Calibrations of the PM4Silt constitutive model are presented for two low-plasticity fine-grained soils that exhibit significantly different cyclic loading be-haviors. The PM4Silt model is a stress-ratio controlled, critical state compatible, bounding surface plasticity model that was recently developed for representing low-plasticity silts and clays in geotechnical earthquake engineering applications. The low-plasticity clayey silt and silty clay examined herein were reconstituted mixtures of silica silt and kaolin with plasticity indices (PIs) of 6 and 20. Un-drained monotonic and undrained cyclic direct simple shear (DSS) tests were per-formed on normally consolidated, slurry deposited specimens. Calibration of the PM4Silt model was based on the monotonic and cyclic DSS test data, plus em-pirical relationships for strain-dependent secant shear moduli and equivalent damping ratios. The calibration process and performance of the PM4Silt constitu-tive model are described for each soil. The results illustrate that PM4Silt is capa-ble of reasonably approximating a range of monotonic and cyclic loading behav-iors important to many earthquake engineering applications and is relatively easy to calibrate.
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PM4Silt (Version 1): A silt plasticity model for earthquake engineering applications
The PM4Silt plasticity model for representing low-plasticity silts and clays in geotechnical earthquake engineering applications is presented herein. The PM4Silt model builds on the framework of the stress-ratio controlled, critical state compatible, bounding surface plasticity PM4Sand model (version 3) described in Boulanger and Ziotopoulou (2015) and Ziotopoulou and Boulanger (2016). Modifications to the model were developed and implemented to improve its ability to approximate undrained monotonic and cyclic loading responses of low-plasticity silts and clays, as opposed to those for purely nonplastic silts or sands. Emphasis was given to obtaining reasonable approximations of undrained monotonic shear strengths, undrained cyclic shear strengths, and shear modulus reduction and hysteretic damping responses across a range of initial static shear stress and overburden stress conditions. The model does not include a cap, and therefore is not suited for simulating consolidation settlements or strength evolution with consolidation stress history. The model is cast in terms of the state parameter relative to a linear critical state line in void ratio versus logarithm of mean effective stress. 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 are most likely to warrant adjustment based on site-specific 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 model is coded as a user defined material in a dynamic link library (DLL) for use with the commercial program FLAC 8.0 (Itasca 2016). The numerical implementation and DLL module are described. The behavior of the model is illustrated by simulations of element loading tests covering a range of conditions, including undrained monotonic and cyclic loading under a range of initial confining and shear stress conditions. The model is shown to provide reasonable approximations of behaviors important to many earthquake engineering applications and to be relatively easy to calibrate.
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- Award ID(s):
- 1635398
- NSF-PAR ID:
- 10079691
- Date Published:
- Journal Name:
- Report No. UCD/CGM-18/01, Center for Geotechnical Modeling, Department of Civil and Environmental Engineering, University of California, Davis, CA, 108 pp.
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Summary Liquefaction is associated with the loss of mean effective stress and increase of the pore water pressure in saturated granular materials due to their contractive tendency under cyclic shear loading. The loss of mean effective stress is linked to loss of grain contacts, bringing the granular material to a “semifluidized state” and leading to development and accumulation of large cyclic shear strains. Constitutive modeling of the cyclic stress‐strain response in earthquake‐induced liquefaction and post‐liquefaction is complex and yet very important for stress‐deformation and performance‐based analysis of sand deposits. A new state internal variable named strain liquefaction factor is introduced that evolves at low mean effective stresses, and its constitutive role is to reduce the plastic shear stiffness and dilatancy while maintaining the same plastic volumetric strain rate in the semifluidized state. This new constitutive ingredient is added to an existing critical state compatible, bounding surface plasticity reference model, that is well established for constitutive modeling of cyclic response of sands in the pre‐liquefaction state. The roles of the key components of the proposed formulation are examined in a series of sensitivity analyses. Their combined effects in improving the performance of the reference model are examined by simulating undrained cyclic simple shear tests on Ottawa sand, with focus on reproducing the increasing shear strain amplitude as well as its saturation in the post‐liquefaction response.
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This paper presents a summary of the element test simulations (calibration simulations) submitted by 11 numerical simulation (prediction) teams that participated in the LEAP-2017 prediction exercise. A significant number of monotonic and cyclic triaxial (Vasko, An investigation into the behavior of Ottawa sand through monotonic and cyclic shear tests. Masters Thesis, The George Washington University, 2015; Vasko et al., LEAP-GWU-2015 Laboratory Tests. DesignSafe-CI, Dataset, 2018; El Ghoraiby et al., LEAP 2017: Soil characterization and element tests for Ottawa F65 sand. The George Washington University, Washington, DC, 2017; El Ghoraiby et al., LEAP-2017 GWU Laboratory Tests. DesignSafe-CI, Dataset, 2018; El Ghoraiby et al., Physical and mechanical properties of Ottawa F65 Sand. In B. Kutter et al. (Eds.), Model tests and numerical simulations of liquefaction and lateral spreading: LEAP-UCD-2017. New York: Springer, 2019) and direct simple shear tests (Bastidas, Ottawa F-65 Sand Characterization. PhD Dissertation, University of California, Davis, 2016) are available for Ottawa F-65 sand. The focus of this element test simulation exercise is to assess the performance of the constitutive models used by participating team in simulating the results of undrained stress-controlled cyclic triaxial tests on Ottawa F-65 sand for three different void ratios (El Ghoraiby et al., LEAP 2017: Soil characterization and element tests for Ottawa F65 sand. The George Washington University, Washington, DC, 2017; El Ghoraiby et al., LEAP-2017 GWU Laboratory Tests. DesignSafe-CI, Dataset, 2018; El Ghoraiby et al., Physical and mechanical properties of Ottawa F65 Sand. In B. Kutter et al. (Eds.), Model tests and numerical simulations of liquefaction and lateral spreading: LEAP-UCD-2017. New York: Springer, 2019). The simulated stress paths, stress-strain responses, and liquefaction strength curves show that majority of the models used in this exercise are able to provide a reasonably good match to liquefaction strength curves for the highest void ratio (0.585) but the differences between the simulations and experiments become larger for the lower void ratios (0.542 and 0.515).more » « less
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