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 π [-] 4 Parameters for Ottawa sand. Hypoplasticity (Wolfferdorff) ππ βπ ππ΅ ππ π ππ π ππ π πΌ π½ Intergranular strain parameters ππ = ππ π π½β π0 Extension for repetitive loading by Poblete, Fuentes, and Triantafyllidis (2016): πΆπ ππππ₯ Control for rate of eacc [-] 0.15 Maximum value of π [-] 15 Extension for cyclic mobility πΆπ Cyclic mobility factor [-] 300 ππππ₯ Calibration parameter [-] 3 Input file in Abaqus Specification of initial conditions STATE VARIABLES (see example of initialstate.for, subroutine SDVINI) β’ Void ratio- state variable 1 β’ Intergranular strain- state variables 3-8 β’ Back-Intergranular strain- state variable 9-14 β’ (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 βU, Magnitudeβ