modeling uses any of the models thatare appropriate, as discussed in section on soil modeling in chapters 4 and 7 as well as in thischapter.
It is important to note that initially, due to small shakes and/or forcing, elastic response isexpected. With the increase in amplitude of forcing and/or shaking, development of nonlinearresponse is expected, in both soil and the contact zone.
Inelastic, Nonlinear Concrete Structure. Results of the simulation are shown in Fig. 22.
Simulation using 1D motions. The time series of simulation results is shown in Fig. 23.The response spectrum of motion is shown in Fig. 24.Input files for all 3D ESSI models, using 1D seismic motions are are available at this LINK, and
can be directly simulated using Real ESSI Simulator (http://real-essi.us/), that is availableon Amazon Web Services (https://aws.amazon.com/).
Simulation using 3D motions. The time series of simulation results is shown in Fig. 25.The response spectrum of motion is shown in Fig. 26.Input files for all 3D ESSI models, using 1D seismic motions are are available at this LINK, and
can be directly simulated using Real ESSI Simulator (http://real-essi.us/), that is availableon Amazon Web Services (https://aws.amazon.com/).
3 Summary
Step by step, hierarchical approach is advocated. Expertise in a number of fields is necessary,including soil mechanics, structural mechanics, seismology and earthquake motions as well asnumerical analysis and the finite element method. In addition, sound engineering judgement isneeded for proper model development.
All the examples were analyzed using Real ESSI Simulator system Jeremic et al. (2018). Moreinformation about the Real ESSI Simulator system is available at http://real-essi.info/.
4 Acknowledgements
Funding from and collaboration with US-DOE and CNSC is much appreciated.
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30m
65m
5m3x
20m
2x15m
100m
Soil
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Damping Layers
Contact
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Figure 21: 6 Simulation Model.
Figure 22: 7 Simulation Model.
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0 1 2 3 4 5 6 7 8 9Time [s]
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Figure 23: Simulation Results: Acceleration Time Series with 1D motion.
References
Bielak, J., Loukakis, K., Hisada, Y. & Yoshimura, C. (2003), ‘Domain reduction method forthree–dimensional earthquake modeling in localized regions. part I: Theory’, Bulletin of theSeismological Society of America 93(2), 817–824.
Idriss, I. M. & Sun, J. I. (1992), Excerpts from USER’S Manual for SHAKE91: A Computer Pro-gram for Conducting Equivalent Linear Seismic Response Analyses of Horizontally Layered SoilDeposits, Center for Geotechnical Modeling Department of Civil & Environmental EngineeringUniversity of California Davis, California.
Jeremic, B., Jie, G., Cheng, Z., Tafazzoli, N., Tasiopoulou, P., Abell, F. P. J. A., Watanabe,K., Feng, Y., Sinha, S. K., Behbehani, F., Yang, H. & Wang, H. (2018), The Real ESSISimulator System, University of California, Davis and Lawrence Berkeley National Laboratory.http://real-essi.info/.
Kausel, E. (2006), Fundamental Solutions in Elastodynamics, A Compendium, Cambridge Uni-versity Press, The Edinburgh Building, Cambridge CB2 2RU, UK.
Kausel, E. (2017), Advanced Structural Dynamics, Cambridge University Press.
Kramer, S. L. (1996), Geotechnical Earthquake Engineering, Prentice Hall, Inc, Upper SaddleRiver, New Jersey.
Semblat, J.-F. & Pecker, A. (2009), Waves and Vibrations in Soils: Earthquakes, Traffic, Shocks,Construction works, first edn, IUSS Press.
Yoshimura, C., Bielak, J. & Hisada, Y. (2003), ‘Domain reduction method for three–dimensionalearthquake modeling in localized regions. part II: Verification and examples’, Bulletin of theSeismological Society of America 93(2), 825–840.
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Figure 24: Simulation Results: Response Spectrum of Structure Top with 1D motion.
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0 1 2 3 4 5 6 7 8 9Time [s]
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Figure 25: Simulation Results: Acceleration Time Series with 3D motion.
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Figure 26: Simulation Results: Response Spectrum of Structure Top with 3D motion.
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