UBCHYST- A TOTAL STRESS HYSTERETIC MODEL Abstract
UBCHYST (Byrne and Naesgaard 2010) has been developed at University of British Columbia for dynamic analyses of soil subjected to earthquake loading. In order to speed up the computations the FISH source code was converted to C++ and compiled as a DLL. This report briefly presents the numerical implementation of the UBCHYST constitutive model into the FLAC program. 1.
Soil constitutive model
UBCHYST (Byrne and Naesgaard 2010) model is intended to be used with “undrained” strength parameters in low permeability clayey and silty soils, or in highly permeable granular soils where excess pore water would dissipate as it is generated. The model has been implemented in the two dimensional finite difference program FLAC (Itasca, 2011).
Figure 1. UBCHYST model key variables (from Byrne and Naesgaard 2010).
The essence of this hysteretic model is that the tangent shear modulus (
) is a function of the peak shear
) times a reduction factor that is a function of the developed stress ratio and the change in
modulus (
stress ratio to reach failure. This function is as shown in equation (1) and illustrated in Figure 1.
1 123 Where
stress ratio
⁄ ́ 1
(1)
= stress ratio ⁄ ́ since last reversal = maximum stress ration ( at last reversal = change in stress ratio to reach failure envelope in direction of loading sin cos ⁄ ́ = developed shear stress in horizontal plane ́ = vertical effective stress = peak friction angle , and are calibration parameters with suggested default values 1, 1 and 2 respectively. 1= a reduction factor for first-time or virgin loading (typically 0.6 to 0.8) 2= optional function to account for permanent modulus reduction with large 1 0.1 3= optional function to account for cyclic degradation of modulus with strain or number of cycles, etc. Stress reversals occur if the absolute value of the mobilized stress ratio (η) is less than the previous value and a cross-over occurs if
changes sign. A stress reversal causes
η1 to
be reset to 0 and
to be
recalculated. However, the program retains the previous reversals (η1old and η1fold) so that small hysteretic loops that are subsets of larger loops do not change the behavior of the large loop (Figure 1). With the above equation the tangent shear modulus varies throughout the loading cycle to give hysteretic stressstrain loops with the characteristics illustrated in Figure 1. 2.
Implementation
The original UBCHYST’s FISH source code (Byrne and Naesgaard 2010).was rewritten, optimized, and compiled in C++ in order to maximize the computational speed. The input variables for the UBCHYST model are:
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•
∆ , which is determined by the solver for each computational step by means of the equation of motion and by means of the stress state , which The tensor of the increments of the total strains
has been evaluated using the constitutive law in the previous step. • •
which has been evaluated in the previous step. The stress ration parameters such as , , , and which have been evaluated in the The tensor of the stresses
previous step. The output variables are: • • •
. The new stress ration parameters , , , and . The new tensor of the stresses
The shear modulus using equation 1.
The numerical implementation of the UBCHYST model can be subdivided into three principal blocks: •
evaluation of the first trial elastic stresses;
•
evaluation of plastic corrections;
•
update of the stress ratio parameters;
•
update the moduli (i.e. shear and bulk).
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3.
Model input parameters
List of the parameters associated with UBCHYST model and their corresponding symbols in the DLL version is presented in Table 1. Table 1. UBCHYST input parameters.
4.
Parameter description
Symbol used in constitutive model
Cohesion
hcoh
Friction angle
hfric
Dilation angle
hdil
Tensile strength
hten
Small strain max. shear modulus
hgmax
Bulk modulus
hk
Hysteretic parameter
hn
Hysteretic parameter
hrf
Hysteretic parameter
hrm
Hysteretic parameter
hdfac
Atmospheric pressure
hpa
Soil parameter calibration
The model was calibrated by comparing uniform cyclic response to that inferred from published modulus reduction and damping curves (i.e. Darendeli, 2001) as shown in Figure 2 and/or by comparison to the results of cyclic simple shear laboratory tests for cohesionless soil (sand). The simple shear test is preferred over triaxial loading because the loading path with rotation of principal axes, etc. more closely resembles the stress path from earthquake loading. As Show in in Figure 2a The UBCHYST model best matches to the Darendeli (2001) modulus reduction curves. However, the model did overestimate the damping response at medium to large (>0.1%) shear strains (Figure 2b). The reason for this overestimation of damping factor appeared to be due to width of the hysteresis loop in the UBCHYST model. The calibrated parameters have been used for next step of calibration as described below. The calibrated parameters for cohesionless soil (Sand) for different effective vertical stresses (0.25, 1, 4, 16 atm) are summarized at Table 2.
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1.2
1
0.8
σo'
= 0.25 atm
σo'
= 1.0 atm
σo'
= 4.0 atm
σo'
= 16 atm
FLAC-0.25atm
x a m0.6 G / G
FLAC-1atm FLAC-4atm FLAC-16atm
0.4
0.2
0 1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
Shearing Strain (%)
(a) 25
20
% , 15 g n i p m a10 D
σo'
= 0.25 atm
σo'
= 1.0 atm
σo'
= 4.0 atm
σo'
= 16 atm
FLAC-0.25atm FLAC-1atm FLAC-4atm FLAC-16atm
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0 1.00E-04
1.00E-03
1.00E-02
1.00E-01
1.00E+00
Shearing Strain, %
(b) Figure 2. (a) Modulus reduction and (b) Damping ratio curve estimated by FLAC using UBCHYST
model for cohesionless soil (sand).
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Table 2. Initial input parameters for the UBCHYST soil properties in the FLAC model Parameters
hGmax (kPa)
5.
o' = 25.33 kPa (0.25 atm) 2.70E+04
σ
o' = 101 kPa (1 atm) 5.35E+04
o' = 404 kPa (4 atm) 1.07E+05
σ
σ
o' = 1616 kPa (16 atm) 2.14E+05
σ
hbulk (kPa)
2.70E+04
5.35E+04
1.07E+05
2.14E+05
hcoh (kPa)
0.0
0.0
0.0
0.0
hfric (deg.)
35.0
35.0
35.0
35.0
hdil (deg.)
0.0
0.0
0.0
0.0
hten (kPa)
0.0
0.0
0.0
0.0
hn
3.0
3.3
4.0
4.0
hrf
0.98
0.98
0.98
0.98
hdfac
0.0
0.0
0.0
0.0
hrm
0.5
0.5
0.5
0.5
hpa (kPa)
100.0
100.0
100.0
100.0
hn1
1.0
1.0
1.0
1.0
Included documents / files
V5.0/modelubchyst2D.dll
V6.0/modelubchyst2D.dll
V7.0/modelubchyst2D.dll example/dss.dat
a DLL file of the UBCHYST2D model compiled with Microsoft Visual C++ 2005 at 32bit for FLAC v5.0. a DLL file of the UBCHYST2D model compiled with Microsoft Visual C++ 2005 at 32bit for FLAC v6.0. a DLL file of the UBCHYST2D model compiled with Microsoft Visual C++ 2005 at 32bit for FLAC v7.0. 2D
example input file test for FLAC .
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6.
Contact address
Roozbeh Geraili Mikola, PhD Jacobs Associates 49 Stevenson, 3rd Floor San Francisco, CA 94105 Direct: (415) 249-8216 Fax: (415) 956-8502 Email:
[email protected] or
[email protected]
www.jacobssf.com
Prof. Nicholas Sitar University of California, Berkeley Civil and Environmental Engineering, Geoengineering Department Davis Hall UC Berkeley Berkeley, California 94720-1710 Phone: (510) 643-8623 Fax: (510) 642-7476 Email:
[email protected]
7.
Acknowledgments
This work was performed with funding from NSF-NEES-CR Grant No. CMMI-0936376: Seismic Earth Pressures on Retaining Structures through collaborative project Between University of California, Berkeley and Itasca Consulting Group Inc. Prof. Peter Byrne and Dr. Ernest Neasgaard generously provided the UBCHYST FISH source code and advice on constitutive model performance for the 2D
3D
numerical modeling part of this study. Programs FLAC and FLAC were generously made available by Itasca Consulting Group Inc. under collaborative research agreements. Jacobs Associates generously provided the first author with the opportunity to pursue the research.
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8.
References
Byrne, P.M. and Naesgaard, E., 2010. Personal Communications.
Itasca Consulting Group, Inc. (2011). FLAC (Fast Lagrangian Analysis of Continua) user's manuals, Minneapolis, MN.
Darendeli, M. B. (2001). Development of a new family of normalized modulus reduction and material damping curves. Austin, Texas: The University of Te xas.
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