Ubchyst2d for Flac 2d

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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 modulus () times a reduction factor that is a function of the developed stress ratio and the change in stress ratio to reach failure. This function is as shown in equation (1) and illustrated in Figure 1.

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1 2 3 (1)

Where

stress ratio

2

= 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 () is less than the previous value and a cross-over occurs if changes sign. A stress reversal causes 1 to be reset to 0 and to be recalculated. However, the program retains the previous reversals (1old and 1fold) 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 stress-

strain loops with the characteristics illustrated in Figure 1.

2. Implementation

The original UBCHYSTs 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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The tensor of the increments of the total strains , 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 has been evaluated using the constitutive law in the previous step.

The tensor of the stresses which has been evaluated in the previous step. The stress ration parameters such as , , , and which have been evaluated in the

previous step.

The output variables are:

The new tensor of the stresses . The new stress ration parameters , , , and . 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.

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

4. 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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(a)

(b)

Figure 2. (a) Modulus reduction and (b) Damping ratio curve estimated by FLAC using UBCHYST

model for cohesionless soil (sand).

0

0.2

0.4

0.6

0.8

1

1.2

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00

G/G

max

Shearing Strain (%)

o' = 0.25 atmo' = 1.0 atmo' = 4.0 atmo' = 16 atmFLAC-0.25atm

FLAC-1atm

FLAC-4atm

FLAC-16atm

0

5

10

15

20

25

1.00E-04 1.00E-03 1.00E-02 1.00E-01 1.00E+00

Dam

ping

, %

Shearing Strain, %

o' = 0.25 atmo' = 1.0 atmo' = 4.0 atmo' = 16 atmFLAC-0.25atmFLAC-1atmFLAC-4atmFLAC-16atm

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Table 2. Initial input parameters for the UBCHYST soil properties in the FLAC model

Parameters o' = 25.33 kPa (0.25 atm) o' = 101 kPa

(1 atm) o' = 404 kPa

(4 atm) o' = 1616 kPa

(16 atm) hGmax (kPa) 2.70E+04 5.35E+04 1.07E+05 2.14E+05 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

5. Included documents / files

V5.0/modelubchyst2D.dll a DLL file of the UBCHYST2D model compiled with Microsoft Visual

C++ 2005 at 32bit for FLAC v5.0.





example/dss.dat example input file test for FLAC2D.

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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

numerical modeling part of this study. Programs FLAC2D and FLAC3D 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 Texas.

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Ubchyst2d for Flac 2d