ISA-hypoplastic model.
Abaqus implementation.
Dr.-Ing. William Fuentes (Professor)
University del Norte
http://www.geo-research.info/umats-forsoils-abaqus/
Description of ISA-hypoplasticity
Hypoplastic models alone reproduce well the behavior of soils under
monotonic loading, but fails to simulate its behavior upon cyclic loading.
The Intergranular Strain Anisotropy (ISA) is a mathematical extension of
conventional hypoplastic models for soils, proposed originally by Fuentes
and Triantafyllidis (2015) to improve simulations of cyclic loading. It can be
considered as a reformulation of the conventional intergranular strain
theory by Niemunis and Herle (1997). Basically, this extension reproduces
the following characteristics:
a) Yield surface within the intergranular strain space for elastic strains
b) the stiffness increase upon reversal loading
c) the reduction of the plastic strain rate for same conditions.
ISA-hypoplastic models are also able to reproduce paths of repetitive
cycles, and provide an extension to account for cyclic mobility effects and
thus, enabling simulations of liquefaction phenomena.
Examples of simulations (element
tests)
Example FE-problem
On this analysis a concrete-filled pile driven into a thick
and homogeneous sand layer and subjected to a cyclic
axial load is simulated. The pile has diameter D = 0.80 m
and length L = 13.0 m. Taking advantage of the symmetry
of the problem, an axially symmetric condition is
considered, therefore four-node axisymmetric elements
CAX4 are used. The ground water table lies on the top of
the soil. An axial cyclic load with frequency f = 4 Hz is
applied as a concentrated force at the top of the pile.
Locally undrained conditions are considered. Due to the
cyclic loading, the pore pressure rises and the effective
stress decreases causing zones in which liquefaction may
occur.
Geometry, BCs, and loads
Model parameters
Table 1. Model parameters obtained from the calibration process.
Description
Unity
Value
Critical friction angle
[0]
32o
Granular hardness
[MPa]
300
Barotropy exponent
[-]
0.5
Maximum void ratio
[-]
0.850
Critical void ratio
[-]
0.785
Minimal void ratio
[-]
0.500
Dilatancy exponent
[-]
0.2
Density exponent
[-]
2.0
Stiffness factor
[-]
4.0
IS yield surface radius
[-]
1.0x10-4
IS hardening parameter
[-]
0.2
Minimum value of 𝜒
[-]
4
Parameters for Ottawa sand.
Hypoplasticity (Wolfferdorff)
𝜑𝑐
ℎ𝑠
𝑛𝐵
𝑒𝑖 𝑜
𝑒𝑐 𝑜
𝑒𝑑 𝑜
𝛼
𝛽
Intergranular strain parameters
𝑚𝑅 = 𝑚𝒕
𝑅
𝛽ℎ
𝜒0
Extension for repetitive loading by Poblete, Fuentes, and Triantafyllidis (2016):
𝐶𝑎
𝜒𝑚𝑎𝑥
Control for rate of eacc
[-]
0.15
Maximum value of 𝜒
[-]
15
Extension for cyclic mobility
𝐶𝒛
Cyclic mobility factor
[-]
300
𝒛𝑚𝑎𝑥
Calibration parameter
[-]
3
Input file in Abaqus
Specification of initial conditions
STATE VARIABLES (see example of initialstate.for, subroutine SDVINI)
• Void ratio- state variable 1
• Intergranular strain- state variables 3-8
• Back-Intergranular strain- state variable 9-14
• (only for undrained analysis) pore pressure - state variable 2
STRESS (see example of initialstate.for, subroutine SIGINI)
Results (mean effective stress p)
Fig. 6 Mean effective stress p (SDV69) , for p<10 kPa
Results (deviator stress)
Fig. 7 Mises stress
Results (pore pressure u)
Fig. 8 Pore presure (SDV2)
Results (displacements U)
Fig. 9 Displacement “U, Magnitude”