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# ISA-Hypoplasticity (cyclic)

### Contact

For questions, please write to Prof. William Fuentes (fuentesw@uninorte.edu.co)

Courses on:

-Abaqus for soils. Basic examples on Geotechnical Engineering.

-Abaqus Umat (user material) implementation for beginners.

-Abaqus UEL (user element) implementation for beginners.

### Papers

2) An ISA-plasticity based model for viscous and non-viscous clays. File: Download

Note: All examples with ISA-hypoplasticity for sand were simulated with the following parameters:

### Example 1 Pile under cyclic axial loading simulated with the ISA model

Description:

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. Due to the cyclic loading the pore pressure increases and accumulates and the effective stress decreases causing zones in which liquefaction may occur.

Fig. 1 (a): Problem sketch (b): Overview of the FEM model

Two parts were considered for the 2D-FE model: the soil part and the pile part. The pile material (concrete) is simulated as elastic with E = 25 e6 kPa and Poisson ratio of 0.3. The boundary and initial conditions are set as shown in Figure 1-b. A surface to surface contact interaction is set for the soil-structure behavior, including a penalty friction formulation and the “Hard” Contact normal method.

• On the first step, the geostatic equilibrium is achieved. The initial geostatic stresses are calculated with the initialstate.for file. The total step time is 1 s.
• On the second step a vertical load of 600 kN is gradually applied at the top of the pile. The total step time is 0.1 s and the time increments 0.01 s.
• On the third step the pile is unloaded and reloaded several times. The step is solved under dynamic conditions. The total step time is 5 s and the time increments 0.01 s.

Fig. 2  Cyclic load at the top of the pile

Files:

Description of the constitutive model, element tests, FEproblem.

Results:

Video of the simulation – Liquefaction zones due to cyclic loading on granular soil

Fig. 3 Liquefaction zones at the end of the simulation –  mean effective stress p’ values lower than 10 kPa

Fig.  4 Vertical displacements under the pile

Fig. 5 Mean effective stress p’ under the pile

### Example 2 Pile under cyclic axial loading simulated with the ISA model

Description:

On this analysis a strip footing on a thick and homogeneous sand layer and subjected to a cyclic vertical loading is simulated. The strip footing has a base of B=1.0 m and its base is located 1 m below the surface. A 2D-FE model is constructed with plain-strain condition, therefore four-node plane strain elements CPE4 are used. There is no ground water table near the surface.

Fig. 1 (a): Problem sketch (b): Overview of the FEM model

The boundary and initial conditions are set as shown in Figure 1-b. A coupling constraint is set for the nodes below the footing to assure that they have the same vertical displacement.

• On the first step, the geostatic equilibrium is achieved. On this step, a constant pressure of 17 kN/m3 is applied on the top of the soil part to account for the 1-m soil layer between the surface and the bottom of the footing. The initial geostatic stresses are calculated with the initialstate.for file. The total step time is 1 s.
• On the second step a vertical load of 20 kN/m is gradually applied as a pressure on the base of the footing. The total step time is 0.1 s and the time increments 0.01 s.
• On the third step the footing is unloaded and reloaded several times. The step is solved under dynamic conditions. The total step time is 5 s and the time increments 0.01 s.

Fig. 2 Cyclic load applied on the strip footing

Files:

Results:

Video of the simulation – Vertical displacements

Fig. 3 Final vertical displacements

Fig. 4 Displacements under the footing