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10 APPENDIX A-2 Constitutive Models General Constitutive models (CMs)1 are an integral part of every site response analysis software, including nonlinear effective-stress site response analysis software. To streamline the CM review process, review of the models was performed concurrently with the review of software. This reduced the list of candidate CMs to models that are coded in (or available as UDM-s) in selected software. Required attributes of the CMs were established prior to the detailed review. Models that meet the required attributes are acknowledged herein. However, for practical reasons, only four of these models could be used in this study. This study focusses of undrained response of silty sands. However, because case histories evaluated in this study included soils other than saturated silty sands, other CMs were used as well. A brief description of these CMs is provided at the end of this Appendix. Preliminary Screening (Reviewed Effective-Stress CMs) Table A-1 lists 18 CMs that are coded in software that meets the criteria of this study. These CMs were reviewed in detail. Basic relevant information is provided in the ânoteâ column of Table A-1. Hyperlinks (denoted by âblueâ font) lead to a more detailed information. Table A-1. Candidate CMs (Active Links are shown in âBlueâ) No. Model Name Note 1 BSH Bounding Surface Hypoplasticity model coded in SUMDES. Developed by Li et al. (1992). 2 Dafalias â Manzari A suite of models that formed a basis for PM4Sand, SANISAND, and P2PSand. Available for use with OpenSees and ABAQUS. See Manzari and Dafalias (1997), and Dafalias and Manzari (2004); 3 GQ/H Developed by Hashash, incorporated in DEEPSOIL, used in research; GQ/H isnot available as DLL for use in other programs. As of October 2019, not commercially- available. 4 I-SOIL Developed by Hashash; available upon request from Hashash (user is required to own a LS-DYNA license). 5 MAT-79 Available in LS-DYNA. Developed by ARUP. As of October 2019, not commercially available. 6 MIT - S1 â 1D Available as a user defined material model in PLAXIS. Total-stress only. 7 MIT - S1 â 3D Available as a user defined material model in PLAXIS. Total-stress only. 1 In this study, a loose definition of âconstitutive modelâ is used which includes modulus reduction curves and elastic-ideal plastic models which would otherwise be disqualifying.
11 8 MKZ Developed by Matasovic (1993); published as Matasovic and Vucetic (1993). Effective-stress model with a total-stress option. Used in practice and research. Implemented in D-MOD/ DMOD2000 and DEEPSOIL. 9 NORSAND NorSand is implemented in RS2 and PLAXIS. RS2 is a program developed by Rocscience, Inc. NorSand is a CSSM model developed for sand that was recently added to RS2. It is intended for modeling static liquefaction. 10 P2P-Sand Developed by Itasca group. Available for use with FLAC. as an UDM. 11 PM4SAND Bounding surface plasticity model (effective-stress coupled) developed by Boulanger and Ziotopolou, 2013a; b). Available as UDM in FLAC, PLAXIS and OpenSees. 12 PDMY02 Nested yield surface plasticity model (effective-stress coupled) developed by Elgamal et al. (2002) and Yang et al. (2008). Based on the framework of Parra (1996) and Yang (2000); Implemented in OpenSees. 13 Prevost This model is a basis for UCSDSAND3 model. Not implemented in any presently available commercial software in its original form. 14 ROTH Linear elastic, perfectly plastic model (effective-stress decoupled) developed by Dr. Wolfgang Roth of Dames & Moore (now AECOM); see Roth and Inel (1993). This is the first effective-stress model implemented in FLAC. It is an adaptation of the Seed et al. (1976) and Seed (1979) pore water pressure model for sand. Fish script is available for FLAC 2D; UDM/dll for FLAC 3D (referenced as âDames-Mooreâ on FLAC UDM page) is available. UDM/dll for FLAC 2D may become available in the future. 15 SANISAND Bounding surface plasticity model (effective-stress coupled) developed by Taiebat and Dafalias (2008). Based on Manzari and Dafalias (1997) model. Available as UDM in FLAC3D. 16 UBCSAND Hyperbolic hardening plasticity model (effective-stress coupled) developed by Beaty and Byrne (1998). Available in FLAC and PLAXIS as UDM. Detailed information can be found in Beaty and Byrne (2011) 17 UCSDSAND3 The UCSDSAND3 (Khosarvifar et al. 2018) soil model implemented into FLAC2D/FLAC3D, LS-DYNA, DIANA and ABAQUS as an UDM. UCSDSAND3 is Based on the Prevost (1985) model. 18 WANG2D and WANG3D Bounding surface plasticity model (effective-stress coupled) developed by Wang (1990); Wang and Ma (2007). 1D version implemented in SUMDES. WANG2D effective-stress model was recently updated by Dr. Wang and is available in FLAC and FLAC3D as UDM. UDM = User Defined Model (used by Itasca; option in FLAC); dll = Dynamic link library; CSSM = Critical State Soil Mechanics. Secondary Screening (Reduced List and Selected Effective-Stress Models) The following are the required attributes of CMs implemented in 1D, 2D, and 3D effective- stress SRA software. In defining these attributes, the Research Team considered âstandard attributes,â but also the availability of generic parameters and information on past calibration of these models against results of cyclic testing (i.e., âelement tests;â see example element test in Section 5). Table A-2. Required Attributes for CMs Requirement Note 1. Can be used in both total and effective-stress modes. 2. Can be calibrated against specialty laboratory test results (e.g., CyDSS and CyTX). 3. Has been implemented in at least one effective-stress SRA program. 4. Can Simulate Dilation (advanced models only). 5. Other (number of parameters; ease of useâ¦). 1. One does not want to change a CM to perform effective-stress analysis; see requirements on calibration in Table 3. 2. Both stress-strain and pore water pressure response test results. 3. A must for effective-stress analysis and assessment of soil liquefaction. 4. Simulation of dilation is a plus, but not a requirement (few CM-s have that option and calibration is very difficult, especially on silty sands). 5. The number of total/default model parameters and/or ease of development of model parameters (ease of use). SRA = Site Response Analysis; CyDSS = Cyclic Direct Simple Shear (test); CyTX = Cyclic Triaxial test; CM = Constitutive Model.
12 After applying the screening criteria presented in Table A-2 to the list of reviewed models listed in Table A-1, a set of candidate models has been identified. This reduced set is presented in greater detail in Table A-3. Relevant, more detailed information about the candidate models included in Table A-3 (included hyperlinks) served as a basis for the final selection. Table A-3. Reduced Set of CMs â Models Selected for use in this Study are highlighted in Bold Text (Active Links are highlighted in âBlueâ) No. Model Name Relevant Information(4)(5) 1 GQ/H Total Number of Model Parameters: 9 Required(2)/Default(3) Parameters: 0/9 Generic Parameters Available: Y 2 I-SOIL Total Number of Model Parameters: 10 Required/Default Parameters: 1/9 Generic Parameters Available: Y 3 MAT-79 Total Number of Model Parameters: 10 Required/Default Parameters: 4/6 Generic Parameters Available: Y 4 MKZ Total Number of Model Parameters: 9 Required/Default Parameters: 0/9 Generic Parameters Available: Y 5 PM4SAND Total Number of Model Parameters: 21 Required/Default Parameters: 3/18 Generic Parameters Available: Y 6 ROTH(1) Total Number of Model Parameters: 5 Required/Default Parameters: 5/5 Generic Parameters Available: Y 7 UBCSAND Total Number of Model Parameters: 15 Required/Default Parameters: 6/9 Generic Parameters Available: Y 8 UCSDSAND3 Total Number of Model Parameters: 12 Required/Default Parameters: 12/10 Generic Parameters Available: Y (1) Available only in FLAC 3D (September 2019). (2) Required: Needs single element simulations to be conducted. (3) Can be determined without a single element simulation. (4) With exception of the ROTH model, all of the CMs presented in Table A-3 can be run in both total- and effective-stress modes. The number of parameters, listed in Table A-2, refers to the effective-stress mode. (5) Parameters of these models can be developed from a stress- or strain-controlled CyDSS test run in a laboratory that has a capability to test over an extended strain range (shear strain between 0.01 and 3.13%). This typically requires mounting of LVDT- s or Proxymeters directly on the specimen cap and instrumentation of the caps with bender elements. With exception of the ROTH model, all of the models listed in Table A-3 can be run in total- and effective-stress modes. All of the models have been calibrated against specialty laboratory test results (i.e., element test). Not all of these models, however, can simulate dilation (only models based upon the theory of plasticity can). Only one of these models (the Matasovic-Kondner- Zelasko, MKZ, model) includes generic sets of parameters for total-stress and effective-stress analyses that can be evaluated based upon soil density, grain size analysis, and soil plasticity. CMs GQ/H, I-SOIL, and MAT-79 are listed in Table A-3 as they may, by the time this study is published, become available.
13 Other CMs used in this Study Because case histories evaluated in this study included soils other than saturated silty sands, other CMs were used in this study as well. These models include the S-I (see Section 3.2), LE- MC, HSsmall, PM4SILT and UCSDCLAY models. Both the LE-MC and HSsmall models are coupled with the S-I model in a manner that is explained below. PM4SILT and UCSDCLAY are advanced CMs, i.e., the theory of plasticity-based models. The LE-MC model is a pressure-dependent linear elastic-perfectly plastic CMs that uses the Mohr-Coulomb failure criteria to describe the yield stress. In FLAC, this model is coupled with the Masing rules (Masing, 1926; see Pyke, 1979 for explanation in English) to form a model that includes hysteretic damping. A detailed description of this model is presented in Itasca (2016). In general, the default behavior of the LE-MC CM is linear elastic pre-yield (i.e., stress state remaining within the Mohr-Coulomb failure envelope) and perfectly plastic thereafter. Pre- and/or post-yield behavior can be modified by the user through parameter inputs and/or by writing a program-specific script (or one can formulate CM as UDM and import into program FLAC as a .dll). For dynamic problems, the built-in hysteretic damping feature can be used to change the pre-yield behavior from linear to nonlinear elastic. In PLAXIS, the Hardening Soil with small strain stiffness (HSsmall) CM is used for most soils. A detailed discussion of the HSsmall, and an example of its application, is provided in Laera and Brinkgreve (2015). In general, the function of the HSsmall CM in PLAXIS is analogous to that of the LE-MC in FLAC when used with hysteretic damping. Inputs include the initial tangent shear modulus and one parameter for the shear modulus reduction curve. This allows for a very basic representation of modulus reduction and damping. The only input for this representation is the strain level âat which the shear modulus degrades to 70 percent of its initial value.â The PM4SILT (Boulanger and Ziotopoulou, 2018) an advanced CMs based upon the PM4SAND model. It can be used to model undrained monotonic and cyclic loading response of low- plasticity silts and clays. The primary input parameters are the undrained shear strength ratio (or undrained shear strength), the shear modulus coefficient, the contraction rate parameter, and an optional post-strong shaking shear strength reduction factor. All secondary input parameters are assigned default values based on a generalized calibration. Secondary parameters that warrant adjustment based on site-specific advanced laboratory test data include the shear modulus exponent, plastic modulus coefficient (adjusts modulus reduction with shear strain), bounding stress ratio parameters (affect peak friction angles and undrained stress paths), fabric related parameters (affect rate of shear strain accumulation at larger strains and shape of stress-strain hysteresis loops), maximum excess pore pressure ratio, initial void ratio, and compressibility index. The PM4SILT is incorporated in FLAC and OpenSees.
14 The UCSDCLAY (Elgamal et al. 2008) is an elasto-plastic CMs which reproduces nonlinear hysteric shear behavior of soil and accounts for accumulation of permanent shear deformation. Soil plasticity is exhibited in the deviatoric stress-strain response. Nonlinear response of soil is formulated based on the multi-surface (nested surfaces) concept, with an associative flow rule. The yield surfaces are of the Von Mises type. The primary input parameters include shear modulus, as well as the yield strain and strength (the shear stress-strain curve). The UCSDCLAY model is incorporated in FLAC, OpenSees, FLAC-3D, and LS-DYNA. Special Models (Pore Water Pressure Dissipation Models) A handful of programs have a separate CMs for pore water pressure dissipation. These include programs developed based upon DESRA (e.g., DESRA-2C, MARDESRA, DESRAMOD, DESRAMUSC), DRAIN2D (e.g., D-MOD and D-MOD2000), and D-MOD (DEEPSOIL). The particular dissipation model (e.g., Martin et al., 1975) requires four parameters including saturated hydraulic conductivity, constrained rebound modulus, and two curve-fitting parameters. Generic values of these parameters, over a relatively wide range of relative densities, are available for sands and silty sands. Other programs either do not include a provision for pore water pressure dissipation or include it as part of the overall model (e.g., programs like FLAC, ABAQUS, PLAXIS, and OpenSees have an option to solve a steady-state seepage problem, which is activated when pore water pressure dissipation is required). Some programs, like LS-DYNA, have a provision for pore water pressure dissipation, but, according to Dr. Elgamal of UCSD, a qualified user, this option did not work (as of 2023). Note on use of CMs The variety of CMs formulations are reviewed and briefly discussed in this Appendix. Users of these models should examine the response of a selected model to assess if the model is capturing the aspects of material behavior important to the problem being analyzed. A user should not assume that a model will perform adequately for all problems, all densities, all stress levels, and/or all loading conditions. Users should perform element test(s) (see Appendix D) to verify that the selected model is performing as expected and explore the imitations of the model. References Beaty, M. and Byrne, P.M. (1998). âAn effective stress model for predicting liquefaction behavior of sand,â In: P. Dakoulas, M. Yegian, and R. D. Holtz (Eds.), Geotechnical Earthquake Engineering and Soil Dynamics III, ASCE Geotechnical Special Publication No. 75, Vol. 1, 766â777. Beaty, M. H. and Byrne, P. M. (2011). âUBCSAND constitutive model version 904aR,â Itasca UDM Web Site, 69.
15 Boulanger, R. W. and Ziotopoulou, K. (2013a). âFormulation of a Sand Plasticity Plane-Strain Model for Earthquake Engineering Applications,â Soil Dynamics and Earthquake Engineering, Vol. 53, pp. 254-267. Boulanger, R. W. and Ziotopoulou, K. (2013b). âCalibration and Implementation of a Sand Plasticity Plane-Strain Model for Earthquake Engineering Applications,â Soil Dynamics and Earthquake Engineering, Vol. 53, pp. 268-280. Dafalias, Y. F. and Manzari, M. T. (2004). âSimple plasticity sand model accounting for fabric change effects,â Journal of Engineering mechanics, 130(6), 622-634. Elgamal, A. W., Yang, Z., and Lu, J. (2004). âA Web-based platform for computer simulation of seismic ground response,â Advances in Engineering Software, 35(5), 249-259. Elgamal, A., L. Yan, Z. Yang, and J. P. Conte. (2008). âThree-Dimensional Seismic Response of Humboldt Bay Bridge Foundation-Ground System,â Journal of Structural Engineering, ASCE, Vol. 134, No. 7, pp. 1165-1176. Khosravifar, A., Elgamal, A., Lu, J., and Li, J. (2018). âA 3D Model for Earthquake-Induced Liquefaction Triggering and Post-Liquefaction Response,â Soil Dynamics and Earthquake Engineering, Vol. 110, pp. 43â52. Li, X., Wang, Z., and Shen, C. (1992), âSUMDES: A nonlinear procedure for response analysis of horizontally-layered sites subjected to multi-directional earthquake loading,â Department of Civil Engineering, University of California, Davis, 86. Manzari, M. T. and Dafalias, Y. F. (1997). âA critical state two-surface plasticity model for sands,â Geotechnique, 47(2), 255-272. doi:https://doi.org/10.1680/geot.1997.47.2.255 Matasovic N. (1993), âSeismic Response of Composite Horizontally Layered Soil Deposits,â Ph.D. Dissertation, Civil Engineering Dept., University of California, Los Angeles, 483 p. Matasovic, N. and Vucetic, M. (1993), âCyclic Characterization of Liquefiable Sands,â ASCE Journal of Geotechnical Engineering, Vol. 119, No. 11, pp. 1805 1822. Parra, E. (1996). âNumerical modeling of liquefaction and lateral ground deformation including cyclic mobility and dilation response in soil systems,â (PhD), Department of Civil Engineering, Rensselaer Polytechnic Institute, Troy, NY., Troy, NY. Roth, W. and Inel, S. (1993). âAn Engineering Approach to the Analysis of VELACS Centrifuge Tests,â Proc. Verifications of Numerical Procedures for the Analysis of Soil liquefaction Problems. Arulanandan and Scott (eds.). AA Balkema, Rotterdam. Seed, B. (1979). âSoil liquefaction and cyclic mobility evaluation for level ground during earthquakes,â Journal of Geotechnical and Geoenvironmental Engineering, 105(ASCE 14380), pp 201-255. Seed, H. B., Martin, P. P., and Lysmer, J. (1976), âPore-water pressure changes during soil liquefaction,â Journal of Geotechnical and Geoenvironmental Engineering, Vol. 102, pp 323- 346.
16 Taiebat, M. and Dafalias, Y. F. (2008). âSANISAND: Simple anisotropic sand plasticity model,â International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 32, No. 8, pp. 915-948. Wang, Z. L. (1990). âBounding surface hypoplasticity model for granular soils and its applications,â Ph.D. Dissertation, University of California, Davis, Davis, California. Wang, Z. L. and Ma, F. G. (2007). âA simple soil model for complex loadings,â Proc. International Symposium on Computational Mechanics. Yang, Z. (2000). âNumerical modeling of earthquake site response including dilation and liquefaction,â PhD Thesis, Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York. Yang, Z., Lu, J., and Elgamal, A. (2008). âOpenSees soil models and solid-fluid fully coupled elements,â User's Manual. Ver, 1, 27 p. https://opensees.berkeley.edu/OpenSees/manuals/usermanual/1501.htm